Showing 1–21 of 21 results for author: Lee, C -

Physical properties and electronic structure of the two-gap superconductor V$_{2}$Ga$_{5}$

Authors: P. -Y. Cheng, Mohamed Oudah, T. -L. Hung, C. -E. Hsu, C. -C. Chang, J. -Y. Haung, T. -C. Liu, C. -M. Cheng, M. -N. Ou, W. -T. Chen, L. Z. Deng, C. -C. Lee, Y. -Y. Chen, C. -N. Kuo, C. -S. Lue, Janna Machts, Kenji M. Kojima, Alannah M. Hallas, C. -L. Huang

Abstract: We present a thorough investigation of the physical properties and superconductivity of the binary intermetallic V2Ga5. Electrical resistivity and specific heat measurements show that V2Ga5 enters its superconducting state below Tsc = 3.5 K, with a critical field of Hc2,perp c(Hc2,para c) = 6.5(4.1) kOe. With H perp c, the peak effect was observed in resistivity measurements, indicating the ultrah… ▽ More We present a thorough investigation of the physical properties and superconductivity of the binary intermetallic V2Ga5. Electrical resistivity and specific heat measurements show that V2Ga5 enters its superconducting state below Tsc = 3.5 K, with a critical field of Hc2,perp c(Hc2,para c) = 6.5(4.1) kOe. With H perp c, the peak effect was observed in resistivity measurements, indicating the ultrahigh quality of the single crystal studied. The resistivity measurements under high pressure reveal that the Tsc is suppressed linearly with pressure and reaches absolute zero around 20 GPa. Specific heat and muon spin relaxation measurements both indicate that the two-gap s-wave model best describes the superconductivity of V2Ga5. The spectra obtained from angle-resolved photoemission spectroscopy measurements suggest that two superconducting gaps open at the Fermi surface around the Z and Γ points. These results are verified by first-principles band structure calculations. We therefore conclude that V2Ga5 is a phonon-mediated two-gap s-wave superconductor △ Less

Submitted 6 May, 2024; originally announced May 2024.

Comments: Some images experience distortion during the conversion process to EPS format

Journal ref: Phys. Rev. Research 6 6, 033253 (2024)

Purely in-plane ferroelectricity in monolayer SnS at room temperature

Authors: N. Higashitarumizu, H. Kawamoto, C. -J. Lee, B. -H. Lin, F. -H. Chu, I. Yonemori, T. i Nishimura, K. Wakabayashi, W. -H. Chang, K. Nagashio

Abstract: 2D van der Waals ferroelectric semiconductors have emerged as an attractive building block with immense potential to provide multifunctionality in nanoelectronics. Although several accomplishments have been reported in ferroelectric resistive switching for out-of-plane 2D ferroelectrics down to the monolayer, a purely in-plane ferroelectric has not been experimentally validated at the monolayer th… ▽ More 2D van der Waals ferroelectric semiconductors have emerged as an attractive building block with immense potential to provide multifunctionality in nanoelectronics. Although several accomplishments have been reported in ferroelectric resistive switching for out-of-plane 2D ferroelectrics down to the monolayer, a purely in-plane ferroelectric has not been experimentally validated at the monolayer thickness. Herein, a micrometer-size monolayer SnS is grown on mica by physical vapor deposition, and in-plane ferroelectric switching is demonstrated with a two-terminal device at room temperature (RT). SnS has been commonly regarded to exhibit the odd-even effect, where the centrosymmetry breaks only in the odd-number layers to exhibit ferroelectricity. Remarkably, however, a robust RT ferroelectricity exists in SnS below a critical thickness of 15 layers with both an odd and even number of layers. The lack of the odd-even effect probably originates from the interaction with the mica substrate, suggesting the possibility of controlling the stacking sequence of multilayer SnS, going beyond the limit of ferroelectricity in the monolayer. This work will pave the way for nanoscale ferroelectric applications based on SnS as a new platform for in-plane ferroelectrics. △ Less

Submitted 18 June, 2020; originally announced June 2020.

Journal ref: Nature commun.,2020, 11, 2428

Photocurrent-driven transient symmetry breaking in the Weyl semimetal TaAs

Authors: N Sirica, P. P. Orth, M. S. Scheurer, Y. M. Dai, M. -C. Lee, P. Padmanabhan, L. T. Mix, S. W. Teitelbaum, M. Trigo, L. X. Zhao, G. F. Chen, B. Xu, R. Yang, B. Shen, C. Hu, C. -C. Lee, H. Lin, T. A. Cochran, S. A. Trugman, J. -X. Zhu, M. Z. Hasan, N. Ni, X. G. Qiu, A. J. Taylor, D. A. Yarotski , et al. (1 additional authors not shown)

Abstract: Symmetry plays a central role in conventional and topological phases of matter, making the ability to optically drive symmetry change a critical step in developing future technologies that rely on such control. Topological materials, like the newly discovered topological semimetals, are particularly sensitive to a breaking or restoring of time-reversal and crystalline symmetries, which affect both… ▽ More Symmetry plays a central role in conventional and topological phases of matter, making the ability to optically drive symmetry change a critical step in developing future technologies that rely on such control. Topological materials, like the newly discovered topological semimetals, are particularly sensitive to a breaking or restoring of time-reversal and crystalline symmetries, which affect both bulk and surface electronic states. While previous studies have focused on controlling symmetry via coupling to the crystal lattice, we demonstrate here an all-electronic mechanism based on photocurrent generation. Using second-harmonic generation spectroscopy as a sensitive probe of symmetry change, we observe an ultrafast breaking of time-reversal and spatial symmetries following femtosecond optical excitation in the prototypical type-I Weyl semimetal TaAs. Our results show that optically driven photocurrents can be tailored to explicitly break electronic symmetry in a generic fashion, opening up the possibility of driving phase transitions between symmetry-protected states on ultrafast time scales. △ Less

Submitted 9 November, 2021; v1 submitted 20 May, 2020; originally announced May 2020.

Comments: 28 pages, 15 figures, 4 Tables

Journal ref: Nat. Mater. (2021)

Fast gate-based readout of silicon quantum dots using Josephson parametric amplification

Authors: S. Schaal, I. Ahmed, J. A. Haigh, L. Hutin, B. Bertrand, S. Barraud, M. Vinet, C. -M. Lee, N. Stelmashenko, J. W. A. Robinson, J. Y. Qiu, S. Hacohen-Gourgy, I. Siddiqi, M. F. Gonzalez-Zalba, J. J. L. Morton

Abstract: Spins in silicon quantum devices are promising candidates for large-scale quantum computing. Gate-based sensing of spin qubits offers compact and scalable readout with high fidelity, however further improvements in sensitivity are required to meet the fidelity thresholds and measurement timescales needed for the implementation of fast-feedback in error correction protocols. Here, we combine radio-… ▽ More Spins in silicon quantum devices are promising candidates for large-scale quantum computing. Gate-based sensing of spin qubits offers compact and scalable readout with high fidelity, however further improvements in sensitivity are required to meet the fidelity thresholds and measurement timescales needed for the implementation of fast-feedback in error correction protocols. Here, we combine radio-frequency gate-based sensing at 622 MHz with a Josephson parametric amplifier (JPA), that operates in the 500-800 MHz band, to reduce the integration time required to read the state of a silicon double quantum dot formed in a nanowire transistor. Based on our achieved signal-to-noise ratio (SNR), we estimate that singlet-triplet single-shot readout with an average fidelity of 99.7% could be performed in 1 $μ$s, well-below the requirements for fault-tolerant readout and 30 times faster than without the JPA. Additionally, the JPA allows operation at a lower RF power while maintaining identical SNR. We determine a noise temperature of 200 mK with a contribution from the JPA (25%), cryogenic amplifier (25%) and the resonator (50%), showing routes to further increase the read-out speed. △ Less

Submitted 23 July, 2019; v1 submitted 22 July, 2019; originally announced July 2019.

Comments: Wrong figure reference corrected

Journal ref: Phys. Rev. Lett. 124, 067701 (2020)

Electrical Autonomous Brownian Gyrator

Authors: K. -H. Chiang, C. -L. Lee, P. -Y. Lai, Y. -F. Chen

Abstract: We study experimentally and theoretically the steady-state dynamics of a simple stochastic electronic system featuring two resistor-capacitor circuits coupled by a third capacitor. The resistors are subject to thermal noises at real temperatures. The voltage fluctuation across each resistor can be compared to a one-dimensional Brownian motion. However, the collective dynamical behavior, when the r… ▽ More We study experimentally and theoretically the steady-state dynamics of a simple stochastic electronic system featuring two resistor-capacitor circuits coupled by a third capacitor. The resistors are subject to thermal noises at real temperatures. The voltage fluctuation across each resistor can be compared to a one-dimensional Brownian motion. However, the collective dynamical behavior, when the resistors are subject to distinct thermal baths, is identical to that of a Brownian gyrator, as first proposed by R. Filliger and P. Reimann in Physical Review Letters 99, 230602 (2007). The average gyrating dynamics is originated from the absence of detailed balance due to unequal thermal baths. We look into the details of this stochastic gyrating dynamics, its dependences on the temperature difference and coupling strength, and the mechanism of heat transfer through this simple electronic circuit. Our work affirms the general principle and the possibility of a Brownian ratchet working near room temperature scale. △ Less

Submitted 18 September, 2017; v1 submitted 31 March, 2017; originally announced March 2017.

Comments: 8 pages, 4 figures

Journal ref: Phys. Rev. E 96, 032123 (2017)

Fluctuations of Entropy Production in Partially Masked Electric Circuits: Theoretical Analysis

Authors: K. -H. Chiang, C. -W. Chou, C. -L. Lee, P. -Y. Lai, Y. -F. Chen

Abstract: In this work we perform theoretical analysis about a coupled RC circuit with constant driven currents. Starting from stochastic differential equations, where voltages are subject to thermal noises, we derive time-correlation functions, steady-state distributions and transition probabilities of the system. The validity of the fluctuation theorem (FT) is examined for scenarios with complete and inco… ▽ More In this work we perform theoretical analysis about a coupled RC circuit with constant driven currents. Starting from stochastic differential equations, where voltages are subject to thermal noises, we derive time-correlation functions, steady-state distributions and transition probabilities of the system. The validity of the fluctuation theorem (FT) is examined for scenarios with complete and incomplete descriptions. △ Less

Submitted 28 January, 2016; v1 submitted 18 January, 2016; originally announced January 2016.

Comments: 4 pages, 1 figure

Similarity solutions of Reaction-Diffusion equation with space- and time-dependent diffusion and reaction terms

Authors: C. -L. Ho, C. -C. Lee

Abstract: We consider solvability of the generalized reaction-diffusion equation with both space- and time-dependent diffusion and reaction terms by means of the similarity method. By introducing the similarity variable, the reaction-diffusion equation is reduced to an ordinary differential equation. Matching the resulting ordinary differential equation with known exactly solvable equations, one can obtain… ▽ More We consider solvability of the generalized reaction-diffusion equation with both space- and time-dependent diffusion and reaction terms by means of the similarity method. By introducing the similarity variable, the reaction-diffusion equation is reduced to an ordinary differential equation. Matching the resulting ordinary differential equation with known exactly solvable equations, one can obtain corresponding exactly solvable reaction-diffusion systems. Several representative examples of exactly solvable reaction-diffusion equations are presented. △ Less

Submitted 1 August, 2015; originally announced August 2015.

Comments: 11 pages, 4 figures

Highly resistive epitaxial Mg-doped GdN thin films

Authors: C. -M. Lee, H. Warring, S. Vézian, B. Damilano, S. Granville, M. Al Khalfioui, Y. Cordier, H. J. Trodahl, B. J. Ruck, F. Natali

Abstract: We report the growth by molecular beam epitaxy of highly resistive GdN, using intentional doping with magnesium. Mg-doped GdN layers with resistivities of 1000 Ω.cm and carrier concentrations of 10E16 cm-3 are obtained for films with Mg concentrations up to 5 x 10E19 atoms/cm3. X-ray diffraction rocking curves indicate that Mg-doped GdN films have crystalline quality very similar to undoped GdN fi… ▽ More We report the growth by molecular beam epitaxy of highly resistive GdN, using intentional doping with magnesium. Mg-doped GdN layers with resistivities of 1000 Ω.cm and carrier concentrations of 10E16 cm-3 are obtained for films with Mg concentrations up to 5 x 10E19 atoms/cm3. X-ray diffraction rocking curves indicate that Mg-doped GdN films have crystalline quality very similar to undoped GdN films, showing that the Mg doping did not affect the structural properties of the films. A decrease of the Curie temperature with decreasing the electron density is observed, supporting a recently suggested magnetic polaron scenario [F. Natali et al., Phys. Rev. B 87, 035202 (2013)]. △ Less

Submitted 29 October, 2014; originally announced October 2014.

Universal local pair correlations of Lieb-Liniger bosons at quantum criticality

Authors: M. -S. Wang, J. -H. Huang, C. -H. Lee, X. -G. Yin, X. -W. Guan, M. T. Batchelor

Abstract: The one-dimensional Lieb-Liniger Bose gas is a prototypical many-body system featuring universal Tomonaga-Luttinger liquid (TLL) physics and free fermion quantum criticality. We analytically calculate finite temperature local pair correlations for the strong coupling Bose gas at quantum criticality using the polylog function in the framework of the Yang-Yang thermodynamic equations. We show that t… ▽ More The one-dimensional Lieb-Liniger Bose gas is a prototypical many-body system featuring universal Tomonaga-Luttinger liquid (TLL) physics and free fermion quantum criticality. We analytically calculate finite temperature local pair correlations for the strong coupling Bose gas at quantum criticality using the polylog function in the framework of the Yang-Yang thermodynamic equations. We show that the local pair correlation has the universal value $g^{(2)}(0)\approx 2 p/(n\varepsilon)$ in the quantum critical regime, the TLL phase and the quasi-classical region, where $p$ is the pressure per unit length rescaled by the interaction energy $\varepsilon=\frac{\hbar^2}{2m} c^2$ with interaction strength $c$ and linear density $n$. This suggests the possibility to test finite temperature local pair correlations for the TLL in the relativistic dispersion regime and to probe quantum criticality with the local correlations beyond the TLL phase. Furthermore, thermodynamic properties at high temperatures are obtained by both high temperature and virial expansion of the Yang-Yang thermodynamic equation. △ Less

Submitted 18 March, 2013; v1 submitted 14 November, 2012; originally announced November 2012.

Comments: 8 pages, 6 figures, additional text and references

Journal ref: Phys. Rev. A 87, 043634 (2013)

Electronic reconstruction through the structural and magnetic transitions in detwinned NaFeAs

Authors: M. Yi, D. H. Lu, R. G. Moore, K. Kihou, C. -H. Lee, A. Iyo, H. Eisaki, T. Yoshida, A. Fujimori, Z. -X. Shen

Abstract: We use angle-resolved photoemission spectroscopy to study twinned and detwinned iron pnictide compound NaFeAs. Distinct signatures of electronic reconstruction are observed to occur at the structural (TS) and magnetic (TSDW) transitions. At TS, C4 rotational symmetry is broken in the form of an anisotropic shift of the orthogonal dxz and dyz bands. The magnitude of this orbital anisotropy rapidly… ▽ More We use angle-resolved photoemission spectroscopy to study twinned and detwinned iron pnictide compound NaFeAs. Distinct signatures of electronic reconstruction are observed to occur at the structural (TS) and magnetic (TSDW) transitions. At TS, C4 rotational symmetry is broken in the form of an anisotropic shift of the orthogonal dxz and dyz bands. The magnitude of this orbital anisotropy rapidly develops to near completion upon approaching TSDW, at which temperature band folding occurs via the antiferromagnetic ordering wave vector. Interestingly, the anisotropic band shift onsetting at TS develops in such a way to enhance the nesting conditions in the C2 symmetric state, hence is intimately correlated with the long range collinear AFM order. Furthermore, the similar behaviors of the electronic reconstruction in NaFeAs and Ba(Fe1-xCox)2As2 suggests that this rapid development of large orbital anisotropy between TS and TSDW is likely a general feature of the electronic nematic phase in the iron pnictides, and the associated orbital fluctuations may play an important role in determining the ground state properties. △ Less

Submitted 25 November, 2011; originally announced November 2011.

Journal ref: NJP 14, 073019 (2012)

Possible Multiple Gap Superconductivity with Line Nodes in Heavily Hole-Doped Superconductor KFe2As2 Studied by 75As-NQR and Specific Heat

Authors: H. Fukazawa, Y. Yamada, K. Kondo, T. Saito, Y. Kohori, K. Kuga, Y. Matsumoto, S. Nakatsuji, H. Kito, P. M. Shirage, K. Kihou, N. Takeshita, C. -H. Lee, A. Iyo, H. Eisaki

Abstract: We report the 75As nuclear quadrupole resonance (NQR) and specific heat measurements of the heavily hole-doped superconductor KFe2As2 (Tc = 3.5 K). The spin-lattice relaxation rate 1/T1 in the superconducting state exhibits quite gradual temperature dependence with no coherence peak below Tc. The quasi-particle specific heat C_QP/T shows small specific heat jump which is about 30% of electronic… ▽ More We report the 75As nuclear quadrupole resonance (NQR) and specific heat measurements of the heavily hole-doped superconductor KFe2As2 (Tc = 3.5 K). The spin-lattice relaxation rate 1/T1 in the superconducting state exhibits quite gradual temperature dependence with no coherence peak below Tc. The quasi-particle specific heat C_QP/T shows small specific heat jump which is about 30% of electronic specific heat coefficient just below Tc. In addition, it suggests the existence of low-energy quasi-particle excitation at the lowest measurement temperature T = 0.4 K \simeq Tc/10. These temperature dependence of 1/T1 and C_QP/T can be explained by multiple nodal superconducting gap scenario rather than multiple fully-gapped s_\pm-wave one within simple gap analysis. △ Less

Submitted 25 June, 2009; originally announced June 2009.

Comments: 5 pages, 5 figures, to be published in J. Phys. Soc. Jpn. No.8 issue (2009)

Journal ref: J. Phys. Soc. Jpn. Vol.78 (2009) p083712.

Quantum Monte Carlo study of the two-dimensional fermion Hubbard Model

Authors: C. N. Varney, C. -R. Lee, Z. J. Bai, S. Chiesa, M. Jarrell, R. T. Scalettar

Abstract: We report large scale determinant Quantum Monte Carlo calculations of the effective bandwidth, momentum distribution, and magnetic correlations of the square lattice fermion Hubbard Hamiltonian at half-filling. The sharp Fermi surface of the non-interacting limit is significantly broadened by the electronic correlations, but retains signatures of the approach to the edges of the first Brillouin zo… ▽ More We report large scale determinant Quantum Monte Carlo calculations of the effective bandwidth, momentum distribution, and magnetic correlations of the square lattice fermion Hubbard Hamiltonian at half-filling. The sharp Fermi surface of the non-interacting limit is significantly broadened by the electronic correlations, but retains signatures of the approach to the edges of the first Brillouin zone as the density increases. Finite size scaling of simulations on large lattices allows us to extract the interaction dependence of the antiferromagnetic order parameter, exhibiting its evolution from weak coupling to the strong coupling Heisenberg limit. Our lattices provide improved resolution of the Green's function in momentum space, allowing a more quantitative comparison with time-of-flight optical lattice experiments. △ Less

Submitted 6 April, 2010; v1 submitted 13 March, 2009; originally announced March 2009.

Comments: 8 pages, 11 figures. Published by Phys. Rev. B. on 18 August 2009.

Journal ref: Phys. Rev. B 80, 075116 (2009).

Broadband Dielectric Spectroscopy of Ruddlesden-Popper Sr$_{n+1}$Ti$_{n}$O$_{3n+1}$ ($n$ = 1, 2, 3) Thin Films

Authors: N. D. Orloff, W. Tian, C. J. Fennie, C. -H. Lee, D. Gu, J. Mateu, X. X. Xi, K. M. Rabe, D. G. Schlom, I. Takeuchi, J. C. Booth

Abstract: We explore the frequency-dependent relative permittivity of Ruddlesden-Popper series Sr(n+1)Ti(n)O(3n+1) (n =1,2,3) thin films as a function of temperature and dc electric field. Interdigitated capacitors and coplanar waveguides were used to extract the frequency response from 500 Hz to 40 GHz. At room temperature, the in-plane relative permittivities obtained for Sr(n+1)Ti(n)O(3n+1) (n =1,2,3)… ▽ More We explore the frequency-dependent relative permittivity of Ruddlesden-Popper series Sr(n+1)Ti(n)O(3n+1) (n =1,2,3) thin films as a function of temperature and dc electric field. Interdigitated capacitors and coplanar waveguides were used to extract the frequency response from 500 Hz to 40 GHz. At room temperature, the in-plane relative permittivities obtained for Sr(n+1)Ti(n)O(3n+1) (n =1,2,3) were 42+/-3, 54+/-3, and 77+/-2, respectively, and were independent of frequency. At low temperatures, permittivity increases and electric field tunability develops in Sr(4)Ti(3)O(10). △ Less

Submitted 9 February, 2009; originally announced February 2009.

Covalent bonding and magnetism in cuprates

Authors: A. C. Walters, T. G. Perring, J. -S. Caux, A. T. Savici, G. D. Gu, C. -C. Lee, W. Ku, I. A. Zaliznyak

Abstract: The importance of covalent bonding for the magnetism of 3d metal complexes was first noted by Pauling in 1931. His point became moot, however, with the success of the ionic picture of Van Vleck, where ligands influence magnetic electrons of 3d ions mainly through electrostatic fields. Anderson's theory of spin superexchange later established that covalency is at the heart of cooperative magnetis… ▽ More The importance of covalent bonding for the magnetism of 3d metal complexes was first noted by Pauling in 1931. His point became moot, however, with the success of the ionic picture of Van Vleck, where ligands influence magnetic electrons of 3d ions mainly through electrostatic fields. Anderson's theory of spin superexchange later established that covalency is at the heart of cooperative magnetism in insulators, but its energy scale was believed to be small compared to other inter-ionic interactions and therefore it was considered a small perturbation of the ionic picture. This assertion fails dramatically in copper oxides, which came to prominence following the discovery of high critical temperature superconductors (HTSC). Magnetic interactions in cuprates are remarkably strong and are often considered the origin of the unusually high superconducting transition temperature, Tc. Here we report a detailed survey of magnetic excitations in the one-dimensional cuprate Sr2CuO3 using inelastic neutron scattering (INS). We show that although the experimental dynamical spin structure factor is well described by the model S=1/2 nearest-neighbour Heisenberg Hamiltonian typically used for cuprates, the magnetic intensity is modified dramatically by strong hybridization of Cu 3d states with O p states, showing that the ionic picture of localized 3d Heisenberg spin magnetism is grossly inadequate. Our findings provide a natural explanation for the puzzle of the missing INS magnetic intensity in cuprates and have profound implications for understanding current and future experimental data on these materials. △ Less

Submitted 30 December, 2008; originally announced December 2008.

Comments: 1 pdf file with 4 colour figures

Journal ref: Nature Physics 5, 867-872 (2009)

The effect of ozone oxidation on single-walled carbon nanotubes

Authors: J. M. Simmons, B. M. Nichols, S. E. Baker, Matthew S. Marcus, O. M. Castellini, C. -S. Lee, R. J. Hamers, M. A. Eriksson

Abstract: Exposing single-walled carbon nanotubes to room temperature UV-generated ozone leads to an irreversible increase in their electrical resistance. We demonstrate that the increased resistance is due to ozone oxidation on the sidewalls of the nanotubes rather than at the end caps. Raman and x-ray photoelectron spectroscopy show an increase in the defect density due to the oxidation of the nanotubes… ▽ More Exposing single-walled carbon nanotubes to room temperature UV-generated ozone leads to an irreversible increase in their electrical resistance. We demonstrate that the increased resistance is due to ozone oxidation on the sidewalls of the nanotubes rather than at the end caps. Raman and x-ray photoelectron spectroscopy show an increase in the defect density due to the oxidation of the nanotubes. Using ultraviolet photoelectron spectroscopy we show that these defects represent the removal of pi-conjugated electron states near the Fermi level, leading to the observed increase in electrical resistance. Oxidation of carbon nanotubes is an important first step in many chemical functionalization processes. Since the oxidation rate is controllable with short exposures, UV-generated ozone offers the potential for use as a low-thermal budget processing tool. △ Less

Submitted 3 October, 2007; originally announced October 2007.

Comments: 28 pages, 9 figures

Journal ref: J. Phys. Chem. B 110, 7113 (2006)

Symmetry Algebras of Quantum Matrix Models in the Large-N Limit

Authors: C. -W. H. Lee

Abstract: Quantum matrix models in the large-N limit arise in many physical systems like Yang-Mills theory with or without supersymmetry, quantum gravity, string-bit models, various low energy effective models of string theory, M(atrix) theory, quantum spin chain models, and strongly correlated electron systems like the Hubbard model. We introduce, in a unifying fashion, a hierachy of infinite-dimensional… ▽ More Quantum matrix models in the large-N limit arise in many physical systems like Yang-Mills theory with or without supersymmetry, quantum gravity, string-bit models, various low energy effective models of string theory, M(atrix) theory, quantum spin chain models, and strongly correlated electron systems like the Hubbard model. We introduce, in a unifying fashion, a hierachy of infinite-dimensional Lie superalgebras of quantum matrix models. One of these superalgebras pertains to the open string sector and another one the closed string sector. Physical observables of quantum matrix models like the Hamiltonian can be expressed as elements of these Lie superalgebras. This indicates the Lie superalgebras describe the symmetry of quantum matrix models. We present the structure of these Lie superalgebras like their Cartan subalgebras, root vectors, ideals and subalgebras. They are generalizations of well-known algebras like the Cuntz algebra, the Virasoro algebra, the Toeplitz algebra, the Witt algebra and the Onsager algebra. Just like we learnt a lot about critical phenomena and string theory through their conformal symmetry described by the Virasoro algebra, we may learn a lot about quantum chromodynamics, quantum gravity and condensed matter physics through this symmetry of quantum matrix models described by these Lie superalgebras. △ Less

Submitted 21 July, 1999; v1 submitted 15 July, 1999; originally announced July 1999.

Comments: 150 pages, 21 eps figures, 6 tables; Ph.D. thesis; citation added

A Review of Symmetry Algebras of Quantum Matrix Models in the Large-N Limit

Authors: C. -W. H. Lee, S. G. Rajeev

Abstract: This is a review article in which we will introduce, in a unifying fashion and with more intermediate steps in some difficult calculations, two infinite-dimensional Lie algebras of quantum matrix models, one for the open string sector and one for the closed string sector. Physical observables of quantum matrix models in the large-N limit can be expressed as elements of these Lie algebras. We wil… ▽ More This is a review article in which we will introduce, in a unifying fashion and with more intermediate steps in some difficult calculations, two infinite-dimensional Lie algebras of quantum matrix models, one for the open string sector and one for the closed string sector. Physical observables of quantum matrix models in the large-N limit can be expressed as elements of these Lie algebras. We will see that both algebras arise as quotient algebras of a larger Lie algebra. We will also discuss some properties of these Lie algebras not published elsewhere yet, and briefly review their relationship with well-known algebras like the Cuntz algebra, the Witt algebra and the Virasoro algebra. We will also review how Yang--Mills theory, various low energy effective models of string theory, quantum gravity, string-bit models, and quantum spin chain models can be formulated as quantum matrix models. Studying these algebras thus help us understand the common symmetry of these physical systems. △ Less

Submitted 8 June, 1999; originally announced June 1999.

Comments: 77 pages, 21 eps figures, 1 table, LaTeX2.09; an invited review article

Journal ref: Int.J.Mod.Phys. A14 (1999) 4395-4456

Integrability of Supersymmetric Quantum Matrix Models in the Large-N Limit

Authors: C. -W. H. Lee, S. G. Rajeev

Abstract: Many physical systems like supersymmetric Yang-Mills theories are formulated as quantum matrix models. We discuss how to apply the Beth ansatz to exactly solve some supersymmetric quantum matrix models in the large-N limit. Toy models are constructed out of the one-dimensional Hubbard and t-J models as illustrations. Many physical systems like supersymmetric Yang-Mills theories are formulated as quantum matrix models. We discuss how to apply the Beth ansatz to exactly solve some supersymmetric quantum matrix models in the large-N limit. Toy models are constructed out of the one-dimensional Hubbard and t-J models as illustrations. △ Less

Submitted 19 June, 1998; v1 submitted 2 June, 1998; originally announced June 1998.

Comments: 11 pages, LaTeX2e; minor changes, citations added

Journal ref: Phys.Lett. B436 (1998) 91-96

A Lie Algebra for Closed Strings, Spin Chains and Gauge Theories

Authors: C. -W. H. Lee, S. G. Rajeev

Abstract: We consider quantum dynamical systems whose degrees of freedom are described by $N \times N$ matrices, in the planar limit $N \to \infty$. Examples are gauge theoires and the M(atrix)-theory of strings. States invariant under U(N) are `closed strings', modelled by traces of products of matrices. We have discovered that the U(N)-invariant opertors acting on both open and closed string states form… ▽ More We consider quantum dynamical systems whose degrees of freedom are described by $N \times N$ matrices, in the planar limit $N \to \infty$. Examples are gauge theoires and the M(atrix)-theory of strings. States invariant under U(N) are `closed strings', modelled by traces of products of matrices. We have discovered that the U(N)-invariant opertors acting on both open and closed string states form a remarkable new Lie algebra which we will call the heterix algebra. (The simplest special case, with one degree of freedom, is an extension of the Virasoro algebra by the infinite-dimensional general linear algebra.) Furthermore, these operators acting on closed string states only form a quotient algebra of the heterix algebra. We will call this quotient algebra the cyclix algebra. We express the Hamiltonian of some gauge field theories (like those with adjoint matter fields and dimensionally reduced pure QCD models) as elements of this Lie algebra. Finally, we apply this cyclix algebra to establish an isomorphism between certain planar matrix models and quantum spin chain systems. Thus we obtain some matrix models solvable in the planar limit; e.g., matrix models associated with the Ising model, the XYZ model, models satisfying the Dolan-Grady condition and the chiral Potts model. Thus our cyclix Lie algebra described the dynamical symmetries of quantum spin chain systems, large-N gauge field theories, and the M(atrix)-theory of strings. △ Less

Submitted 8 June, 1999; v1 submitted 30 May, 1998; originally announced June 1998.

Comments: 52 pages, 8 eps figures, LaTeX2.09; this is the published version

Journal ref: J.Math.Phys. 39 (1998) 5199-5230

Symmetry Algebras of Large-N Matrix Models for Open Strings

Authors: C. -W. H. Lee, S. G. Rajeev

Abstract: We have discovered that the gauge invariant observables of matrix models invariant under U($N$) form a Lie algebra, in the planar large-N limit. These models include Quantum Chromodynamics and the M(atrix)-Theory of strings. We study here the gauge invariant states corresponding to open strings (`mesons'). We find that the algebra is an extension of a remarkable new Lie algebra ${\cal V}_Λ$ by a… ▽ More We have discovered that the gauge invariant observables of matrix models invariant under U($N$) form a Lie algebra, in the planar large-N limit. These models include Quantum Chromodynamics and the M(atrix)-Theory of strings. We study here the gauge invariant states corresponding to open strings (`mesons'). We find that the algebra is an extension of a remarkable new Lie algebra ${\cal V}_Λ$ by a product of more well-known algebras such as $gl_{\infty}$ and the Cuntz algebra. ${\cal V}_Λ$ appears to be a generalization of the Lie algebra of vector fields on the circle to non-commutative geometry. We also use a representation of our Lie algebra to establish an isomorphism between certain matrix models (those that preserve `gluon number') and open quantum spin chains. Using known results on quantum spin chains, we are able to identify some exactly solvable matrix models. Finally, the Hamiltonian of a dimensionally reduced QCD model is expressed explicitly as an element of our Lie algebra. △ Less

Submitted 8 June, 1999; v1 submitted 9 December, 1997; originally announced December 1997.

Comments: 44 pages, 8 eps figures, 3 tables, LaTeX2.09; this is the published version

Journal ref: Nucl.Phys. B529 (1998) 656-688

Symmetries of Large N Matrix Models for Closed Strings

Authors: C. - W. H. Lee, S. G. Rajeev

Abstract: We obtain the symmetry algebra of multi-matrix models in the planar large N limit. We use this algebra to associate these matrix models with quantum spin chains. In particular, certain multi-matrix models are exactly solved by using known results of solvable spin chain systems. We obtain the symmetry algebra of multi-matrix models in the planar large N limit. We use this algebra to associate these matrix models with quantum spin chains. In particular, certain multi-matrix models are exactly solved by using known results of solvable spin chain systems. △ Less

Submitted 30 May, 1998; v1 submitted 7 November, 1997; originally announced November 1997.

Comments: 12 pages, 1 eps figure, RevTex, some minor typos in the publised version are corrected

Journal ref: Phys.Rev.Lett. 80 (1998) 2285-2288