-
The evolution of pairing correlation with $3d_{z^{2}}$ electron filling in a bilayer two-orbital model for La$_3$Ni$_2$O$_7$
Authors:
Y. F. Chen,
Y. Shen,
X. J. Qian,
G. M. Zhang,
M. P. Qin
Abstract:
The discovery of high-${T_c}$ superconductivity in pressurized bilayer nickelate La$_3$Ni$_2$O$_7$ presents a new arena for exploring unconventional pairing mechanisms. A pivotal yet unresolved issue is the specific role of the $3d_{z^{2}}$ orbital of Ni. While its inter-layer super-exchange antiferromagnetic coupling is widely considered crucial for superconductivity, the role of its itinerancy r…
▽ More
The discovery of high-${T_c}$ superconductivity in pressurized bilayer nickelate La$_3$Ni$_2$O$_7$ presents a new arena for exploring unconventional pairing mechanisms. A pivotal yet unresolved issue is the specific role of the $3d_{z^{2}}$ orbital of Ni. While its inter-layer super-exchange antiferromagnetic coupling is widely considered crucial for superconductivity, the role of its itinerancy remains undetermined. Early studies showed that the superconductivity is accompanied by the emergence of a small Fermi pocket of the $3d_{z^{2}}$ orbitals. However, recent experiments show controversial results on the role of the $3d_{z^{2}}$ Fermi pocket on superconductivity. Motivated by these experimental results, we investigate an effective bilayer two-orbital model for La$_3$Ni$_2$O$_7$ using density-matrix renormalization group (DMRG) on a minimal one-dimensional geometry. By systematically varying the $3d_{z^{2}}$ orbital filling from $1/12$ doping to half-filling, we observe a pronounced suppression of superconducting correlations near half-filling. Our results demonstrate the itinerancy of $3d_{z^{2}}$ orbital is favorable for the pairing in the bilayer two-orbital model for La$_3$Ni$_2$O$_7$. Moreover, we observe that the pairing correlation is enhanced in regions where charge fluctuations are large, suggesting a competition between charge order and superconductivity in the model.
△ Less
Submitted 25 May, 2026;
originally announced May 2026.
-
Partial long-range order in antiferromagnetic Potts models
Authors:
M. P. Qin,
Q. N. Chen,
Z. Y. Xie,
J. Chen,
J. F. Yu,
H. H. Zhao,
B. Normand,
T. Xiang
Abstract:
The Potts model plays an essential role in classical statistical mechanics, illustrating many fundamental phenomena. One example is the existence of partially long-range-ordered states, in which some degrees of freedom remain disordered. This situation may arise from frustration of the interactions, but also from an irregular but unfrustrated lattice structure. We study partial long-range order in…
▽ More
The Potts model plays an essential role in classical statistical mechanics, illustrating many fundamental phenomena. One example is the existence of partially long-range-ordered states, in which some degrees of freedom remain disordered. This situation may arise from frustration of the interactions, but also from an irregular but unfrustrated lattice structure. We study partial long-range order in a range of antiferromagnetic $q$-state Potts models on different two-dimensional lattices and for all relevant values of $q$. We exploit the power of tensor-based numerical methods to evaluate the partition function of these models and hence to extract the key thermodynamic properties -- entropy, specific heat, magnetization, and susceptibility -- giving deep insight into the phase transitions and ordered states of each system. Our calculations reveal a range of phenomena related to partial ordering, including different types of entropy-driven phase transition, the role of lattice irregularity, very large values of the critical $q_c$, and double phase transitions.
△ Less
Submitted 23 October, 2014;
originally announced October 2014.
-
Controlling sign problems in spin models using tensor renormalization
Authors:
Alan Denbleyker,
Yuzhi Liu,
Y. Meurice,
M. P. Qin,
T. Xiang,
Z. Y. Xie,
J. F. Yu,
Haiyuan Zou
Abstract:
We consider the sign problem for classical spin models at complex $β=1/g_0^2$ on $L\times L$ lattices. We show that the tensor renormalization group method allows reliable calculations for larger Im$β$ than the reweighting Monte Carlo method. For the Ising model with complex $β$ we compare our results with the exact Onsager-Kaufman solution at finite volume. The Fisher zeros can be determined prec…
▽ More
We consider the sign problem for classical spin models at complex $β=1/g_0^2$ on $L\times L$ lattices. We show that the tensor renormalization group method allows reliable calculations for larger Im$β$ than the reweighting Monte Carlo method. For the Ising model with complex $β$ we compare our results with the exact Onsager-Kaufman solution at finite volume. The Fisher zeros can be determined precisely with the TRG method. We check the convergence of the TRG method for the O(2) model on $L\times L$ lattices when the number of states $D_s$ increases. We show that the finite size scaling of the calculated Fisher zeros agrees very well with the Kosterlitz-Thouless transition assumption and predict the locations for larger volume. The location of these zeros agree with Monte Carlo reweighting calculation for small volume. The application of the method for the O(2) model with a chemical potential is briefly discussed.
△ Less
Submitted 25 September, 2013;
originally announced September 2013.
-
Tensor renormalization group study of classical XY model on the square lattice
Authors:
J. F. Yu,
Z. Y. Xie,
Y. Meurice,
Yuzhi Liu,
A. Denbleyker,
Haiyuan Zou,
M. P. Qin,
J. Chen,
T. Xiang
Abstract:
Using the tensor renormalization group method based on the higher-order singular value decom- position, we have studied the thermodynamic properties of the continuous XY model on the square lattice. The temperature dependence of the free energy, the internal energy and the specific heat agree with the Monte Carlo calculations. From the field dependence of the magnetic susceptibility, we find the K…
▽ More
Using the tensor renormalization group method based on the higher-order singular value decom- position, we have studied the thermodynamic properties of the continuous XY model on the square lattice. The temperature dependence of the free energy, the internal energy and the specific heat agree with the Monte Carlo calculations. From the field dependence of the magnetic susceptibility, we find the Kosterlitz-Thouless transition temperature to be 0.8921 \pm 0.0019, consistent with the Monte Carlo as well as the high temperature series expansion results. At the transition temperature, the critical exponent δis estimated as 14.5, close to the analytic value by Kosterlitz.
△ Less
Submitted 19 September, 2013;
originally announced September 2013.
-
Exact blocking formulas for spin and gauge models
Authors:
Yuzhi Liu,
Y. Meurice,
M. P. Qin,
J. Unmuth-Yockey,
T. Xiang,
Z. Y. Xie,
J. F. Yu,
Haiyuan Zou
Abstract:
Using the example of the two-dimensional (2D) Ising model, we show that in contrast to what can be done in configuration space, the tensor renormalization group (TRG) formulation allows one to write exact, compact, and manifestly local blocking formulas and exact coarse grained expressions for the partition function. We argue that similar results should hold for most models studied by lattice gaug…
▽ More
Using the example of the two-dimensional (2D) Ising model, we show that in contrast to what can be done in configuration space, the tensor renormalization group (TRG) formulation allows one to write exact, compact, and manifestly local blocking formulas and exact coarse grained expressions for the partition function. We argue that similar results should hold for most models studied by lattice gauge theorists. We provide exact blocking formulas for several 2D spin models (the O(2) and O(3) sigma models and the SU(2) principal chiral model) and for the 3D gauge theories with groups Z_2, U(1) and SU(2). We briefly discuss generalizations to other groups, higher dimensions and practical implementations.
△ Less
Submitted 24 July, 2013;
originally announced July 2013.
-
Partial order in Potts models on the generalized decorated square lattice
Authors:
M. P. Qin,
J. Chen,
Q. N. Chen,
Z. Y. Xie,
X. Kong,
H. H. Zhao,
B. Normand,
T. Xiang
Abstract:
We explore the Potts model on the generalized decorated square lattice, with both nearest (J1) and next-neighbor (J2) interactions. Using the tensor renormalization-group method augmented by higher-order singular value decompositions, we calculate the spontaneous magnetization of the Potts model with q = 2, 3, and 4. The results for q = 2 allow us to benchmark our numerics using the exact solution…
▽ More
We explore the Potts model on the generalized decorated square lattice, with both nearest (J1) and next-neighbor (J2) interactions. Using the tensor renormalization-group method augmented by higher-order singular value decompositions, we calculate the spontaneous magnetization of the Potts model with q = 2, 3, and 4. The results for q = 2 allow us to benchmark our numerics using the exact solution. For q = 3, we find a highly degenerate ground state with partial order on a single sublattice, but with vanishing entropy per site, and we obtain the phase diagram as a function of the ratio J2=J1. There is no finite-temperature transition for the q = 4 case when J1 = J2, but the magnetic susceptibility diverges as the temperature goes to zero, showing that the model is critical at T = 0.
△ Less
Submitted 26 April, 2013;
originally announced April 2013.
-
The Quantum Torus Chain
Authors:
M. P. Qin,
J. M. Leinaas,
S. Ryu,
E. Ardonne,
T. Xiang,
D. -H. Lee
Abstract:
We introduce a new set of one dimensional quantum lattice models which we refer to as The quantum torus chain. These models have discrete global symmetry, and projective on-site representations. They possess an integer-valued parameter which controls the presence or absence of frustration. Depending on whether this parameter is even or odd these models either exhibit gapped symmetry breaking phase…
▽ More
We introduce a new set of one dimensional quantum lattice models which we refer to as The quantum torus chain. These models have discrete global symmetry, and projective on-site representations. They possess an integer-valued parameter which controls the presence or absence of frustration. Depending on whether this parameter is even or odd these models either exhibit gapped symmetry breaking phases with isolated critical points, or gapped symmetry breaking phases separated by gapless phases. We discuss the property of these phases and phase transitions for two special values of the parameter and point out many open problems
△ Less
Submitted 29 October, 2012; v1 submitted 7 May, 2012;
originally announced May 2012.
-
Coarse-graining renormalization by higher-order singular value decomposition
Authors:
Z. Y. Xie,
J. Chen,
M. P. Qin,
J. W. Zhu,
L. P. Yang,
T. Xiang
Abstract:
We propose a novel coarse graining tensor renormalization group method based on the higher-order singular value decomposition. This method provides an accurate but low computational cost technique for studying both classical and quantum lattice models in two- or three-dimensions. We have demonstrated this method using the Ising model on the square and cubic lattices. By keeping up to 16 bond basis…
▽ More
We propose a novel coarse graining tensor renormalization group method based on the higher-order singular value decomposition. This method provides an accurate but low computational cost technique for studying both classical and quantum lattice models in two- or three-dimensions. We have demonstrated this method using the Ising model on the square and cubic lattices. By keeping up to 16 bond basis states, we obtain by far the most accurate numerical renormalization group results for the 3D Ising model. We have also applied the method to study the ground state as well as finite temperature properties for the two-dimensional quantum transverse Ising model and obtain the results which are consistent with published data.
△ Less
Submitted 7 August, 2012; v1 submitted 5 January, 2012;
originally announced January 2012.
-
Partial order and finite-temperature phase transitions in Potts models on irregular lattices
Authors:
Q. N. Chen,
M. P. Qin,
J. Chen,
Z. C. Wei,
H. H. Zhao,
B. Normand,
T. Xiang
Abstract:
We evaluate the thermodynamic properties of the 4-state antiferromagnetic Potts model on the Union- Jack lattice using tensor-based numerical methods. We present strong evidence for a previously unknown, "entropy-driven," finite-temperature phase transition to a partially ordered state. From the thermodynamics of Potts models on the diced and centered diced lattices, we propose that finite-tempera…
▽ More
We evaluate the thermodynamic properties of the 4-state antiferromagnetic Potts model on the Union- Jack lattice using tensor-based numerical methods. We present strong evidence for a previously unknown, "entropy-driven," finite-temperature phase transition to a partially ordered state. From the thermodynamics of Potts models on the diced and centered diced lattices, we propose that finite-temperature transitions and partially ordered states are ubiquitous on irregular lattices.
△ Less
Submitted 16 October, 2011; v1 submitted 25 May, 2011;
originally announced May 2011.
-
Plaquette order and deconfined quantum critical point in the spin-1 bilinear-biquadratic Heisenberg model on the honeycomb lattice
Authors:
H. H. Zhao,
Cenke Xu,
Q. N. Chen,
Z. C. Wei,
M. P. Qin,
G. M. Zhang,
T. Xiang
Abstract:
We have precisely determined the ground state phase diagram of the quantum spin-1 bilinear-biquadratic Heisenberg model on the honeycomb lattice using the tensor renormalization group method. We find that the ferromagnetic, ferroquadrupolar, and a large part of the antiferromagnetic phases are stable against quantum fluctuations. However, around the phase where the ground state is antiferroquadrup…
▽ More
We have precisely determined the ground state phase diagram of the quantum spin-1 bilinear-biquadratic Heisenberg model on the honeycomb lattice using the tensor renormalization group method. We find that the ferromagnetic, ferroquadrupolar, and a large part of the antiferromagnetic phases are stable against quantum fluctuations. However, around the phase where the ground state is antiferroquadrupolar ordered in the classical limit, quantum fluctuations suppress completely all magnetic orders, leading to a plaquette order phase which breaks the lattice symmetry but preserves the spin SU(2) symmetry. On the evidence of our numerical results, the quantum phase transition between the antiferromagnetic phase and the plaquette phase is found to be either a direct second order or a very weak first order transition.
△ Less
Submitted 23 April, 2012; v1 submitted 13 May, 2011;
originally announced May 2011.
-
Translation invariant tensor product states in a finite lattice system
Authors:
J. W. Cai,
Q. N. Chen,
H. H. Zhao,
Z. Y. Xie,
M. P. Qin,
Z. C. Wei,
T. Xiang
Abstract:
We show that the matrix (or more generally tensor) product states in a finite translation invariant system can be accurately constructed from the same set of local matrices (or tensors) that are determined from an infinite lattice system in one or higher dimensions. This provides an efficient approach for studying translation invariant tensor product states in finite lattice systems. Two methods a…
▽ More
We show that the matrix (or more generally tensor) product states in a finite translation invariant system can be accurately constructed from the same set of local matrices (or tensors) that are determined from an infinite lattice system in one or higher dimensions. This provides an efficient approach for studying translation invariant tensor product states in finite lattice systems. Two methods are introduced to determine these size-independent local tensors.
△ Less
Submitted 9 November, 2010;
originally announced November 2010.
-
Fractality of Hofstadter Butterfly in Specific Heat Oscillation
Authors:
L. P. Yang,
W. H. Xu,
M. P. Qin,
T. Xiang
Abstract:
We calculate thermodynamical properties of the Hofstadter model using a recently developed quantum transfer matrix method. We find intrinsic oscillation features in specific heat that manifest the fractal structure of the Hofstadter butterfly. We also propose experimental approaches which use specific heat as an access to detect the Hofstadter butterfly.
We calculate thermodynamical properties of the Hofstadter model using a recently developed quantum transfer matrix method. We find intrinsic oscillation features in specific heat that manifest the fractal structure of the Hofstadter butterfly. We also propose experimental approaches which use specific heat as an access to detect the Hofstadter butterfly.
△ Less
Submitted 28 September, 2010;
originally announced September 2010.
-
Probing the Hofstadter butterfly with the quantum oscillation of magnetization
Authors:
W. H. Xu,
L. P. Yang,
M. P. Qin,
T. Xiang
Abstract:
We have developed a different quantum transfer matrix method to accurately determine thermodynamic properties of the Hofstadter model. This method resolves a technical problem which is intractable by other methods and makes the calculation of physical quantities of the Hofstadter model in the thermodynamic limit at finite temperatures feasible. It is shown that the quantum correction to the de Haa…
▽ More
We have developed a different quantum transfer matrix method to accurately determine thermodynamic properties of the Hofstadter model. This method resolves a technical problem which is intractable by other methods and makes the calculation of physical quantities of the Hofstadter model in the thermodynamic limit at finite temperatures feasible. It is shown that the quantum correction to the de Haas-van Alphen (dHvA) oscillation of magnetization bears the energy structure of Hofstadter butterfly. The measurement of this quantum correction, which can be materialized on the superlattice or cold atom systems, can reveal unambiguously the Hofstadter fractal energy spectrum.
△ Less
Submitted 6 July, 2015; v1 submitted 1 August, 2008;
originally announced August 2008.