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

arXiv:1102.4994 · Europhysics Letters (EPL)

On the thermalization of a Luttinger liquid after a sequence of sudden interaction quenches

Enrico Perfetto, Gianluca Stefanucci

Published Jun 22, 2011• 33 citations
arXivHTMLPDF

Abstract

We present a comprehensive analysis of the relaxation dynamics of a Luttinger liquid subject to a sequence of sudden interaction quenches. The critical exponent β governing the decay of the steady-state propagator is expressed as an explicit functional of the switching protocol. At long distances β depends only on the initial state while at short distances it is also history dependent. Continuous protocols of arbitrary complexity can be realized with infinitely long sequences. For quenches of finite duration we prove that there exists no protocol to bring the initial non-interacting system in the ground state of the Luttinger liquid, albeit thermalization occurs at short distances. The adiabatic theorem is then investigated with ramp switchings of increasing duration and several analytic results for both the propagator and the excitation energy are derived.

DOI
10.1209/0295-5075/95/10006

Related papers

Interaction quench in nonequilibrium Luttinger liquids

Stéphane Ngo Dinh, Dmitry Bagrets, A. D. Mirlin

We study the relaxation dynamics of a nonequilibrium Tomonaga-Luttinger model after a sudden interaction switch-on (``quench''), focusing on a double-step initial momentum distribution function. In the framework of the nonequilibrium bosonization, the results are obtained in terms of singular Fredholm determinants that are evaluated numerically and whose asymptotics are found analytically. While the quasiparticle weights decay exponentially with time after the quench, this is not a relaxation into a thermal state, in view of the integrability of the model. The steady-state distribution emerging at infinite times retains two edges which support Luttinger-liquid-like power-law singularities smeared by dephasing. The obtained critical exponents and the dephasing length are found to depend on the initial nonequilibrium state.

arXiv:1310.0735•Physical Review B•Dec 3, 2013•25 citations

Crossover from Adiabatic to Sudden Interaction Quench in a Luttinger Liquid

Balázs Dóra, Masudul Haque, Gergely Zaránd

Motivated by recent experiments on interacting cold atoms, we analyze interaction quenches in Luttinger liquids (LLs), where the interaction is ramped from zero to a finite value within a finite time. The fermionic single particle density matrix reveals several regions of spatial and temporal coordinates relative to the quench time, termed as Fermi liquid, sudden quench LL, adiabatic LL regime, and a LL regime with a time-dependent exponent. The various regimes can also be observed in the momentum distribution of the fermions, directly accessible through time of flight experiments. Most of our results apply to arbitrary quench protocols.

arXiv:1011.6655•Physical Review Letters•Apr 14, 2011•68 citations

Optimal protocols for quantum quenches of finite duration in the Luttinger model

Ádám Bácsi, Masudul Haque, Balázs Dóra

Reaching a target quantum state from an initial state within a finite temporal window is a challenging problem due to nonadiabaticity. We study the optimal protocol for switching on interactions to reach the ground state of a weakly interacting Luttinger liquid within a finite time $\ensuremath{\tau}$, starting from the noninteracting ground state. The protocol is optimized by minimizing the excess energy at the end of the quench, or by maximizing the overlap with the interacting ground state. We find that the optimal protocol is symmetric with respect to $\ensuremath{\tau}/2$, and can be expressed as a functional of the occupation numbers of the bosonic modes in the final state. For short quench durations, the optimal protocol exhibits fast oscillation and excites high-energy modes. In the limit of large $\ensuremath{\tau}$, minimizing energy requires a smooth protocol while maximizing overlap requires a linear quench protocol. In this limit, the minimal energy and maximal overlap are both universal functions of the system size and the duration of the protocol.

arXiv:1902.09320•Physical review. B./Physical review. B•Jun 6, 2019•4 citations

Time evolution during and after finite-time quantum quenches in Luttinger liquids

Piotr Chudziński, Dirk Schuricht

We consider finite-time quantum quenches in the interacting Tomonaga-Luttinger model, for example time-dependent changes of the nearest-neighbor interactions for spinless fermions. We use the exact solutions for specific protocols including the linear and cosine ramps (or, more generally, periodic pumping). We study the dynamics of the total and kinetic energy as well as the Green's functions during as well as after the quench. For the latter we find that the light-cone picture remains applicable; however, the propagating front is delayed as compared to the sudden quench. We extract the universal behavior of the Green's functions and in particular provide analytic, nonperturbative results for the delay applicable to quenches of short to moderate duration but arbitrary time dependency.

arXiv:1606.02576•Physical review. B./Physical review. B•Aug 15, 2016•14 citations

Out-of-equilibrium density dynamics of a spinful Luttinger liquid

Filippo Maria Gambetta, S. Porta

Using a Luttinger liquid theory we investigate the time evolution of the particle density of a one-dimensional spinful fermionic system with open boundaries and subject to a finite-duration quench of the inter-particle interaction. Taking into account also the turning on of an umklapp perturbation to the system Hamiltonian as a result of the quench, we study the possible formation of a Wigner molecule inside the system, focusing in particular on the sudden and adiabatic regimes. We show that the creation of this correlated state is essentially due to the propagation of "light-cone" perturbations through system which arise after both switching on and switching off the quenching protocol and that its behavior strongly depends on the quench duration.

arXiv:1703.04331•Il Nuovo Cimento C•Mar 13, 2017•0 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
We present a comprehensive analysis of the relaxation dynamics of a Luttinger liquid subject to a sequence of sudden interaction quenches. The critical exponent β governing the decay of the steady-state propagator is expressed as an explicit functional of the switching protocol. At long distances β depends only on the initial state while at short distances it is also history dependent. Continuous protocols of arbitrary complexity can be realized with infinitely long sequences. For quenches of finite duration we prove that there exists no protocol to bring the initial non-interacting system in the ground state of the Luttinger liquid, albeit thermalization occurs at short distances. The adiabatic theorem is then investigated with ramp switchings of increasing duration and several analytic results for both the propagator and the excitation energy are derived.
We study the relaxation dynamics of a nonequilibrium Tomonaga-Luttinger model after a sudden interaction switch-on (``quench''), focusing on a double-step initial momentum distribution function. In the framework of the nonequilibrium bosonization, the results are obtained in terms of singular Fredholm determinants that are evaluated numerically and whose asymptotics are found analytically. While the quasiparticle weights decay exponentially with time after the quench, this is not a relaxation into a thermal state, in view of the integrability of the model. The steady-state distribution emerging at infinite times retains two edges which support Luttinger-liquid-like power-law singularities smeared by dephasing. The obtained critical exponents and the dephasing length are found to depend on the initial nonequilibrium state.
Motivated by recent experiments on interacting cold atoms, we analyze interaction quenches in Luttinger liquids (LLs), where the interaction is ramped from zero to a finite value within a finite time. The fermionic single particle density matrix reveals several regions of spatial and temporal coordinates relative to the quench time, termed as Fermi liquid, sudden quench LL, adiabatic LL regime, and a LL regime with a time-dependent exponent. The various regimes can also be observed in the momentum distribution of the fermions, directly accessible through time of flight experiments. Most of our results apply to arbitrary quench protocols.
Reaching a target quantum state from an initial state within a finite temporal window is a challenging problem due to nonadiabaticity. We study the optimal protocol for switching on interactions to reach the ground state of a weakly interacting Luttinger liquid within a finite time $\ensuremath{\tau}$, starting from the noninteracting ground state. The protocol is optimized by minimizing the excess energy at the end of the quench, or by maximizing the overlap with the interacting ground state. We find that the optimal protocol is symmetric with respect to $\ensuremath{\tau}/2$, and can be expressed as a functional of the occupation numbers of the bosonic modes in the final state. For short quench durations, the optimal protocol exhibits fast oscillation and excites high-energy modes. In the limit of large $\ensuremath{\tau}$, minimizing energy requires a smooth protocol while maximizing overlap requires a linear quench protocol. In this limit, the minimal energy and maximal overlap are both universal functions of the system size and the duration of the protocol.
We consider finite-time quantum quenches in the interacting Tomonaga-Luttinger model, for example time-dependent changes of the nearest-neighbor interactions for spinless fermions. We use the exact solutions for specific protocols including the linear and cosine ramps (or, more generally, periodic pumping). We study the dynamics of the total and kinetic energy as well as the Green's functions during as well as after the quench. For the latter we find that the light-cone picture remains applicable; however, the propagating front is delayed as compared to the sudden quench. We extract the universal behavior of the Green's functions and in particular provide analytic, nonperturbative results for the delay applicable to quenches of short to moderate duration but arbitrary time dependency.
Using a Luttinger liquid theory we investigate the time evolution of the particle density of a one-dimensional spinful fermionic system with open boundaries and subject to a finite-duration quench of the inter-particle interaction. Taking into account also the turning on of an umklapp perturbation to the system Hamiltonian as a result of the quench, we study the possible formation of a Wigner molecule inside the system, focusing in particular on the sudden and adiabatic regimes. We show that the creation of this correlated state is essentially due to the propagation of "light-cone" perturbations through system which arise after both switching on and switching off the quenching protocol and that its behavior strongly depends on the quench duration.
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.