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:1905.02678 · Physical review. B./Physical review. B

Finite-time quantum quenches in the XXZ Heisenberg chain

Benedikt Schoenauer, Dirk Schuricht

Published Sep 12, 2019• 3 citations
arXivHTMLPDF

Abstract

We study the time evolution of the two-point correlation functions in the XXZ Heisenberg chain after a finite-time quantum quench in the anisotropy. We compare results from numerical simulations to ones obtained in the Luttinger model and find good agreement. We analyze the spreading of the correlations and the associated light-cone features. We observe a delay in the appearance of the light cone as compared to the sudden-quench setup, and link this delay to the properties of the quench protocol.

DOI
10.1103/physrevb.100.115418

Related papers

Relaxation after quantum quenches in the spin- 1 2 Heisenberg XXZ chain

Maurizio Fagotti, Mario Collura, Fabian H. L. Eßler +1 more

We consider the time evolution after quantum quenches in the spin-$\frac{1}{2}$ Heisenberg XXZ quantum spin chain with Ising-type anisotropy. The time evolution of short-distance spin-spin correlation functions is studied by numerical tensor network techniques for a variety of initial states, including N\'eel and Majumdar-Ghosh states and the ground state of the XXZ chain at large values of the anisotropy. The various correlators appear to approach stationary values, which are found to be in good agreement with the results of exact calculations of stationary expectation values in appropriate generalized Gibbs ensembles. In particular, our analysis shows how symmetries of the post-quench Hamiltonian that are broken by particular initial states are restored at late times.

arXiv:1311.5216•Physical Review B•Mar 3, 2014•210 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

Quantum quench within the gapless phase of the spin−12 Heisenberg XXZ spin chain

Mario Collura, Pasquale Calabrese, Fabian H. L. Eßler

We consider an interaction quench in the critical $\text{spin}\ensuremath{-}\frac{1}{2}$ Heisenberg XXZ chain. We numerically compute the time evolution of the two-point correlation functions of spin operators in the thermodynamic limit and compare the results to predictions obtained in the framework of the Luttinger liquid approximation. We find that the transverse correlation function $\ensuremath{\langle}{S}_{j}^{x}{S}_{j+\ensuremath{\ell}}^{x}\ensuremath{\rangle}$ agrees with the Luttinger model prediction to a surprising level of accuracy. The agreement for the longitudinal two-point function $\ensuremath{\langle}{S}_{j}^{z}{S}_{j+\ensuremath{\ell}}^{z}\ensuremath{\rangle}$ is found to be much poorer. We speculate that this difference between transverse and longitudinal correlations has its origin in the locality properties of the respective spin operator with respect to the underlying fermionic modes.

arXiv:1507.03492•Physical Review B•Sep 17, 2015•69 citations

Linear quantum quench in the Heisenberg XXZ chain: Time-dependent Luttinger-model description of a lattice system

Frank Pollmann, Masudul Haque, Balázs Dóra

We study variable-rate linear quenches in the anisotropic Heisenberg (XXZ) chain, starting at the XX point. This is equivalent to switching on a nearest-neighbor interaction for hard-core bosons or an interaction quench for free fermions. The physical observables we investigate are the energy pumped into the system during the quench, the spin-flip correlation function, and the bipartite fluctuations of the $z$ component of the spin in a box. We find excellent agreement between exact numerics (infinite system time-evolving block decimation) and analytical results from bosonization, as a function of the quench time, spatial coordinate, and interaction strength. This provides a stringent and much-needed test of Luttinger liquid theory in a nonequilibrium situation.

arXiv:1211.1195•Physical Review B•Jan 31, 2013•39 citations

“Light-Cone” Dynamics After Quantum Quenches in Spin Chains

Lars Bonnes, Fabian H. L. Eßler, Andreas Martin Läuchli

Signal propagation in the nonequilibrium evolution after quantum quenches has recently attracted much experimental and theoretical interest. A key question arising in this context is what principles, and which of the properties of the quench, determine the characteristic propagation velocity. Here we investigate such issues for a class of quench protocols in one of the central paradigms of interacting many-particle quantum systems, the spin-1/2 Heisenberg XXZ chain. We consider quenches from a variety of initial thermal density matrices to the same final Hamiltonian using matrix product state methods. The spreading velocities are observed to vary substantially with the initial density matrix. However, we achieve a striking data collapse when the spreading velocity is considered to be a function of the excess energy. Using the fact that the XXZ chain is integrable, we present an explanation of the observed velocities in terms of "excitations" in an appropriately defined generalized Gibbs ensemble.

arXiv:1404.4062•Physical Review Letters•Oct 30, 2014•244 citations

Quantum quench dynamics of the Coulomb Luttinger model

Nicolás Nessi, Anı́bal Iucci

We study the nonequilibrium dynamics of the Luttinger model after suddenly turning on and off the bare Coulomb interaction between the fermions. We analyze several correlation functions such as the one particle density matrix and vertex correlations, its finite time dynamics, and the stationary state limit. Correlations exhibit a nonlinear light-cone effect: The spreading of the initial signal accelerates as a consequence of the quantum nature of the excitations, whose peculiar dispersion of plasmonic type in one dimension (1D) gives rise to a logarithmic divergence in the group velocity at $q=0$. In addition, we show that both the static and dynamic stationary state correlations can be reproduced with a simple generalized Gibbs ensemble despite the long-range character of the interactions which precludes the application of the Lieb-Robinson bounds. We propose a suitable experimental setup in which these effect can be observed based on ultracold ions loaded on linear traps.

arXiv:1301.3809•Physical Review B•Feb 28, 2013•21 citations
We study the time evolution of the two-point correlation functions in the XXZ Heisenberg chain after a finite-time quantum quench in the anisotropy. We compare results from numerical simulations to ones obtained in the Luttinger model and find good agreement. We analyze the spreading of the correlations and the associated light-cone features. We observe a delay in the appearance of the light cone as compared to the sudden-quench setup, and link this delay to the properties of the quench protocol.
We consider the time evolution after quantum quenches in the spin-12\frac{1}{2}21​ Heisenberg XXZ quantum spin chain with Ising-type anisotropy. The time evolution of short-distance spin-spin correlation functions is studied by numerical tensor network techniques for a variety of initial states, including N\'eel and Majumdar-Ghosh states and the ground state of the XXZ chain at large values of the anisotropy. The various correlators appear to approach stationary values, which are found to be in good agreement with the results of exact calculations of stationary expectation values in appropriate generalized Gibbs ensembles. In particular, our analysis shows how symmetries of the post-quench Hamiltonian that are broken by particular initial states are restored at late times.
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.
We consider an interaction quench in the critical $\text{spin}\ensuremath{-}\frac{1}{2}$ Heisenberg XXZ chain. We numerically compute the time evolution of the two-point correlation functions of spin operators in the thermodynamic limit and compare the results to predictions obtained in the framework of the Luttinger liquid approximation. We find that the transverse correlation function $\ensuremath{\langle}{S}_{j}^{x}{S}_{j+\ensuremath{\ell}}^{x}\ensuremath{\rangle}$ agrees with the Luttinger model prediction to a surprising level of accuracy. The agreement for the longitudinal two-point function $\ensuremath{\langle}{S}_{j}^{z}{S}_{j+\ensuremath{\ell}}^{z}\ensuremath{\rangle}$ is found to be much poorer. We speculate that this difference between transverse and longitudinal correlations has its origin in the locality properties of the respective spin operator with respect to the underlying fermionic modes.
We study variable-rate linear quenches in the anisotropic Heisenberg (XXZ) chain, starting at the XX point. This is equivalent to switching on a nearest-neighbor interaction for hard-core bosons or an interaction quench for free fermions. The physical observables we investigate are the energy pumped into the system during the quench, the spin-flip correlation function, and the bipartite fluctuations of the zzz component of the spin in a box. We find excellent agreement between exact numerics (infinite system time-evolving block decimation) and analytical results from bosonization, as a function of the quench time, spatial coordinate, and interaction strength. This provides a stringent and much-needed test of Luttinger liquid theory in a nonequilibrium situation.
Signal propagation in the nonequilibrium evolution after quantum quenches has recently attracted much experimental and theoretical interest. A key question arising in this context is what principles, and which of the properties of the quench, determine the characteristic propagation velocity. Here we investigate such issues for a class of quench protocols in one of the central paradigms of interacting many-particle quantum systems, the spin-1/2 Heisenberg XXZ chain. We consider quenches from a variety of initial thermal density matrices to the same final Hamiltonian using matrix product state methods. The spreading velocities are observed to vary substantially with the initial density matrix. However, we achieve a striking data collapse when the spreading velocity is considered to be a function of the excess energy. Using the fact that the XXZ chain is integrable, we present an explanation of the observed velocities in terms of "excitations" in an appropriately defined generalized Gibbs ensemble.
We study the nonequilibrium dynamics of the Luttinger model after suddenly turning on and off the bare Coulomb interaction between the fermions. We analyze several correlation functions such as the one particle density matrix and vertex correlations, its finite time dynamics, and the stationary state limit. Correlations exhibit a nonlinear light-cone effect: The spreading of the initial signal accelerates as a consequence of the quantum nature of the excitations, whose peculiar dispersion of plasmonic type in one dimension (1D) gives rise to a logarithmic divergence in the group velocity at q=0q=0q=0. In addition, we show that both the static and dynamic stationary state correlations can be reproduced with a simple generalized Gibbs ensemble despite the long-range character of the interactions which precludes the application of the Lieb-Robinson bounds. We propose a suitable experimental setup in which these effect can be observed based on ultracold ions loaded on linear traps.