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Phase transitions in the $\mathbb{Z}_p$ and U(1) clock models
Authors:
G. Sun,
T. Vekua,
E. Cobanera,
G. Ortiz
Abstract:
Quantum phase transitions are studied in the non-chiral $p$-clock chain, and a new explicitly U(1)-symmetric clock model, by monitoring the ground-state fidelity susceptibility. For $p\ge 5$, the self-dual $\mathbb{Z}_p$-symmetric chain displays a double-hump structure in the fidelity susceptibility with both peak positions and heights scaling logarithmically to their corresponding thermodynamic v…
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Quantum phase transitions are studied in the non-chiral $p$-clock chain, and a new explicitly U(1)-symmetric clock model, by monitoring the ground-state fidelity susceptibility. For $p\ge 5$, the self-dual $\mathbb{Z}_p$-symmetric chain displays a double-hump structure in the fidelity susceptibility with both peak positions and heights scaling logarithmically to their corresponding thermodynamic values. This scaling is precisely as expected for two Beresinskii-Kosterlitz-Thouless (BKT) transitions located symmetrically about the self-dual point, and so confirms numerically the theoretical scenario that sets $p=5$ as the lowest $p$ supporting BKT transitions in $\mathbb{Z}_p$-symmetric clock models. For our U(1)-symmetric, non-self-dual minimal modification of the $p$-clock model we find that the phase diagram depends strongly on the parity of $p$ and only one BKT transition survives for $p\geq 5$. Using asymptotic calculus we map the self-dual clock model exactly, in the large $p$ limit, to the quantum $O(2)$ rotor chain. Finally, using bond-algebraic dualities we estimate the critical BKT transition temperatures of the classical planar $p$-clock models defined on square lattices, in the limit of extreme spatial anisotropy. Our values agree remarkably well with those determined via classical Monte Carlo for isotropic lattices. This work highlights the power of the fidelity susceptibility as a tool for diagnosing the BKT transitions even when only discrete symmetries are present.
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Submitted 19 September, 2019; v1 submitted 21 July, 2019;
originally announced July 2019.
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Vortex-hole duality: a unified picture of weak and strong-coupling regimes of bosonic ladders with flux
Authors:
S. Greschner,
T. Vekua
Abstract:
Two-leg bosonic ladders with flux harbor a remarkable vortex-hole duality between the weak-coupling vortex lattice superfluids and strong-coupling charge-density-wave crystals. The strong-coupling crystalline states, which are realized in the vicinity of $π$-flux, are independent of particle statistics, and are related with the incompressible fractional quantum Hall states in the thin-cylinder lim…
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Two-leg bosonic ladders with flux harbor a remarkable vortex-hole duality between the weak-coupling vortex lattice superfluids and strong-coupling charge-density-wave crystals. The strong-coupling crystalline states, which are realized in the vicinity of $π$-flux, are independent of particle statistics, and are related with the incompressible fractional quantum Hall states in the thin-cylinder limit. These fully gapped ground states, away of $π$-flux, develop nonzero chiral (spin) currents. Contact-interacting quantum gases permit exploration of this vortex-hole duality in experiments.
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Submitted 21 April, 2017;
originally announced April 2017.
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Magnetic field induced criticality in superconducting two-leg ladders
Authors:
Temo Vekua
Abstract:
We study critical singularities in the d-wave-like superconducting phase of the hole-doped Hubbard model of repulsively interacting electrons, defined on a two-leg ladder, induced by a magnetic field applied parallel to the ladder plane. We argue that, provided the lowest energy spin excitations in doped ladders carry as well charge quantum numbers, the low temperature thermodynamic quantities, su…
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We study critical singularities in the d-wave-like superconducting phase of the hole-doped Hubbard model of repulsively interacting electrons, defined on a two-leg ladder, induced by a magnetic field applied parallel to the ladder plane. We argue that, provided the lowest energy spin excitations in doped ladders carry as well charge quantum numbers, the low temperature thermodynamic quantities, such as specific heat coefficient and magnetic susceptibility will show logarithmic singularities in quantum critical regime. This behavior is in drastic contrast with the magnetic field induced criticality in undoped Mott insulator ladders, which is governed by the zero scle-factor universality with its hallmark square root singularities.
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Submitted 30 November, 2016;
originally announced November 2016.
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Symmetry-broken states in a system of interacting bosons on a two-leg ladder with a uniform Abelian gauge field
Authors:
S. Greschner,
M. Piraud,
F. Heidrich-Meisner,
I. P. McCulloch,
U. Schollwöck,
T. Vekua
Abstract:
We study the quantum phases of bosons with repulsive contact interactions on a two-leg ladder in the presence of a uniform Abelian gauge field. The model realizes many interesting states, including Meissner phases, vortex-fluids, vortex-lattices, charge-density-waves and the biased-ladder phase. Our work focuses on the subset of these states that break a discrete symmetry. We use density matrix re…
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We study the quantum phases of bosons with repulsive contact interactions on a two-leg ladder in the presence of a uniform Abelian gauge field. The model realizes many interesting states, including Meissner phases, vortex-fluids, vortex-lattices, charge-density-waves and the biased-ladder phase. Our work focuses on the subset of these states that break a discrete symmetry. We use density matrix renormalization group simulations to demonstrate the existence of three vortex-lattice states at different vortex densities and we characterize the phase transitions from these phases into neighboring states. Furthermore, we provide an intuitive explanation of the chiral-current reversal effect that is tied to some of these vortex lattices. We also study a charge-density-wave state that exists at 1/4 particle filling at large interaction strengths and flux values close to half a flux quantum. By changing the system parameters, this state can transition into a completely gapped vortex-lattice Mott-insulating state. We elucidate the stability of these phases against nearest-neighbor interactions on the rungs of the ladder relevant for experimental realizations with a synthetic lattice dimension. A charge-density-wave state at 1/3 particle filling can be stabilized for flux values close to half a flux-quantum and for very strong on-site interactions in the presence of strong repulsion on the rungs. Finally, we analytically describe the emergence of these phases in the low-density regime, and, in particular, we obtain the boundaries of the biased-ladder phase, i.e., the phase that features a density imbalance between the legs. We make contact to recent quantum-gas experiments that realized related models and discuss signatures of these quantum states in experimentally accessible observables.
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Submitted 29 December, 2016; v1 submitted 7 October, 2016;
originally announced October 2016.
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Exact asymptotic correlation functions of bilinear spin operators of the Heisenberg antiferromagnetic spin-$\frac{1}{2}$ chain
Authors:
Temo Vekua,
Gaoyong Sun
Abstract:
Exact asymptotic expressions of the uniform parts of the two-point correlation functions of bilinear spin operators in the Heisenberg antiferromagnetic spin-$\frac{1}{2}$ chain are obtained. Apart from the algebraic decay, the logarithmic contribution is identified, and the numerical prefactor is determined. We also confirm numerically the multiplicative logarithmic correction of the staggered par…
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Exact asymptotic expressions of the uniform parts of the two-point correlation functions of bilinear spin operators in the Heisenberg antiferromagnetic spin-$\frac{1}{2}$ chain are obtained. Apart from the algebraic decay, the logarithmic contribution is identified, and the numerical prefactor is determined. We also confirm numerically the multiplicative logarithmic correction of the staggered part of the bilinear spin operators $\langle\langle S^{a}_0S^{a}_{1}S^{b}_{r}S^{b}_{r+1} \rangle\rangle=(-1)^rd/(r \ln^{\frac{3}{2}}r) +(3δ_{a,b}-1) \ln^2r /(12 π^4 r^4)$, and estimate the numerical prefactor as $d\simeq 0.067$. The relevance of our results for ground state fidelity susceptibility at the Berezinskii-Kosterlitz-Thouless quantum phase transition points in one-dimensional systems is discussed at the end of our work.
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Submitted 15 July, 2016; v1 submitted 4 April, 2016;
originally announced April 2016.
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Topological quasi-one-dimensional state of interacting spinless electrons
Authors:
G. Sun,
T. Vekua
Abstract:
By decreasing the transversal confinement potential in interacting one-dimensional spinless electrons and populating the second energetically lowest sub-band, for not too strong interactions system transitions into a quasi-one-dimensional state with dominant superconducting correlations and one gapless mode. By combining effective field theory approach and numerical density matrix renormalization…
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By decreasing the transversal confinement potential in interacting one-dimensional spinless electrons and populating the second energetically lowest sub-band, for not too strong interactions system transitions into a quasi-one-dimensional state with dominant superconducting correlations and one gapless mode. By combining effective field theory approach and numerical density matrix renormalization group simulations we show that this quasi-one-dimensional state is a topological state that hosts zero-energy edge modes. We also study the single-particle correlations across the interface between this quasi-one-dimensional and single-channel states.
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Submitted 24 May, 2016; v1 submitted 12 January, 2016;
originally announced January 2016.
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Ground-state phases of rung-alternated spin-1/2 Heisenberg ladder
Authors:
F. Amiri,
G. Sun,
H. -J. Mikeska,
T. Vekua
Abstract:
The ground-state phase diagram of Heisenberg spin-1/2 system on a two-leg ladder with rung alternation is studied by combining analytical approaches with numerical simulations. For the case of ferromagnetic leg exchanges a unique ferrimagnetic ground state emerges, whereas for the case of antiferromagnetic leg exchanges several different ground states are stabilized depending on the ratio between…
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The ground-state phase diagram of Heisenberg spin-1/2 system on a two-leg ladder with rung alternation is studied by combining analytical approaches with numerical simulations. For the case of ferromagnetic leg exchanges a unique ferrimagnetic ground state emerges, whereas for the case of antiferromagnetic leg exchanges several different ground states are stabilized depending on the ratio between exchanges along legs and rungs. For the more general case of a honeycomb-ladder model for the case of ferromagnetic leg exchanges besides usual rung-singlet and saturated ferromagnetic states we obtain a ferrimagnetic Luttinger liquid phase with both linear and quadratic low energy dispersions and ground state magnetization continuously changing with system parameters. For the case of antiferromagnetic exchanges along legs, different dimerized states including states with additional topological order are suggested to be realized.
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Submitted 14 September, 2015;
originally announced September 2015.
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Spontaneous increase of magnetic flux and chiral-current reversal in bosonic ladders: Swimming against the tide
Authors:
S. Greschner,
M. Piraud,
F. Heidrich-Meisner,
I. P. McCulloch,
U. Schollwöck,
T. Vekua
Abstract:
The interplay between spontaneous symmetry breaking in many-body systems, the wavelike nature of quantum particles and lattice effects produces an extraordinary behavior of the chiral current of bosonic particles in the presence of a uniform magnetic flux defined on a two-leg ladder. While non-interacting as well as strongly interacting particles, stirred by the magnetic field, circulate along the…
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The interplay between spontaneous symmetry breaking in many-body systems, the wavelike nature of quantum particles and lattice effects produces an extraordinary behavior of the chiral current of bosonic particles in the presence of a uniform magnetic flux defined on a two-leg ladder. While non-interacting as well as strongly interacting particles, stirred by the magnetic field, circulate along the system's boundary in the counterclockwise direction in the ground state, interactions stabilize vortex lattices. These states break translational symmetry, which can lead to a reversal of the circulation direction. Our predictions could readily be accessed in quantum gas experiments with existing setups or in arrays of Josephson junctions.
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Submitted 19 December, 2016; v1 submitted 24 April, 2015;
originally announced April 2015.
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Vortex and Meissner phases of strongly-interacting bosons on a two-leg ladder
Authors:
M. Piraud,
F. Heidrich-Meisner,
I. P. McCulloch,
S. Greschner,
T. Vekua,
U. Schollwoeck
Abstract:
We establish the phase diagram of the strongly-interacting Bose-Hubbard model defined on a two-leg ladder geometry in the presence of a homogeneous flux. Our work is motivated by a recent experiment [Atala et al., Nature Phys. 10, 588 (2014)], which studied the same system, in the complementary regime of weak interactions. Based on extensive density matrix renormalization group simulations and a b…
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We establish the phase diagram of the strongly-interacting Bose-Hubbard model defined on a two-leg ladder geometry in the presence of a homogeneous flux. Our work is motivated by a recent experiment [Atala et al., Nature Phys. 10, 588 (2014)], which studied the same system, in the complementary regime of weak interactions. Based on extensive density matrix renormalization group simulations and a bosonization analysis, we fully explore the parameter space spanned by filling, inter-leg tunneling, and flux. As a main result, we demonstrate the existence of gapless and gapped Meissner and vortex phases, with the gapped states emerging in Mott-insulating regimes. We calculate experimentally accessible observables such as chiral currents and vortex patterns.
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Submitted 14 April, 2015; v1 submitted 24 September, 2014;
originally announced September 2014.
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Fidelity at Berezinskii-Kosterlitz-Thouless quantum phase transitions
Authors:
G. Sun,
A. K. Kolezhuk,
T. Vekua
Abstract:
We clarify the long-standing controversy concerning the behavior of the ground state fidelity in the vicinity of a quantum phase transition of the Berezinskii-Kosterlitz-Thouless type in one-dimensional systems. Contrary to the prediction based on the Gaussian approximation of the Luttinger liquid approach, it is shown that the fidelity susceptibility does not diverge at the transition, but has a…
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We clarify the long-standing controversy concerning the behavior of the ground state fidelity in the vicinity of a quantum phase transition of the Berezinskii-Kosterlitz-Thouless type in one-dimensional systems. Contrary to the prediction based on the Gaussian approximation of the Luttinger liquid approach, it is shown that the fidelity susceptibility does not diverge at the transition, but has a cusp-like peak $χ_c- χ(λ)\sim \sqrt{|λ_c-λ|} $, where $λ$ is a parameter driving the transition, and $χ_c$ is the peak value at the transition point $λ=λ_c$. Numerical claims of the logarithmic divergence of fidelity susceptibility with the system size (or temperature) are explained by logarithmic corrections due to marginal operators, which is supported by numerical calculations for large systems.
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Submitted 16 January, 2015; v1 submitted 12 August, 2014;
originally announced August 2014.
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Universal logarithmic temperature dependence of magnetic susceptibility of one-dimensional electrons at critical values of magnetic field
Authors:
Temo Vekua
Abstract:
We study the leading low temperature dependence of magnetic susceptibility of one-dimensional electrons with fixed total number of particles at the magnetic fields equal to zero temperature critical values where magnetic field induces commensurate-incommensurate quantum phase transitions. For free and repulsively interacting electrons there is only one such critical field corresponding to the tran…
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We study the leading low temperature dependence of magnetic susceptibility of one-dimensional electrons with fixed total number of particles at the magnetic fields equal to zero temperature critical values where magnetic field induces commensurate-incommensurate quantum phase transitions. For free and repulsively interacting electrons there is only one such critical field corresponding to the transition to the fully polarized state. For attractively interacting electrons besides saturation field there is another critical field equal to the spin gap where zero temperature magnetization sets in. For all cases, except of the lattice models at half filling, the magnetic susceptibility at critical values of magnetic field has a universal logarithmic temperature dependence,x(T)=x(0)(1+2/Log(T)+...) for T -> 0.
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Submitted 27 February, 2014;
originally announced February 2014.
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Topological order-by-disorder in orbitally degenerate dipolar bosons in zig-zag lattice
Authors:
G. Sun,
T. Vekua
Abstract:
Spinor bosons offer conceptually simple picture of macroscopic quantum behavior of topological order-by-disorder: Paramagnetic state of two-component dipolar bosons in orbitally degenerate zig-zag lattice is unstable against infinitezimal quantum fluctuations of orbitals towards developing non-local hidden order. Adjacent to the topological state locally correlated exact ground state with spontane…
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Spinor bosons offer conceptually simple picture of macroscopic quantum behavior of topological order-by-disorder: Paramagnetic state of two-component dipolar bosons in orbitally degenerate zig-zag lattice is unstable against infinitezimal quantum fluctuations of orbitals towards developing non-local hidden order. Adjacent to the topological state locally correlated exact ground state with spontaneously quadrupoled lattice constant is realized for the broad parameter regime.
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Submitted 24 January, 2014;
originally announced January 2014.
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Helical multiferroics for electric field controlled quantum information processing
Authors:
M. Azimi,
L. Chotorlishvili,
S. K. Mishra,
S. Greschner,
T. Vekua,
J. Berakdar
Abstract:
Magnetoelectric coupling in helical multiferroics allows to steer spin order with electric fields. Here we show theoretically that in a helical multiferroic chain quantum information processing as well as quantum phases are highly sensitive to electric (E) field. Applying E-field, the quantum state transfer fidelity can be increased and made directionally dependent.
We also show that E field tra…
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Magnetoelectric coupling in helical multiferroics allows to steer spin order with electric fields. Here we show theoretically that in a helical multiferroic chain quantum information processing as well as quantum phases are highly sensitive to electric (E) field. Applying E-field, the quantum state transfer fidelity can be increased and made directionally dependent.
We also show that E field transforms the spin-density-wave/nematic or multipolar phases of frustrated ferromagnetic spin-1/2 chain in chiral phase with a strong magnetoelectric coupling. We find sharp reorganization of the entanglement spectrum as well as a large enhancement of fidelity susceptibility at Ising quantum phase transition from nematic to chiral states driven by electric field. These findings point to a new tool for quantum information with low power consumption.
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Submitted 14 November, 2013;
originally announced November 2013.
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Ferromagnetic spin-orbital liquid of dipolar fermions in zigzag lattices
Authors:
G. Sun,
A. K. Kolezhuk,
L. Santos,
T. Vekua
Abstract:
Two-component dipolar fermions in zigzag optical lattices allow for the engineering of spin-orbital models. We show that dipolar lattice fermions permit the exploration of a regime typically unavailable in solid-state compounds that is characterized by a novel spin-liquid phase with a finite magnetization and spontaneously broken SU(2) symmetry. This peculiar spin liquid may be understood as a Lut…
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Two-component dipolar fermions in zigzag optical lattices allow for the engineering of spin-orbital models. We show that dipolar lattice fermions permit the exploration of a regime typically unavailable in solid-state compounds that is characterized by a novel spin-liquid phase with a finite magnetization and spontaneously broken SU(2) symmetry. This peculiar spin liquid may be understood as a Luttinger liquid of composite particles consisting of bound states of spin waves and orbital domain walls moving in an unsaturated ferromagnetic background. In addition, we show that the system exhibits a boundary phase transitions involving non-local entanglement of edge spins.
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Submitted 26 August, 2013;
originally announced August 2013.
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Current fidelity susceptibility and conductivity in one-dimensional lattice models with open and periodic boundary conditions
Authors:
S. Greschner,
A. K. Kolezhuk,
T. Vekua
Abstract:
We study, both numerically and analytically, the finite size scaling of the fidelity susceptibility χ_{J} with respect to the charge or spin current in one-dimensional lattice models, and relate it to the low-frequency behavior of the corresponding conductivity. It is shown that in gapless systems with open boundary conditions the leading dependence on the system size L stems from the singular par…
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We study, both numerically and analytically, the finite size scaling of the fidelity susceptibility χ_{J} with respect to the charge or spin current in one-dimensional lattice models, and relate it to the low-frequency behavior of the corresponding conductivity. It is shown that in gapless systems with open boundary conditions the leading dependence on the system size L stems from the singular part of the conductivity and is quadratic, with a universal form χ_{J}= 7KL^2 ζ(3)/2π^4 where K is the Luttinger liquid parameter. In contrast to that, for periodic boundary conditions the leading system size dependence is directly connected with the regular part of the conductivity (giving alternative possibility to study low frequency behavior of the regular part of conductivity) and is subquadratic, χ_{J} \propto L^γ(K), (with a K dependent constant γ) in most situations linear, γ=1. For open boundary conditions, we also study another current-related quantity, the fidelity susceptibility to the lattice tilt χ_{P} and show that it scales as the quartic power of the system size, χ_{P}=31KL^4 ζ(5)/8 u^2 π^6, where u is the sound velocity. We comment on the behavior of the current fidelity susceptibility in gapped phases, particularly in the topologically ordered Haldane state.
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Submitted 21 August, 2013;
originally announced August 2013.
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Spin-orbit coupled fermions in ladder-like optical lattices at half-filling
Authors:
G. Sun,
J. Jaramillo,
L. Santos,
T. Vekua
Abstract:
We study the ground-state phase diagram of two-component fermions loaded in a ladder-like lattice at half filling in the presence of spin-orbit coupling. For repulsive fermions with unidirectional spin-orbit coupling along the legs we identify a Néel state which is separated from rung-singlet and ferromagnetic states by Ising phase transition lines. These lines cross for maximal spin-orbit couplin…
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We study the ground-state phase diagram of two-component fermions loaded in a ladder-like lattice at half filling in the presence of spin-orbit coupling. For repulsive fermions with unidirectional spin-orbit coupling along the legs we identify a Néel state which is separated from rung-singlet and ferromagnetic states by Ising phase transition lines. These lines cross for maximal spin-orbit coupling and a direct Gaussian phase transition between rung-singlet and ferro phases is realized. For the case of Rashba-like spin-orbit coupling, besides the rung singlet phases two distinct striped ferromagnetic phases are formed. In case of attractive fermions with spin-orbit coupling at half-filling for decoupled chains we identify a dimerized state that separates a singlet superconductor and a ferromagnetic states.
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Submitted 5 July, 2013;
originally announced July 2013.
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Magnetic field induced band insulator to Mott insulator transformations in 4-component alkali fermions at half-filling
Authors:
J. Jaramillo,
S. Greschner,
T. Vekua
Abstract:
Under the influence of an external magnetic field and spin-changing collisions, the band insulator (BI) state of one-dimensional (1D) s-wave repulsively interacting 4-component fermions at half-filling transforms into Mott insulator (MI) states with spontaneously broken translational symmetry: a dimerized state for shallow lattices and a N{é}el state for deep lattices via an intermediate topologic…
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Under the influence of an external magnetic field and spin-changing collisions, the band insulator (BI) state of one-dimensional (1D) s-wave repulsively interacting 4-component fermions at half-filling transforms into Mott insulator (MI) states with spontaneously broken translational symmetry: a dimerized state for shallow lattices and a N{é}el state for deep lattices via an intermediate topological state. Since a BI has vanishing entropy per particle, these MI phases could be particularly inviting for experimental realization under the similar conditions as those for $^{40}$K atoms [1], provided the magnetic field is changed adiabatically.
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Submitted 4 May, 2013;
originally announced May 2013.
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Ultra-cold bosons in zig-zag optical lattices
Authors:
S. Greschner,
L. Santos,
T. Vekua
Abstract:
Ultra-cold bosons in zig-zag optical lattices present a rich physics due to the interplay between frustration, induced by lattice geometry, two-body interaction and three-body constraint. Unconstrained bosons may develop chiral superfluidity and a Mott-insulator even at vanishingly small interactions. Bosons with a three-body constraint allow for a Haldane-insulator phase in non-polar gases, as we…
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Ultra-cold bosons in zig-zag optical lattices present a rich physics due to the interplay between frustration, induced by lattice geometry, two-body interaction and three-body constraint. Unconstrained bosons may develop chiral superfluidity and a Mott-insulator even at vanishingly small interactions. Bosons with a three-body constraint allow for a Haldane-insulator phase in non-polar gases, as well as pair-superfluidity and density wave phases for attractive interactions. These phases may be created and detected within the current state of the art techniques.
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Submitted 7 September, 2016; v1 submitted 24 February, 2012;
originally announced February 2012.
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Frustrated spin chains in strong magnetic field: dilute two-component Bose gas regime
Authors:
A. K. Kolezhuk,
F. Heidrich-Meisner,
S. Greschner,
T. Vekua
Abstract:
We study the ground state of frustrated spin-S chains in a strong magnetic field in the immediate vicinity of saturation. In strongly frustrated chains, the magnon dispersion has two degenerate minima at inequivalent momenta $\pm Q$, and just below the saturation field the system can be effectively represented as a dilute one-dimensional lattice gas of two species of bosons that correspond to magn…
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We study the ground state of frustrated spin-S chains in a strong magnetic field in the immediate vicinity of saturation. In strongly frustrated chains, the magnon dispersion has two degenerate minima at inequivalent momenta $\pm Q$, and just below the saturation field the system can be effectively represented as a dilute one-dimensional lattice gas of two species of bosons that correspond to magnons with momenta around $\pm Q$. We present a theory of effective interactions in such a dilute magnon gas that allows us to make quantitative predictions for arbitrary values of the spin. With the help of this method, we are able to establish the magnetic phase diagram of frustrated chains close to saturation and study phase transitions between several nontrivial states, including a two-component Luttinger liquid, a vector chiral phase, and phases with bound magnons. We study those phase transitions numerically and find a good agreement with our analytical predictions.
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Submitted 2 April, 2012; v1 submitted 24 December, 2011;
originally announced December 2011.
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Exploring spin-orbital models with dipolar fermions in zig-zag optical lattices
Authors:
G. Sun,
G. Jackeli,
L. Santos,
T. Vekua
Abstract:
Ultra-cold dipolar spinor fermions in zig-zag type optical lattices can mimic spin-orbital models relevant in solid-state systems, as transition-metal oxides with partially filled d-levels, with the interesting advantage of reviving the quantum nature of orbital fluctuations. We discuss two different physical systems in which these models may be simulated, showing that the interplay between lattic…
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Ultra-cold dipolar spinor fermions in zig-zag type optical lattices can mimic spin-orbital models relevant in solid-state systems, as transition-metal oxides with partially filled d-levels, with the interesting advantage of reviving the quantum nature of orbital fluctuations. We discuss two different physical systems in which these models may be simulated, showing that the interplay between lattice geometry and spin-orbital quantum dynamics produces a wealth of novel quantum phases.
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Submitted 11 January, 2012; v1 submitted 21 December, 2011;
originally announced December 2011.
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Resonances in a dilute gas of magnons and metamagnetism of isotropic frustrated ferromagnetic spin chains
Authors:
M. Arlego,
F. Heidrich-Meisner,
A. Honecker,
G. Rossini,
T. Vekua
Abstract:
We show that spin-S chains with SU(2)-symmetric, ferromagnetic nearest-neighbor and frustrating antiferromagnetic next-nearest-neighbor exchange interactions exhibit metamagnetic behavior under the influence of an external magnetic field for small S, in the form of a first-order transition to the fully polarized state. The corresponding magnetization jump increases gradually starting from an S-dep…
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We show that spin-S chains with SU(2)-symmetric, ferromagnetic nearest-neighbor and frustrating antiferromagnetic next-nearest-neighbor exchange interactions exhibit metamagnetic behavior under the influence of an external magnetic field for small S, in the form of a first-order transition to the fully polarized state. The corresponding magnetization jump increases gradually starting from an S-dependent critical value of exchange couplings and takes a maximum in the vicinity of a ferromagnetic Lifshitz point. The metamagnetism results from resonances in the dilute magnon gas caused by an interplay between quantum fluctuations and frustration.
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Submitted 23 November, 2011; v1 submitted 27 May, 2011;
originally announced May 2011.
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Field-induced phase transitions of repulsive spin-1 bosons in optical lattices
Authors:
K. Rodriguez,
A. Argüelles,
A. K. Kolezhuk,
L. Santos,
T. Vekua
Abstract:
We study the phase diagram of repulsively interacting spin-1 bosons in optical lattices at unit filling, showing that an externally induced quadratic Zeeman effect may lead to a rich physics characterized by various phases and phase transitions. We find that the main properties of the system may be described by an effective field model, which provides the precise location of the phase boundaries f…
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We study the phase diagram of repulsively interacting spin-1 bosons in optical lattices at unit filling, showing that an externally induced quadratic Zeeman effect may lead to a rich physics characterized by various phases and phase transitions. We find that the main properties of the system may be described by an effective field model, which provides the precise location of the phase boundaries for any dimension, being in excellent agreement with our numerical calculations for one-dimensional systems. Our work provides a quantitative guide for the experimental analysis of various types of field-induced quantum phase transitions in spin-1 lattice bosons. These transitions, which are precluded in spin-1/2 systems, may be realized using an externally modified quadratic Zeeman coupling, similar to recent experiments with spinor condensates in the continuum.
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Submitted 20 September, 2010;
originally announced September 2010.
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Adiabatic spin cooling using high-spin Fermi gases
Authors:
M. Colomé-Tatché,
C. Klempt,
L. Santos,
T. Vekua
Abstract:
Spatial entropy redistribution plays a key role in adiabatic cooling of ultra-cold lattice gases. We show that high-spin fermions with a spatially variable quadratic Zeeman coupling may allow for the creation of an inner spin-1/2 core surrounded by high-spin wings. The latter are always more entropic than the core at high temperatures and, remarkably, at all temperatures in the presence of frustra…
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Spatial entropy redistribution plays a key role in adiabatic cooling of ultra-cold lattice gases. We show that high-spin fermions with a spatially variable quadratic Zeeman coupling may allow for the creation of an inner spin-1/2 core surrounded by high-spin wings. The latter are always more entropic than the core at high temperatures and, remarkably, at all temperatures in the presence of frustration. Combining thermodynamic Bethe Ansatz with local density approximation, we study the spatial entropy distribution for the particular case of one-dimensional spin-3/2 lattice fermions in the Mott phase. Interestingly, this spatially dependent entropy opens a possible path for an adiabatic cooling technique that, in contrast to previous proposals, would specifically target the spin degree of freedom. We discuss a possible realization of this adiabatic cooling, which may allow for a highly efficient entropy decrease in the spin-1/2 core and help access antiferromagnetic order in experiments on ultracold spinor fermions.
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Submitted 13 March, 2012; v1 submitted 14 September, 2010;
originally announced September 2010.
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Magnetic phases of spin-3/2 fermions on a spatially anisotropic square lattice
Authors:
A. K. Kolezhuk,
T. Vekua
Abstract:
We study the magnetic phase diagram of spin-3/2 fermions in a spatially anisotropic square optical lattice at quarter filling (corresponding to one particle per lattice site). In the limit of the large on-site repulsion the system can be mapped to the so-called Sp(N) Heisenberg spin model with N=4. We analyze the Sp(N) spin model with the help of the large-N field-theoretical approach and show tha…
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We study the magnetic phase diagram of spin-3/2 fermions in a spatially anisotropic square optical lattice at quarter filling (corresponding to one particle per lattice site). In the limit of the large on-site repulsion the system can be mapped to the so-called Sp(N) Heisenberg spin model with N=4. We analyze the Sp(N) spin model with the help of the large-N field-theoretical approach and show that the effective theory corresponds to the Sp(N) extension of the CP^{N-1} model, with the Lorentz invariance generically broken. We obtain the renormalization flow of the model couplings and show that although the Sp(N) terms are seemingly irrelevant, their presence leads to a renormalization of the CP^{N-1} part of the action, driving a phase transition. We further consider the influence of the external magnetic field (the quadratic Zeeman effect), and present the qualitative analysis of the ground state phase diagram.
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Submitted 5 December, 2010; v1 submitted 3 August, 2010;
originally announced August 2010.
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Mott-insulator phases of spin-3/2 fermions in the presence of quadratic Zeeman coupling
Authors:
Karen Rodriguez,
Arturo Argüelles,
Maria Colomé-Tatché,
Temo Vekua,
Luis Santos
Abstract:
We study the influence of the quadratic Zeeman effect in the Mott-insulator phases of hard-core spin-3/2 fermions. We show that contrary to spinor bosons, any quadratic Zeeman coupling preserves a $SU(2)\otimes SU(2)$ symmetry, leading for large-enough quadratic Zeeman coupling to an isotropic pseudo-spin-1/2 Heisenberg antiferromagnet. Depending on the scattering lengths, on 1D lattices the qua…
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We study the influence of the quadratic Zeeman effect in the Mott-insulator phases of hard-core spin-3/2 fermions. We show that contrary to spinor bosons, any quadratic Zeeman coupling preserves a $SU(2)\otimes SU(2)$ symmetry, leading for large-enough quadratic Zeeman coupling to an isotropic pseudo-spin-1/2 Heisenberg antiferromagnet. Depending on the scattering lengths, on 1D lattices the quadratic Zeeman coupling can induce either a Kosterlitz-Thouless transition between a gapped dimerized spin-3/2 phase and a gapless pseudo-spin-1/2 antiferromagnet, or a commensurate-incommensurate transition from a gapless spin-liquid into the pseudo-spin-1/2 antiferromagnet. Similar arguments allow to foresee corresponding transitions on ladder type and square lattices. We analyze various observables which should reveal in experiments these phases.
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Submitted 8 February, 2010; v1 submitted 1 February, 2010;
originally announced February 2010.
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Low temperature specific heat of 1D multicomponent systems at commensurate- incommensurate phase transition point
Authors:
Temo Vekua
Abstract:
Low temperature dependence of specific heat of one- dimensional multicomponent systems at the commensurate- incommensurate phase transition point is studied. It is found that for canonical systems, with a fixed total number of particles, low temperature specific heat linearly depends on temperature with a diverging prefactor.
Low temperature dependence of specific heat of one- dimensional multicomponent systems at the commensurate- incommensurate phase transition point is studied. It is found that for canonical systems, with a fixed total number of particles, low temperature specific heat linearly depends on temperature with a diverging prefactor.
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Submitted 23 February, 2010; v1 submitted 22 September, 2009;
originally announced September 2009.
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Susceptibility at the edge points of magnetization plateau of 1D electron/spin systems
Authors:
Temo Vekua
Abstract:
We study the behavior of magnetization curve as a function of magnetic field in the immediate vicinity of the magnetization plateaus of 1D electron systems within the bosonization formalism. First we discuss the plateau that is formed at the saturation magnetization of 1D electron system. Interactions between electrons we treat in the lowest order of perturbation. We show that for isolated syste…
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We study the behavior of magnetization curve as a function of magnetic field in the immediate vicinity of the magnetization plateaus of 1D electron systems within the bosonization formalism. First we discuss the plateau that is formed at the saturation magnetization of 1D electron system. Interactions between electrons we treat in the lowest order of perturbation. We show that for isolated systems, where total number of electrons is not allowed to vary, magnetic susceptibility stays always finite away of half filling. Similar statement holds for many other magnetization plateaus supporting nonmagnetic gapless excitations encountered in 1D electron/spin systems in the absence of special symmetries or features responsible for the mode decoupling. We demonstrate it on example of the plateaus at irrational values of magnetization in doped modulated Hubbard chains. Finally we discuss the connection between the weak coupling description of saturation magnetization plateau and strong coupling description of zero magnetization plateau of attractively interacting electrons/ antiferromagnetically interacting spin 1 Bosons.
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Submitted 13 August, 2009;
originally announced August 2009.
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Critical properties of 1D spin-gapped fermions at the onset of magnetization
Authors:
T. Vekua,
S. I. Matveenko,
G. V. Shlyapnikov
Abstract:
We develop an effective field theory for finding critical properties of 1D spin gapped fermions at the onset of magnetization. It is shown how the spin-charge interaction leads to a linear critical behavior and finite susceptibility for a wide range of models. We also discuss possible manifestations of spin-charge coupling in cold atomic gases.
We develop an effective field theory for finding critical properties of 1D spin gapped fermions at the onset of magnetization. It is shown how the spin-charge interaction leads to a linear critical behavior and finite susceptibility for a wide range of models. We also discuss possible manifestations of spin-charge coupling in cold atomic gases.
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Submitted 25 July, 2008;
originally announced July 2008.
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The Mott metal-insulator transition in the 1D Hubbard model in an external magnetic field
Authors:
Holger Frahm,
Temo Vekua
Abstract:
We study the low energy behavior of the one dimensional Hubbard model across the Mott metal-insulator phase transition in an external magnetic field. In particular we calculate elements of the dressed charge matrix at the critical point of the Mott transition for arbitrary Hubbard repulsion and magnetization numerically and, in certain limiting cases, analytically. These results are combined wit…
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We study the low energy behavior of the one dimensional Hubbard model across the Mott metal-insulator phase transition in an external magnetic field. In particular we calculate elements of the dressed charge matrix at the critical point of the Mott transition for arbitrary Hubbard repulsion and magnetization numerically and, in certain limiting cases, analytically. These results are combined with a non-perturbative effective field theory approach to reveal how the breaking of time reversal symmetry influences the Mott transition.
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Submitted 8 January, 2008; v1 submitted 24 October, 2007;
originally announced October 2007.
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Correlation functions and excitation spectrum of the frustrated ferromagnetic spin-1/2 chain in an external magnetic field
Authors:
T. Vekua,
A. Honecker,
H. -J. Mikeska,
F. Heidrich-Meisner
Abstract:
Magnetic field effects on the one-dimensional frustrated ferromagnetic chain are studied by means of effective field theory approaches in combination with numerical calculations utilizing Lanczos diagonalization and the density matrix renormalization group method. The nature of the ground state is shown to change from a spin-density-wave region to a nematic-like one upon approaching the saturati…
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Magnetic field effects on the one-dimensional frustrated ferromagnetic chain are studied by means of effective field theory approaches in combination with numerical calculations utilizing Lanczos diagonalization and the density matrix renormalization group method. The nature of the ground state is shown to change from a spin-density-wave region to a nematic-like one upon approaching the saturation magnetization. The excitation spectrum is analyzed and the behavior of the single spin-flip excitation gap is studied in detail, including the emergent finite-size corrections.
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Submitted 26 November, 2007; v1 submitted 5 April, 2007;
originally announced April 2007.
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Quantum phase transitions in trimerized zig-zag spin ladders
Authors:
H. D. Rosales,
D. C. Cabra,
M. D. Grynberg,
G. L. Rossini,
T. Vekua
Abstract:
We analyze the effects of a trimerized modulation in a quantum spin $S=\frac12$ zig-zag ladder at the magnetization plateau $M=1/3$. Such periodicity is argued to be stemmed from lattice deformations by phonons. The interplay between frustration and exchange modulation is well described by an effective triple sine-Gordon field theory close to the homogeneous ladder and by block-spin perturbation…
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We analyze the effects of a trimerized modulation in a quantum spin $S=\frac12$ zig-zag ladder at the magnetization plateau $M=1/3$. Such periodicity is argued to be stemmed from lattice deformations by phonons. The interplay between frustration and exchange modulation is well described by an effective triple sine-Gordon field theory close to the homogeneous ladder and by block-spin perturbation theory in the weakly coupled trimers regime. The characteristic triple degeneracy of the ground state for homogeneous ladders gives place to modulation driven quantum phase transitions, leading to a rich phase diagram including up-up-down, quantum plateau and gapless plateau states.
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Submitted 13 April, 2007; v1 submitted 12 December, 2006;
originally announced December 2006.
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Excitations with fractional spin less than 1/2 in frustrated magnetoelastic chains
Authors:
C. J. Gazza,
A. O. Dobry,
D. C. Cabra,
T. Vekua
Abstract:
We study the magnetic excitations on top of the plateaux states recently discovered in spin-Peierls systems in a magnetic field. We show by means of extensive density matrix renormalization group (DMRG) computations and an analytic approach that one single spin-flip on top of $M=1-\frac2N$ ($N=3,4,...$) plateau decays into $N$ elementary excitations each carrying a fraction $\frac1N$ of the spin…
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We study the magnetic excitations on top of the plateaux states recently discovered in spin-Peierls systems in a magnetic field. We show by means of extensive density matrix renormalization group (DMRG) computations and an analytic approach that one single spin-flip on top of $M=1-\frac2N$ ($N=3,4,...$) plateau decays into $N$ elementary excitations each carrying a fraction $\frac1N$ of the spin. This fractionalization goes beyond the well-known decay of one magnon into two spinons taking place on top of the M=0 plateau. Concentrating on the $\frac13$ plateau (N=3) we unravel the microscopic structure of the domain walls which carry fractional spin-$\frac13$, both from theory and numerics. These excitations are shown to be noninteracting and should be observable in x-ray and nuclear magnetic resonance experiments.
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Submitted 25 February, 2007; v1 submitted 15 August, 2006;
originally announced August 2006.
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Frustrated ferromagnetic spin-1/2 chain in a magnetic field: The phase diagram and thermodynamic properties
Authors:
F. Heidrich-Meisner,
A. Honecker,
T. Vekua
Abstract:
The frustrated ferromagnetic spin-1/2 Heisenberg chain is studied by means of a low-energy field theory as well as the density-matrix renormalization group and exact diagonalization methods. Firstly, we study the ground-state phase diagram in a magnetic field and find an `even-odd' (EO) phase characterized by bound pairs of magnons in the region of two weakly coupled antiferromagnetic chains. A…
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The frustrated ferromagnetic spin-1/2 Heisenberg chain is studied by means of a low-energy field theory as well as the density-matrix renormalization group and exact diagonalization methods. Firstly, we study the ground-state phase diagram in a magnetic field and find an `even-odd' (EO) phase characterized by bound pairs of magnons in the region of two weakly coupled antiferromagnetic chains. A jump in the magnetization curves signals a first-order transition at the boundary of the EO phase, but otherwise the curves are smooth. Secondly, we discuss thermodynamic properties at zero field, where we confirm a double-peak structure in the specific heat for moderate frustrating next-nearest neighbor interactions.
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Submitted 5 September, 2006; v1 submitted 8 May, 2006;
originally announced May 2006.
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Quantum dimer phases in a frustrated spin ladder: Effective field theory approach and exact diagonalization
Authors:
Temo Vekua,
Andreas Honecker
Abstract:
The phase diagram of a frustrated S=1/2 antiferromagnetic spin ladder with additional next-nearest neighbor exchanges, both diagonal and inchain, is studied by a weak-coupling effective field theory approach combined with exact diagonalization for finite systems. In addition to two known phases with rung-singlet and Haldane-type ground states, we observe two new phases with dimerization along th…
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The phase diagram of a frustrated S=1/2 antiferromagnetic spin ladder with additional next-nearest neighbor exchanges, both diagonal and inchain, is studied by a weak-coupling effective field theory approach combined with exact diagonalization for finite systems. In addition to two known phases with rung-singlet and Haldane-type ground states, we observe two new phases with dimerization along the chains. Furthermore, the transitions between the different phases are studied and shown to be either first order or to belong to the universality class of the two-dimensional Ising model. The nature of elementary excitations is discussed briefly.
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Submitted 7 June, 2006; v1 submitted 24 January, 2006;
originally announced January 2006.
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Magnetization plateaux induced by a coupling to the lattice
Authors:
T. Vekua,
D. C. Cabra,
A. Dobry,
C. Gazza,
D. Poilblanc
Abstract:
We investigate a simple model of a frustrated spin-1/2 Heisenberg chain coupled to adiabatic phonons under an external magnetic field. Using field theoretic methods complemented by extensive Density Matrix Renormalisation Group techniques generalized to include self-consistent lattice distortions, we show that magnetization plateaux at non-trivial rational values of the magnetization can be stab…
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We investigate a simple model of a frustrated spin-1/2 Heisenberg chain coupled to adiabatic phonons under an external magnetic field. Using field theoretic methods complemented by extensive Density Matrix Renormalisation Group techniques generalized to include self-consistent lattice distortions, we show that magnetization plateaux at non-trivial rational values of the magnetization can be stabilized by the lattice coupling. We suggest that such a scenario could be relevant for some low dimensional frustrated spin-Peierls compounds.
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Submitted 15 November, 2005;
originally announced November 2005.
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Field-induced chiral phase in isotropic frustrated spin chains
Authors:
Alexei Kolezhuk,
Temo Vekua
Abstract:
It is shown that an external magnetic field applied to a spin-S isotropic zigzag chain induces a phase with spontaneously broken parity, characterized by long range ordering of vector chirality. This is in contrast to the two-component Luttinger liquid scenario proposed in the literature. Relevance to real materials is discussed.
It is shown that an external magnetic field applied to a spin-S isotropic zigzag chain induces a phase with spontaneously broken parity, characterized by long range ordering of vector chirality. This is in contrast to the two-component Luttinger liquid scenario proposed in the literature. Relevance to real materials is discussed.
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Submitted 21 February, 2005;
originally announced February 2005.
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Magnetic field induced phase transitions in spin ladders with ferromagnetic legs
Authors:
T. Vekua,
G. I. Japaridze,
H. -J. Mikeska
Abstract:
We study the phase diagram of spin ladders with ferromagnetic legs under the influence of a symmetry breaking magnetic field in the weak coupling effective field theory by bosonization. For antiferromagnetic interleg coupling we identify two phase transitions introduced by the external magnetic field. In order to establish the universality of the phases we supplement the bosonization approach by…
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We study the phase diagram of spin ladders with ferromagnetic legs under the influence of a symmetry breaking magnetic field in the weak coupling effective field theory by bosonization. For antiferromagnetic interleg coupling we identify two phase transitions introduced by the external magnetic field. In order to establish the universality of the phases we supplement the bosonization approach by results from a strong coupling (rung) expansion and from spin wave analysis.
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Submitted 16 January, 2004;
originally announced January 2004.
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Phase diagrams of spin ladders with ferromagnetic legs
Authors:
T. Vekua,
G. I. Japaridze,
H. -J. Mikeska
Abstract:
The low-temperature properties of the spin S=1/2 ladder with anisotropic ferromagnetic legs are studied using the continuum limit bosonization approach. The weak-coupling ground state phase diagram of the model is obtained for a wide range of coupling constants and several unconventional gapless ''spin-liquid'' phases are shown to exist for ferromagnetic coupling. The behavior of the ladder syst…
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The low-temperature properties of the spin S=1/2 ladder with anisotropic ferromagnetic legs are studied using the continuum limit bosonization approach. The weak-coupling ground state phase diagram of the model is obtained for a wide range of coupling constants and several unconventional gapless ''spin-liquid'' phases are shown to exist for ferromagnetic coupling. The behavior of the ladder system in the vicinity of the ferromagnetic instability point is discussed in detail.
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Submitted 30 September, 2002;
originally announced September 2002.
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Perturbation theories for the S=1/2 spin ladder with four-spin ring exchange
Authors:
M. Mueller,
T. Vekua,
H. -J. Mikeska
Abstract:
The isotropic S=1/2 antiferromagnetic spin ladder with additional four-spin ring exchange is studied perturbatively in the strong coupling regime with the help of cluster expansion technique, and by means of bosonization in the weak coupling limit. It is found that a sufficiently large strength of ring exchange leads to a second-order phase transition, and the shape of the boundary in the vicini…
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The isotropic S=1/2 antiferromagnetic spin ladder with additional four-spin ring exchange is studied perturbatively in the strong coupling regime with the help of cluster expansion technique, and by means of bosonization in the weak coupling limit. It is found that a sufficiently large strength of ring exchange leads to a second-order phase transition, and the shape of the boundary in the vicinity of the known exact transition point is obtained. The critical exponent for the gap is found to be $η\simeq1$, in agreement both with exact results available for the dimer line and with the bosonization analysis. The phase emerging for high values of the ring exchange is argued to be gapped and spontaneously dimerized. The results for the transition line from strong coupling and from weak coupling match with each other naturally.
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Submitted 15 June, 2002; v1 submitted 6 June, 2002;
originally announced June 2002.