Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Chinese Physics Letters

Spin-charge Separation of the Luttinger Model after an Interaction Quench

Zhou Zong-Li, Guoshun Zhang, Ping Lou

Published Jun 1, 2010• 3 citations
Publisher

Abstract

A Luttinger model of spin-½ fermions is considered after the interaction is suddenly switched on at time t = 0. By means of the bosonization technique, we evaluate analytically the one-particle correlation functions in detail, mainly involving equal-time correlations and propagators. The critical exponent which governs the power-law behavior of equal-time correlations for this spinful non-equilibrium system is obtained. In comparison with the published results, the difference between critical exponents of correlations in spinful and spinless non-equilibrium systems is found and explained. Furthermore, it is found that the propagator exhibits different power-law behavior from other equal-time correlations in this non-equilibrium system.

DOI
10.1088/0256-307x/27/6/067305

Related papers

Time-Dependent Evolution of Two Coupled Luttinger Models of Spin-1/2 Fermions

Zhou Zong-Li, Ping Lou

Based on the field-theoretical bosonization we consider the spinful system consisting of two disconnected Luttinger liquids, which are coupled at time t = 0 through chiral density-density interactions. We show the well-known spin-charge separation in this 1D system by means of bosonization and Bogoliubov transformation. To evaluate analytically the one-particle equal-time correlation functions, Cazalilla's methods are extended to spin-charge sectors. It is found that in long time limit the behavior of correlations does not coincide with that of equilibrium equal-time correlations of two coupled spinful Luttinger liquids. In order to compare with experimental results, the improved exponent that governs the power-law behavior of equal-time correlations of the non-equilibrium system is obtained at the end of this work.

Communications in Theoretical Physics•Jun 1, 2009•2 citations

Density-Density Propagator of the Luttinger Model of Spin-Half Fermions after an Interaction Quench

Zong-Li Zhou, Xinghong Yuan, MU Shu-hui +3 more

Motivated by recent research achievement of quantum interacting systems in non-equilibrium, we consider a Luttinger model with a suddenly switched-on interaction proposed by Cazalilla [M.A. Cazalilla, Phys. Rev. Lett. 97 (2006) 156403 ]. In order to compare with real systems, we extend Cazalilla's scenario to the spinful system. To find the influence of initial states on the time evolution of some non-equilibrium systems, we mainly focus on the density-density propagator. By comparison and analysis, we discover the different behavior of this non-equilibrium system. Further, it is found that the propagator saves strong memory of initial state, and the effects of right-left interaction cancel out in total density-density propagator.

Communications in Theoretical Physics•Aug 1, 2012•0 citations

Effect of Suddenly Turning on Interactions in the Luttinger Model

Miguel A. Cazalilla

The evolution of correlations in the exactly solvable Luttinger model (a model of interacting fermions in one dimension) after a suddenly switched-on interaction is analytically studied. When the model is defined on a finite-size ring, zero-temperature correlations are periodic in time. However, in the thermodynamic limit, the system relaxes algebraically towards a stationary state which is well described, at least for some simple correlation functions, by the generalized Gibbs ensemble recently introduced by Rigol et al. (cond-mat/0604476). The critical exponent that characterizes the decay of the one-particle correlation function is different from the known equilibrium exponents. Experiments for which these results can be relevant are also discussed.

arXiv:cond-mat/0606236•Physical Review Letters•Oct 12, 2006•523 citations

Quantum quench dynamics of the Luttinger model

Anı́bal Iucci, Miguel A. Cazalilla

The dynamics of the Luttinger model after a quantum quench is studied. We compute in detail one- and two-point correlation functions for two types of quenches: from a noninteracting to an interacting Luttinger model and vice versa. In the former case, the noninteracting Fermi gas features in the momentum distribution and other correlation functions are destroyed as time evolves. In the infinite-time limit, equal-time correlations are power laws but the critical exponents are found to differ from their equilibrium values. In all cases, we find that these correlations are well described by a generalized Gibbs ensemble [M. Rigol, V. Dunjko, V. Yurovsky, and M. Olshanii, Phys. Rev. Lett. 98, 050405 (2007)], which assigns a momentum-dependent temperature to each eigenmode.

arXiv:0903.1205•Physical Review A•Dec 8, 2009•299 citations

Quench dynamics of the Tomonaga–Luttinger model with momentum-dependent interaction

J Rentrop, Dirk Schuricht, V. Meden

We study the relaxation dynamics of the one-dimensional Tomonaga–Luttinger model after an interaction quench, paying particular attention to the momentum dependence of the two-particle interaction. Several potentials of different analytical forms are investigated that all lead to universal Luttinger liquid (LL) physics in equilibrium. The steady-state fermionic momentum distribution shows universal behavior in the sense of the LL phenomenology. For generic regular potentials, the large time decay of the momentum distribution function toward the steady-state value is characterized by a power law with a universal exponent that depends only on the potential at zero momentum transfer. The commonly employed ad hoc procedure fails to give this exponent. In addition to quenches from zero to positive interactions, we also consider the abrupt changes in the interaction between two arbitrary values. Additionally, we discuss the appearance of a factor of two between the steady-state momentum distribution function and that obtained in equilibrium at equal two-particle interaction.

arXiv:1203.0932•New Journal of Physics•Jul 3, 2012•46 citations

Quench dynamics of the Tomonaga-Luttinger model with momentum-dependent interaction

Rentrop, J., Dirk Schuricht, V. Meden

We study the relaxation dynamics of the one-dimensional Tomonaga–Luttinger model after an interaction quench, paying particular attention to the momentum dependence of the two-particle interaction. Several potentials of different analytical forms are investigated that all lead to universal Luttinger liquid (LL) physics in equilibrium. The steady-state fermionic momentum distribution shows universal behavior in the sense of the LL phenomenology. For generic regular potentials, the large time decay of the momentum distribution function toward the steady-state value is characterized by a power law with a universal exponent that depends only on the potential at zero momentum transfer. The commonly employed ad hoc procedure fails to give this exponent. In addition to quenches from zero to positive interactions, we also consider the abrupt changes in the interaction between two arbitrary values. Additionally, we discuss the appearance of a factor of two between the steady-state momentum distribution function and that obtained in equilibrium at equal two-particle interaction.

•Jan 1, 2012•51 citations
A Luttinger model of spin-½ fermions is considered after the interaction is suddenly switched on at time t = 0. By means of the bosonization technique, we evaluate analytically the one-particle correlation functions in detail, mainly involving equal-time correlations and propagators. The critical exponent which governs the power-law behavior of equal-time correlations for this spinful non-equilibrium system is obtained. In comparison with the published results, the difference between critical exponents of correlations in spinful and spinless non-equilibrium systems is found and explained. Furthermore, it is found that the propagator exhibits different power-law behavior from other equal-time correlations in this non-equilibrium system.
Based on the field-theoretical bosonization we consider the spinful system consisting of two disconnected Luttinger liquids, which are coupled at time t = 0 through chiral density-density interactions. We show the well-known spin-charge separation in this 1D system by means of bosonization and Bogoliubov transformation. To evaluate analytically the one-particle equal-time correlation functions, Cazalilla's methods are extended to spin-charge sectors. It is found that in long time limit the behavior of correlations does not coincide with that of equilibrium equal-time correlations of two coupled spinful Luttinger liquids. In order to compare with experimental results, the improved exponent that governs the power-law behavior of equal-time correlations of the non-equilibrium system is obtained at the end of this work.
Motivated by recent research achievement of quantum interacting systems in non-equilibrium, we consider a Luttinger model with a suddenly switched-on interaction proposed by Cazalilla [M.A. Cazalilla, Phys. Rev. Lett. 97 (2006) 156403 ]. In order to compare with real systems, we extend Cazalilla's scenario to the spinful system. To find the influence of initial states on the time evolution of some non-equilibrium systems, we mainly focus on the density-density propagator. By comparison and analysis, we discover the different behavior of this non-equilibrium system. Further, it is found that the propagator saves strong memory of initial state, and the effects of right-left interaction cancel out in total density-density propagator.
The evolution of correlations in the exactly solvable Luttinger model (a model of interacting fermions in one dimension) after a suddenly switched-on interaction is analytically studied. When the model is defined on a finite-size ring, zero-temperature correlations are periodic in time. However, in the thermodynamic limit, the system relaxes algebraically towards a stationary state which is well described, at least for some simple correlation functions, by the generalized Gibbs ensemble recently introduced by Rigol et al. (cond-mat/0604476). The critical exponent that characterizes the decay of the one-particle correlation function is different from the known equilibrium exponents. Experiments for which these results can be relevant are also discussed.
The dynamics of the Luttinger model after a quantum quench is studied. We compute in detail one- and two-point correlation functions for two types of quenches: from a noninteracting to an interacting Luttinger model and vice versa. In the former case, the noninteracting Fermi gas features in the momentum distribution and other correlation functions are destroyed as time evolves. In the infinite-time limit, equal-time correlations are power laws but the critical exponents are found to differ from their equilibrium values. In all cases, we find that these correlations are well described by a generalized Gibbs ensemble [M. Rigol, V. Dunjko, V. Yurovsky, and M. Olshanii, Phys. Rev. Lett. 98, 050405 (2007)], which assigns a momentum-dependent temperature to each eigenmode.
We study the relaxation dynamics of the one-dimensional Tomonaga–Luttinger model after an interaction quench, paying particular attention to the momentum dependence of the two-particle interaction. Several potentials of different analytical forms are investigated that all lead to universal Luttinger liquid (LL) physics in equilibrium. The steady-state fermionic momentum distribution shows universal behavior in the sense of the LL phenomenology. For generic regular potentials, the large time decay of the momentum distribution function toward the steady-state value is characterized by a power law with a universal exponent that depends only on the potential at zero momentum transfer. The commonly employed ad hoc procedure fails to give this exponent. In addition to quenches from zero to positive interactions, we also consider the abrupt changes in the interaction between two arbitrary values. Additionally, we discuss the appearance of a factor of two between the steady-state momentum distribution function and that obtained in equilibrium at equal two-particle interaction.
We study the relaxation dynamics of the one-dimensional Tomonaga–Luttinger model after an interaction quench, paying particular attention to the momentum dependence of the two-particle interaction. Several potentials of different analytical forms are investigated that all lead to universal Luttinger liquid (LL) physics in equilibrium. The steady-state fermionic momentum distribution shows universal behavior in the sense of the LL phenomenology. For generic regular potentials, the large time decay of the momentum distribution function toward the steady-state value is characterized by a power law with a universal exponent that depends only on the potential at zero momentum transfer. The commonly employed ad hoc procedure fails to give this exponent. In addition to quenches from zero to positive interactions, we also consider the abrupt changes in the interaction between two arbitrary values. Additionally, we discuss the appearance of a factor of two between the steady-state momentum distribution function and that obtained in equilibrium at equal two-particle interaction.