Quantum quenches in one-dimensional gapless systems

Coira, Emanuele; Becca, Federico; Parola, Alberto

doi:10.1140/epjb/e2012-30978-y

Cited by 21 publications

(24 citation statements)

References 31 publications

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“…Since one-dimensional spin models like the XXZ Heisenberg chain can be mapped to fermionic chains of the form (5), the results presented in our paper can be applied to the analysis of the time evolution during and after finite-time quenches in spin chains. A similar analysis has been performed for the dynamics of several observables in the XXZ chain after sudden quenches 13,14,17,29,33 as well as during linear ramps in the anisotropy. 44 …”

Section: B Relation To Fermionic Systemsmentioning

confidence: 89%

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

Chudziński

Schuricht

2016

Phys. Rev. B

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We consider finite-time quantum quenches in the interacting Tomonaga-Luttinger model, for example time-dependent changes of the nearest-neighbour 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 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 behaviour of the Green functions and in particular provide analytic, nonperturbative results for the delay applicable to quenches of short to moderate duration but arbitrary time dependency.

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Section: B Relation To Fermionic Systemsmentioning

confidence: 89%

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

Chudziński

Schuricht

2016

Phys. Rev. B

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“…One dimensional systems are notoriously strongly correlated due to the limited phase space for scattering. The non-interacting ground state is immediately destroyed by interactions, forming a Luttinger liquid (LL) in many instances [8,9], and described by critical phenomena of collective modes with anomalous (non-integer) power-law dependence of correlation functions.Quantum quenches in Luttinger liquids have been addressed by several authors [10][11][12][13][14][15][16][17]. However, it is not clear to what extent the Luttinger liquid (LL) picture, which is a genuine low energy description, is applicable under non-equilibrium circumstances [17].…”

mentioning

confidence: 99%

“…Quantum quenches in Luttinger liquids have been addressed by several authors [10][11][12][13][14][15][16][17]. However, it is not clear to what extent the Luttinger liquid (LL) picture, which is a genuine low energy description, is applicable under non-equilibrium circumstances [17].…”

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confidence: 99%

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

2013

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We study variable-rate linear quenches in the anisotropic Heisenberg (XXZ) chain, starting at the XX point. This is equivalent to swithcing on a nearest neighbour 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, iTEBD) 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 non-equilibrium situation.PACS numbers: 71.10. Pm,75.10.Jm,05.70.Ln, While it is difficult to study genuine non-equilibrium dynamics in solid state systems due to the presence of many relaxation channels (phonons, impurities, interactions etc.), cold atoms in optical lattices provide an ideal laboratory for non-equilibrium investigations due to the high degree of control over various dissipation mechanisms. Cold-atom experiments in the past decade have explored a wide variety of non-equilibrium quantum dynamics in previously inaccessible regimes [1,2]. This has also led to an increasing amount of theoretical activity [2,3]. Key issues include thermalization as well as equilibration and their relation to integrability [2], pumping beyond the adiabatic limit or quantum fluctuation relations [4], and universal near-adiabatic dynamics in quantum critical systems [2,3]. Linear quenches occuring over a finite time can interpolate between the more familiar limits of an instantaneous quench and an adiabatic sweep. Very recently, a few experiments have examined the response of many-body experiments to such finitetime quenches [5,6]. It is thus of vital current interest to address the dynamics under linear sweeps of system parameters such as interaction strength.The response of a system to an external perturbation depends sensitively on its spatial dimension, as famously demonstrated in the experiment of Ref. [7]. There, one dimensional interacting bosons did not reach thermalization within the experimental timescale, while their higher dimensional realizations did. One dimensional systems are notoriously strongly correlated due to the limited phase space for scattering. The non-interacting ground state is immediately destroyed by interactions, forming a Luttinger liquid (LL) in many instances [8,9], and described by critical phenomena of collective modes with anomalous (non-integer) power-law dependence of correlation functions.Quantum quenches in Luttinger liquids have been addressed by several authors [10][11][12][13][14][15][16][17]. However, it is not clear to what extent the Luttinger liquid (LL) picture, which is a genuine low energy description, is applicable under non-equilibrium circumstances [17]. For an abrupt interaction change, certain observables revealed universal LL ...

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“…We note that S * (q, U ) ∼ A + B |q| may also explains the contradictory one-dimensional results of Ref. 23.…”

Section: Second Order Perturbation Theory Resultsmentioning

confidence: 66%

Absence of thermalization in a Fermi liquid

Maraga¹,

Silva²,

Fabrizio³

2014

Phys. Rev. B

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We study a weak interaction quench in a three-dimensional Fermi gas. We first show that, under some general assumptions on time-dependent perturbation theory, the perturbative expansion of the long-wavelength structure factor S(q) is not compatible with the hypothesis that steady-state averages correspond to thermal ones. In particular, S(q) does develop an analytical component ∼ const.+O(q 2 ) at q → 0, as implied by thermalization, but, in contrast, it maintains a non-analytic part ∼ |q| characteristic of a Fermi-liquid at zero-temperature. In real space, this non-analyticity corresponds to persisting power-law decaying density-density correlations, whereas thermalization would predict only an exponential decay. We next consider the case of a dilute gas, where one can obtain non-perturbative results in the interaction strength but at lowest order in the density. We find that in the steady-state the momentum distribution jump at the Fermi surface remains finite, though smaller than in equilibrium, up to second order in kF f0, where f0 is the scattering length of two particles in the vacuum. Both results question the emergence of a finite length scale in the quench-dynamics as expected by thermalization.

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Quantum quenches in one-dimensional gapless systems

Cited by 21 publications

References 31 publications

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

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

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

Absence of thermalization in a Fermi liquid

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