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:1303.4103 · Physical Review Letters

Quantum Quenches and Work Distributions in Ultralow-Density Systems

Yulia E. Shchadilova, Pedro Ribeiro, Masudul Haque

Published Feb 19, 2014• 30 citations
arXivHTMLPDF

Abstract

We present results on quantum quenches in lattice systems with a fixed number of particles in a much larger number of sites. Both local and global quenches in this limit generically have power-law work distributions ("edge singularities"). We show that this regime allows for large edge singularity exponents beyond that allowed by the constraints of the usual thermodynamic limit. This large-exponent singularity has observable consequences in the time evolution, leading to a distinct intermediate power-law regime in time. We demonstrate these results first using local quantum quenches in a low-density Kondo-like system, and additionally through global and local quenches in Bose-Hubbard, Aubry-Andre, and hard-core boson systems at low densities.

DOI
10.1103/physrevlett.112.070601

Related papers

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

Singular dynamics and emergence of nonlocality in long-range quantum models

Luca Lepori, Andrea Trombettoni, Davide Vodola

Abstract We discuss how nonlocality originates in long-range quantum systems and how it affects their dynamics at and out of equilibrium. We focus in particular on the Kitaev chains with long-range pairings and on the quantum Ising chain with long-range antiferromagnetic coupling (both having a power-law decay with exponent α ). By studying the dynamic correlation functions, we find that for every finite α two different behaviours can be identified, one typical of short-range systems and the other connected with locality violation. The latter behaviour is shown related also with the known power-law decay tails previously observed in the static correlation functions, and originated by modes—having in general energies far from the minima of the spectrum—where particular singularities develop as a consequence of the long-rangedness of the system. We refer to these modes as to ‘singular’ modes, and as to ‘singular dynamics’ to their dynamics. For the Kitaev model they are manifest, at finite α , in derivatives of the quasiparticle energy, the order of the derivatives at which the singularity occurs is increasing with α . The features of the singular modes and their physical consequences are clarified by studying an effective theory for them and by a critical comparison of the results from this theory with the lattice ones. Moreover, a numerical study of the effects of the singular modes on the time evolution after various types of global quenches is performed. We finally present and discuss the presence of singular modes and their consequences in interacting long-range systems by investigating in the long-range Ising quantum chain, both in the deep paramagnetic regime and at criticality, where they also play a central role for the breakdown of conformal invariance.

arXiv:1607.05358•Journal of Statistical Mechanics Theory and Experiment•Mar 1, 2017•45 citations

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

Emanuele Coira, Federico Becca, Alberto Parola

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.

arXiv:1205.2967•May 14, 2012•0 citations

Quantum work of an optical lattice

Colin Rylands, Natan Andrei

A classic example of a quantum quench concerns the release of an interacting Bose gas from an optical lattice. The local properties of quenches such as this have been extensively studied; however, the global properties of these nonequilibrium quantum systems have received far less attention. Here we study several aspects of global nonequilibrium behavior by calculating the amount of work done by the quench as measured through the work distribution function. Using Bethe ansatz techniques, we determine the Loschmidt amplitude and work distribution function of the Lieb-Liniger gas after it is released from an optical lattice. We find the average work and its universal edge exponents from which we determine the long-time decay of the Loschmidt echo and highlight striking differences caused by the interactions as well as changes in the geometry of the system. We extend our calculation to the attractive regime of the model and show that the system exhibits properties similar to the super-Tonks-Girardeau gas. Finally, we examine the prominent role played by bound states in the work distribution and show that, with low probability, they allow for work to be extracted from the quench.

arXiv:1904.07995•Physical review. B./Physical review. B•Aug 26, 2019•11 citations

Work distribution and edge singularities for generic time-dependent protocols in extended systems

Pietro Smacchia, Alessandro Silva

We study the statistics of the work done by globally changing in time with a generic protocol the mass in a free bosonic field theory with relativistic dispersion and the transverse field in the one-dimensional Ising chain both globally and locally. In the latter case we make the system start from the critical point and we describe it in the scaling limit. We provide exact formulas in all these cases for the full statistics of the work and we show that the low-energy part of the distribution of the work displays an edge singularity whose exponent does not depend on the specifics of the protocol that is chosen and may only depend on the position of the initial and final values with respect to the critical point of the system. We also show that the condensation transition found in the bosonic system for sudden quenches [A. Gambassi and A. Silva, Phys. Rev. Lett. 109, 250602 (2012)] is robust with respect to the choice of the protocol.

arXiv:1305.2822•Physical Review E•Oct 7, 2013•68 citations

Universal work statistics in quenched gapless quantum systems

Donny Dwiputra, Mir Faizal, Francesco Marino +1 more

We study the universality of work statistics performed during a quench in gapless quantum systems. We show that the cumulants of work scale separately in the fast and slow quench regimes, following a power law analogous to the universal scaling in the Kibble-Zurek mechanism for topological defect formation in phase transition. As an example, we analyze the nonequilibrium dynamics of a quenched Heisenberg XXZ chain at its critical gapless state using the bosonization picture, resulting in a Tomonaga-Luttinger liquid. The analytical scaling is in agreement with the exact numerical calculation for the fast and slow quench regimes. In finite systems, the characteristic function display an oscillatory pattern which disappears in the thermodynamic limit. This study is particularly useful for understanding the thermodynamics of adiabatic quantum computation.

quant-pharXiv:2511.15971•Nov 21, 2025•0 citations
We present results on quantum quenches in lattice systems with a fixed number of particles in a much larger number of sites. Both local and global quenches in this limit generically have power-law work distributions ("edge singularities"). We show that this regime allows for large edge singularity exponents beyond that allowed by the constraints of the usual thermodynamic limit. This large-exponent singularity has observable consequences in the time evolution, leading to a distinct intermediate power-law regime in time. We demonstrate these results first using local quantum quenches in a low-density Kondo-like system, and additionally through global and local quenches in Bose-Hubbard, Aubry-Andre, and hard-core boson systems at low densities.
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.
Abstract We discuss how nonlocality originates in long-range quantum systems and how it affects their dynamics at and out of equilibrium. We focus in particular on the Kitaev chains with long-range pairings and on the quantum Ising chain with long-range antiferromagnetic coupling (both having a power-law decay with exponent α ). By studying the dynamic correlation functions, we find that for every finite α two different behaviours can be identified, one typical of short-range systems and the other connected with locality violation. The latter behaviour is shown related also with the known power-law decay tails previously observed in the static correlation functions, and originated by modes—having in general energies far from the minima of the spectrum—where particular singularities develop as a consequence of the long-rangedness of the system. We refer to these modes as to ‘singular’ modes, and as to ‘singular dynamics’ to their dynamics. For the Kitaev model they are manifest, at finite α , in derivatives of the quasiparticle energy, the order of the derivatives at which the singularity occurs is increasing with α . The features of the singular modes and their physical consequences are clarified by studying an effective theory for them and by a critical comparison of the results from this theory with the lattice ones. Moreover, a numerical study of the effects of the singular modes on the time evolution after various types of global quenches is performed. We finally present and discuss the presence of singular modes and their consequences in interacting long-range systems by investigating in the long-range Ising quantum chain, both in the deep paramagnetic regime and at criticality, where they also play a central role for the breakdown of conformal invariance.
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.
A classic example of a quantum quench concerns the release of an interacting Bose gas from an optical lattice. The local properties of quenches such as this have been extensively studied; however, the global properties of these nonequilibrium quantum systems have received far less attention. Here we study several aspects of global nonequilibrium behavior by calculating the amount of work done by the quench as measured through the work distribution function. Using Bethe ansatz techniques, we determine the Loschmidt amplitude and work distribution function of the Lieb-Liniger gas after it is released from an optical lattice. We find the average work and its universal edge exponents from which we determine the long-time decay of the Loschmidt echo and highlight striking differences caused by the interactions as well as changes in the geometry of the system. We extend our calculation to the attractive regime of the model and show that the system exhibits properties similar to the super-Tonks-Girardeau gas. Finally, we examine the prominent role played by bound states in the work distribution and show that, with low probability, they allow for work to be extracted from the quench.
We study the statistics of the work done by globally changing in time with a generic protocol the mass in a free bosonic field theory with relativistic dispersion and the transverse field in the one-dimensional Ising chain both globally and locally. In the latter case we make the system start from the critical point and we describe it in the scaling limit. We provide exact formulas in all these cases for the full statistics of the work and we show that the low-energy part of the distribution of the work displays an edge singularity whose exponent does not depend on the specifics of the protocol that is chosen and may only depend on the position of the initial and final values with respect to the critical point of the system. We also show that the condensation transition found in the bosonic system for sudden quenches [A. Gambassi and A. Silva, Phys. Rev. Lett. 109, 250602 (2012)] is robust with respect to the choice of the protocol.
We study the universality of work statistics performed during a quench in gapless quantum systems. We show that the cumulants of work scale separately in the fast and slow quench regimes, following a power law analogous to the universal scaling in the Kibble-Zurek mechanism for topological defect formation in phase transition. As an example, we analyze the nonequilibrium dynamics of a quenched Heisenberg XXZ chain at its critical gapless state using the bosonization picture, resulting in a Tomonaga-Luttinger liquid. The analytical scaling is in agreement with the exact numerical calculation for the fast and slow quench regimes. In finite systems, the characteristic function display an oscillatory pattern which disappears in the thermodynamic limit. This study is particularly useful for understanding the thermodynamics of adiabatic quantum computation.