Relaxation of Antiferromagnetic Order in Spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:math>Chains Following a Quantum Quench

Barmettler, Peter; Punk, Matthias; Gritsev, Vladimir; Demler, Eugene; Altman, Ehud

doi:10.1103/physrevlett.102.130603

Cited by 207 publications

(241 citation statements)

References 30 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: 90%

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: 90%

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

Chudziński

Schuricht

2016

Phys. Rev. B

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“…(1.4) is satisfied then the question moves to the finite-size corrections ofρ (L) in Eq. (1.2) and to the approach to the stationary state ρ ∞ in the infinite chain (see also Refs 35,[47][48][49][50][51][52] ). In order to investigate these questions we consider quenches in models with a free-fermion representation, in which the late time behavior of correlation functions and entanglement entropies is known, and we compute the leading finite-size correction for time average correlation functions and entropies.…”

Section: Introductionmentioning

confidence: 99%

Finite-size corrections versus relaxation after a sudden quench

Fagotti

2013

Phys. Rev. B

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We consider the time evolution after sudden quenches of global parameters in translational invariant Hamiltonians and study the time average expectation values and entanglement entropies in finite chains. We show that in noninteracting models the time average of spin correlation functions is asymptotically equal to the infinite time limit in the infinite chain, which is known to be described by a generalized Gibbs ensemble. The equivalence breaks down considering nonlocal operators, and we establish that this can be traced back to the existence of conservation laws common to the Hamiltonian before and after the quench. We develop a method to compute the leading finite-size correction for time average correlation functions and entanglement entropies. We find that large corrections are generally associated to observables with slow relaxation dynamics.

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“…Previous studies have in particular focused on the dynamics near quantum phase transitions in low dimensional systems (e. g., Refs. [15][16][17][18]). Higher dimensional systems are usually expected to show a thermal criticality out of equilibrium since quantum fluctuations are well suppressed.…”

mentioning

confidence: 99%

Nonthermal Antiferromagnetic Order and Nonequilibrium Criticality in the Hubbard Model

2013

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We study dynamical phase transitions from antiferromagnetic to paramagnetic states driven by an interaction quench in the fermionic Hubbard model using the nonequilibrium dynamical mean-field theory. We identify two dynamical transition points where the relaxation behavior qualitatively changes: one corresponds to the thermal phase transition at which the order parameter decays critically slowly in a power law ∝ t −1/2 , and the other is connected to the existence of nonthermal antiferromagnetic order in systems with effective temperature above the thermal critical temperature. The frequency of the amplitude mode extrapolates to zero as one approaches the nonthermal (quasi)critical point, and thermalization is significantly delayed by the trapping in the nonthermal state. A slow relaxation of the nonthermal order is followed by a faster thermalization process. PACS numbers: 71.10.Fd, 64.60.Ht In many physical systems out of equilibrium, phase transitions occur as a real-time process of symmetry breaking or symmetry recovery. Examples for such "dynamical phase transitions" include the evolution of the Universe [1], liquid helium [2], and photoinduced phase transition in solids [3][4][5]. The macroscopic aspects are often described by the timedependent Ginzburg-Landau theory, where the order parameter is supposed to vary sufficiently slowly in time and space, so that the system can be considered to be locally close to thermal equilibrium. On the other hand, recent experimental developments of time-resolved measurement techniques in solids [6] and cold atoms [7] allow one to study dynamical phase transitions very far from equilibrium on the microscopic time scale of correlated quantum systems. In these cases, a "near-equilibrium" description might not be applicable. For instance, it has been recently suggested that superconductivity can be induced above the equilibrium critical temperature (T c ) by coherently exciting certain lattice vibrations, and that it lasts for a relatively long time (a few tens of ps) before thermalization occurs [5]. This observation is reminiscent of the prethermalization phenomenon [8][9][10][11], or the dynamics in the presence of a nonthermal fixed point in relativistic quantum field theories [12]. A fundamental question that we pose here is if the existence of such a nonthermal fixed point in correlated condensed matter systems allows symmetry broken states to survive above T c , and how it affects the dynamics.An important and still unresolved issue is how to characterize a nonequilibrium phase transition and its critical behavior for quantum systems [13,14]. Previous studies have in particular focused on the dynamics near quantum phase transitions in low dimensional systems (e. g., Refs. [15][16][17][18]). Higher dimensional systems are usually expected to show a thermal criticality out of equilibrium since quantum fluctuations are well suppressed. In this Letter, we study a dynamical phase transition for a simple microscopic model of correlated materials, namely the Hubbard mode...

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Relaxation of Antiferromagnetic Order in Spin-1/2Chains Following a Quantum Quench

Cited by 207 publications

References 30 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

Finite-size corrections versus relaxation after a sudden quench

Nonthermal Antiferromagnetic Order and Nonequilibrium Criticality in the Hubbard Model

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