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:1205.2967

Quantum quenches in one-dimensional gapless systems: Does bosonization work?

Emanuele Coira, Federico Becca, Alberto Parola

Published May 14, 2012• 0 citations
arXivHTMLPDF

Abstract

We present a comparison between the bosonization results for quantum quenches and exact diagonalizations in microscopic models of interacting spinless fermions in a one-dimensional lattice. We show that important features are missed by the bosonization technique, which predicts the persistence of long-wavelength critical properties in the long-time evolution. Instead, numerical analysis provides puzzling evidences: while the momentum distribution appears to be consistent with the presence of a singularity at $k_F$, density-density correlations at small momenta clearly display a thermal-like behavior, namely ${\bar{N}}_q \simeq {\rm const}$ (where the overbar indicates the long-time average). This feature at small momenta is preserved in presence of an interaction term that breaks integrability, together with a rounding of the singularities at finite $q$'s, showing that the bosonization approach is not able to represent the time evolution of generic one-dimensional models after a quantum quench.

DOI
10.48550/arxiv.1205.2967

Related papers

Quantum quenches and thermalization in one-dimensional fermionic systems

Marcos Rigol

We study the dynamics and thermalization of strongly correlated fermions in finite one-dimensional lattices after a quantum quench. Our calculations are performed using exact diagonalization. We focus on one- and two-body observables such as the momentum distribution function $[n(k)]$ and the density-density structure factor $[N(k)]$, respectively, and study the effects of approaching an integrable point. We show that while the relaxation dynamics and thermalization of $N(k)$ for fermions is very similar to the one of hardcore bosons, the behavior of $n(k)$ is distinctively different. The latter observable exhibits a slower relaxation dynamics in fermionic systems. We identify the origin of this behavior, which is related to the off-diagonal matrix elements of $n(k)$ in the basis of the eigenstates of the Hamiltonian. More generally, we find that thermalization occurs far away from integrability and that it breaks down as one approaches the integrable point.

arXiv:0908.3188•Physical Review A•Nov 9, 2009•243 citations

Small quenches and thermalization

Dante Marvin Kennes, Joel C. Pommerening, Jan Diekmann +2 more

We study the expectation values of observables and correlation functions at long times after a global quantum quench. Our focus is on metallic (``gapless'') fermionic many-body models and small quenches. The system is prepared in an eigenstate of an initial Hamiltonian, and the time evolution is performed with a final Hamiltonian which differs from the initial one in the value of one global parameter. We first derive general relations between time-averaged expectation values of observables as well as correlation functions and those obtained in an eigenstate of the final Hamiltonian. Our results are valid to linear and quadratic order in the quench parameter $g$ and generalize prior insights in several essential ways. This allows us to develop a phenomenology for the thermalization of local quantities up to a given order in $g$. Our phenomenology is put to a test in several case studies of one-dimensional models representative of four distinct classes of Hamiltonians: quadratic ones, effectively quadratic ones, those characterized by an extensive set of (quasi-) local integrals of motion, and those for which no such set is known (and believed to be nonexistent). We show that for each of these models, all observables and correlation functions thermalize to linear order in $g$. The more local a given quantity, the longer the linear behavior prevails when increasing $g$. Typical local correlation functions and observables for which the term $\mathcal{O}(g)$ vanishes thermalize even to order ${g}^{2}$. Our results show that lowest-order thermalization of local observables is an ubiquitous phenomenon even in models with extensive sets of integrals of motion.

arXiv:1610.03284•Physical review. B./Physical review. B•Jan 26, 2017•3 citations

Small quenches and (pre-)thermalization

Dante Marvin Kennes, Joel C. Pommerening, Jan Diekmann +2 more

We study the expectation values of observables and correlation functions at long times after a global quantum quench. Our focus is on metallic (`gapless') fermionic many-body models and small quenches. The system is prepared in an eigenstate of an initial Hamiltonian, and the time evolution is performed with a final Hamiltonian which differs from the initial one in the value of one global parameter. We first derive general relations between time-averaged expectation values of observables as well as correlation functions and those obtained in an eigenstate of the final Hamiltonian. Our results are valid to linear and quadratic order in the quench parameter g and generalize prior insights in several essential ways. This allows us to develop a phenomenology for the thermalization of local quantities up to a given order in g. Our phenomenology is put to a test in several case studies of one-dimensional models representative of four distinct classes of Hamiltonians: quadratic ones, effectively quadratic ones, those characterized by an extensive set of (quasi-) local integrals of motion, and those for which no such set is known (and believed to be nonexistent). We show that for each of these models, all observables and correlation functions thermalize to linear order in g. The more local a given quantity, the longer the linear behavior prevails when increasing g. Typical local correlation functions and observables for which the term O(g) vanishes thermalize even to order g^2. Our results show that lowest order thermalization of local observables is an ubiquitous phenomenon even in models with extensive sets of integrals of motion.

•Oct 11, 2016•0 citations

One-dimensional fermionic systems after interaction quenches and their description by bosonic field theories

Simone A Hamerla, Götz Silvester Uhrig

We study the time evolution of two fermionic one-dimensional models (spinless fermions with nearest-neighbor repulsion and the Hubbard model) exposed to an interaction quench for short and moderate times. The method used to calculate the time dependence is a semi-numerical approach based on the Heisenberg equation of motion. We compare the results of this approach with the results obtained by bosonization implying power law behavior. Indeed, we find that power laws describe our results well, but our results raise the issue of which exponents occur. For spinless fermions, it seems that the Tomonaga–Luttinger parameters work well, which also describe the equilibrium low-energy physics. But for the Hubbard model this is not the case. Instead, we find that exponents from the bosonization around the initial state work well. Finally, we discuss what can be expected for the long-time behavior.

arXiv:1207.2006•New Journal of Physics•Jul 3, 2013•19 citations

Finite-size effects in global quantum quenches: Examples from free bosons in an harmonic trap and the one-dimensional Bose-Hubbard model

Guillaume Roux

We investigate finite-size effects in quantum quenches on the basis of simple energetic arguments. Distinguishing between the low-energy part of the excitation spectrum, below a microscopic energy scale, and the high-energy regime enables one to define a crossover number of particles that is shown to diverge in the small quench limit. Another crossover number is proposed based on the fidelity between the initial and final ground states. Both criteria can be computed using ground-state techniques that work for systems larger than full-spectrum diagonalization. As examples, two models are studied: one with free bosons in an harmonic trap whose frequency is quenched and the one-dimensional Bose-Hubbard model that is known to be nonintegrable and for which recent studies have uncovered remarkable nonequilibrium behaviors. The diagonal weights of the time-averaged density matrix are computed, and observables obtained from this diagonal ensemble are compared with the ones from statistical ensembles. It is argued that the ``thermalized'' regime of the Bose-Hubbard model, previously observed in the small quench regime, experiences strong finite-size effects that make a thorough comparison with statistical ensembles difficult. In addition, we show that the nonthermalized regime, emerging on finite-size systems and for large interaction quenches, is not related to the existence of an equilibrium quantum critical point but to the high-energy structure of the energy spectrum in the atomic limit. Its features are reminiscent of the quench from the noninteracting limit to the atomic limit.

arXiv:0909.4620•Physical Review A•May 10, 2010•97 citations

One-particle entanglement for one-dimensional spinless fermions after an interaction quantum quench

Matthias Thamm, Harini Radhakrishnan, Hatem Barghathi +2 more

Particle entanglement provides information on quantum correlations in systems of indistinguishable particles. Here, we study the one-particle entanglement entropy for an integrable model of spinless, interacting fermions both at equilibrium and after an interaction quantum quench. Using both large-scale exact diagonalization and time-dependent density matrix renormalization group calculations, we numerically compute the one-body reduced density matrix for the $J\ensuremath{-}V$ model, as well as its postquench dynamics. We include an analysis of the fermionic momentum distribution, showcasing its time evolution after a quantum quench. Our numerical results, extrapolated to the thermodynamic limit, can be compared with field theoretic bosonization in the Tomonaga-Luttinger liquid regime. Excellent agreement is obtained using an interaction cutoff that can be determined uniquely in the ground state.

arXiv:2206.11301•Physical review. B./Physical review. B•Oct 18, 2022•6 citations
We present a comparison between the bosonization results for quantum quenches and exact diagonalizations in microscopic models of interacting spinless fermions in a one-dimensional lattice. We show that important features are missed by the bosonization technique, which predicts the persistence of long-wavelength critical properties in the long-time evolution. Instead, numerical analysis provides puzzling evidences: while the momentum distribution appears to be consistent with the presence of a singularity at kFk_FkF​, density-density correlations at small momenta clearly display a thermal-like behavior, namely Nˉq≃const{\bar{N}}_q \simeq {\rm const}Nˉq​≃const (where the overbar indicates the long-time average). This feature at small momenta is preserved in presence of an interaction term that breaks integrability, together with a rounding of the singularities at finite qqq's, showing that the bosonization approach is not able to represent the time evolution of generic one-dimensional models after a quantum quench.
We study the dynamics and thermalization of strongly correlated fermions in finite one-dimensional lattices after a quantum quench. Our calculations are performed using exact diagonalization. We focus on one- and two-body observables such as the momentum distribution function [n(k)][n(k)][n(k)] and the density-density structure factor [N(k)][N(k)][N(k)], respectively, and study the effects of approaching an integrable point. We show that while the relaxation dynamics and thermalization of N(k)N(k)N(k) for fermions is very similar to the one of hardcore bosons, the behavior of n(k)n(k)n(k) is distinctively different. The latter observable exhibits a slower relaxation dynamics in fermionic systems. We identify the origin of this behavior, which is related to the off-diagonal matrix elements of n(k)n(k)n(k) in the basis of the eigenstates of the Hamiltonian. More generally, we find that thermalization occurs far away from integrability and that it breaks down as one approaches the integrable point.
We study the expectation values of observables and correlation functions at long times after a global quantum quench. Our focus is on metallic (``gapless'') fermionic many-body models and small quenches. The system is prepared in an eigenstate of an initial Hamiltonian, and the time evolution is performed with a final Hamiltonian which differs from the initial one in the value of one global parameter. We first derive general relations between time-averaged expectation values of observables as well as correlation functions and those obtained in an eigenstate of the final Hamiltonian. Our results are valid to linear and quadratic order in the quench parameter ggg and generalize prior insights in several essential ways. This allows us to develop a phenomenology for the thermalization of local quantities up to a given order in ggg. Our phenomenology is put to a test in several case studies of one-dimensional models representative of four distinct classes of Hamiltonians: quadratic ones, effectively quadratic ones, those characterized by an extensive set of (quasi-) local integrals of motion, and those for which no such set is known (and believed to be nonexistent). We show that for each of these models, all observables and correlation functions thermalize to linear order in ggg. The more local a given quantity, the longer the linear behavior prevails when increasing ggg. Typical local correlation functions and observables for which the term O(g)\mathcal{O}(g)O(g) vanishes thermalize even to order g2{g}^{2}g2. Our results show that lowest-order thermalization of local observables is an ubiquitous phenomenon even in models with extensive sets of integrals of motion.
We study the expectation values of observables and correlation functions at long times after a global quantum quench. Our focus is on metallic (`gapless') fermionic many-body models and small quenches. The system is prepared in an eigenstate of an initial Hamiltonian, and the time evolution is performed with a final Hamiltonian which differs from the initial one in the value of one global parameter. We first derive general relations between time-averaged expectation values of observables as well as correlation functions and those obtained in an eigenstate of the final Hamiltonian. Our results are valid to linear and quadratic order in the quench parameter g and generalize prior insights in several essential ways. This allows us to develop a phenomenology for the thermalization of local quantities up to a given order in g. Our phenomenology is put to a test in several case studies of one-dimensional models representative of four distinct classes of Hamiltonians: quadratic ones, effectively quadratic ones, those characterized by an extensive set of (quasi-) local integrals of motion, and those for which no such set is known (and believed to be nonexistent). We show that for each of these models, all observables and correlation functions thermalize to linear order in g. The more local a given quantity, the longer the linear behavior prevails when increasing g. Typical local correlation functions and observables for which the term O(g) vanishes thermalize even to order g^2. Our results show that lowest order thermalization of local observables is an ubiquitous phenomenon even in models with extensive sets of integrals of motion.
We study the time evolution of two fermionic one-dimensional models (spinless fermions with nearest-neighbor repulsion and the Hubbard model) exposed to an interaction quench for short and moderate times. The method used to calculate the time dependence is a semi-numerical approach based on the Heisenberg equation of motion. We compare the results of this approach with the results obtained by bosonization implying power law behavior. Indeed, we find that power laws describe our results well, but our results raise the issue of which exponents occur. For spinless fermions, it seems that the Tomonaga–Luttinger parameters work well, which also describe the equilibrium low-energy physics. But for the Hubbard model this is not the case. Instead, we find that exponents from the bosonization around the initial state work well. Finally, we discuss what can be expected for the long-time behavior.
We investigate finite-size effects in quantum quenches on the basis of simple energetic arguments. Distinguishing between the low-energy part of the excitation spectrum, below a microscopic energy scale, and the high-energy regime enables one to define a crossover number of particles that is shown to diverge in the small quench limit. Another crossover number is proposed based on the fidelity between the initial and final ground states. Both criteria can be computed using ground-state techniques that work for systems larger than full-spectrum diagonalization. As examples, two models are studied: one with free bosons in an harmonic trap whose frequency is quenched and the one-dimensional Bose-Hubbard model that is known to be nonintegrable and for which recent studies have uncovered remarkable nonequilibrium behaviors. The diagonal weights of the time-averaged density matrix are computed, and observables obtained from this diagonal ensemble are compared with the ones from statistical ensembles. It is argued that the ``thermalized'' regime of the Bose-Hubbard model, previously observed in the small quench regime, experiences strong finite-size effects that make a thorough comparison with statistical ensembles difficult. In addition, we show that the nonthermalized regime, emerging on finite-size systems and for large interaction quenches, is not related to the existence of an equilibrium quantum critical point but to the high-energy structure of the energy spectrum in the atomic limit. Its features are reminiscent of the quench from the noninteracting limit to the atomic limit.
Particle entanglement provides information on quantum correlations in systems of indistinguishable particles. Here, we study the one-particle entanglement entropy for an integrable model of spinless, interacting fermions both at equilibrium and after an interaction quantum quench. Using both large-scale exact diagonalization and time-dependent density matrix renormalization group calculations, we numerically compute the one-body reduced density matrix for the $J\ensuremath{-}V$ model, as well as its postquench dynamics. We include an analysis of the fermionic momentum distribution, showcasing its time evolution after a quantum quench. Our numerical results, extrapolated to the thermodynamic limit, can be compared with field theoretic bosonization in the Tomonaga-Luttinger liquid regime. Excellent agreement is obtained using an interaction cutoff that can be determined uniquely in the ground state.