Quantum quenches in the anisotropic spin-\frac{1}{2} Heisenberg chain: different approaches to many-body dynamics far from equilibrium

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

doi:10.1088/1367-2630/12/5/055017

Cited by 120 publications

(127 citation statements)

References 193 publications

(309 reference statements)

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“…This may even be more severe in the case of finite-time quenches since the quench time τ will introduce an additional energy scale in the problem, which may increase the importance of marginal and irrelevant perturbations to the TLM. Nevertheless, various numerical studies 13,14,17,20,26,28,29,33 of observables in onedimensional lattice models after sudden quenches showed a surprisingly good agreement with the results obtained in the TLM; a finding also obtained for the time evolution during finite-time interaction quenches 39,41,45 in the Bose-Hubbard model. Still, from a practical point of view the study of the time evolution after finite-time quenches is complicated by the restriction of the achievable times in numerical simulations due to the finite quench time and the unknown effects of perturbations to the TLM as well as the energy (and thus time) scales involved.…”

Section: Conclusion and Discussionsupporting

confidence: 76%

“…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%

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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: Conclusion and Discussionsupporting

confidence: 76%

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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“…The literature on quantum quenches in interacting bosonic and fermionic systems is by now very broad, see for example the recent topical reviews [13][14][15][16] For what concerns strongly correlated electrons in more than one dimension, the subject is still largely unexplored and progresses have been done only very recently. The single band Hubbard model [17][18][19] represent one of the simplest yet non trivial models encoding the physics of strong correlations, namely the competition between electronic wave function delocalization due to hopping t and charge localization due to large Coulomb repulsion U .…”

Section: Introductionmentioning

confidence: 99%

Quantum quenches in the Hubbard model: Time-dependent mean-field theory and the role of quantum fluctuations

2011

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We study the non equilibrium dynamics in the fermionic Hubbard model after a sudden change of the interaction strength. To this scope, we introduce a time dependent variational approach in the spirit of the Gutzwiller ansatz. At the saddle-point approximation, we find at half filling a sharp transition between two different regimes of small and large coherent oscillations, separated by a critical line of quenches where the system is found to relax. Any finite doping washes out the transition, leaving aside just a sharp crossover. In order to investigate the role of quantum fluctuations, we map the model onto an auxiliary Quantum Ising Model in a transverse field coupled to free fermionic quasiparticles. Remarkably, the Gutzwiller approximation turns out to correspond to the mean field decoupling of this model in the limit of infinite coordination lattices. The advantage is that we can go beyond mean field and include gaussian fluctuations around the non equilibrium mean field dynamics. Unlike at equilibrium, we find that quantum fluctuations become massless and eventually unstable before the mean field dynamical critical line, which suggests they could even alter qualitatively the mean field scenario.

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“…Although the nonanalyticities of the dynamical free energy on the real time axis do not indicate the presence or absence of an EPT, the structure of Fisher lines for complex times reveals a qualitative difference. Interest in nonequilibrium dynamics has grown immensely in the past few years [1][2][3][4] thanks to experimental advances made with ultracold atomic gases. The wide controllability of these systems allows experimentalists to prepare different kinds of nonequilibrium initial states and it is also possible to study the dynamics with time resolution that is unreachable in other physical systems [5][6][7][8][9].…”

mentioning

confidence: 99%

Disentangling dynamical phase transitions from equilibrium phase transitions

2014

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Dynamical phase transitions (DPTs) occur after quenching some global parameters in quantum systems, and are signalled by the nonanalytical time evolution of the dynamical free energy, which is calculated from the Loschmidt overlap between the initial and time evolved states. In a recent Letter [M. Heyl et al., Phys. Rev. Lett. 110, 135704 (2013)], it was suggested that DPTs are closely related to equilibrium phase transitions (EPTs) for the transverse field Ising model. By studying a minimal model, the XY chain in a transverse magnetic field, we show analytically that this connection does not hold generally. We present examples where DPT occurs without crossing any equilibrium critical lines by the quench, and a nontrivial example with no DPT but crossing a critical line by the quench. Although the nonanalyticities of the dynamical free energy on the real time axis do not indicate the presence or absence of an EPT, the structure of Fisher lines for complex times reveals a qualitative difference. Interest in nonequilibrium dynamics has grown immensely in the past few years [1][2][3][4] thanks to experimental advances made with ultracold atomic gases. The wide controllability of these systems allows experimentalists to prepare different kinds of nonequilibrium initial states and it is also possible to study the dynamics with time resolution that is unreachable in other physical systems [5][6][7][8][9]. Some of the main questions concern when and how thermalization, or more generally, equilibration, occurs and its connection to ergodicity and integrability. These were first posed by von Neumann in 1929 [10].The nonequilibrium time evolution can be characterized in many different ways, borrowing ideas from equilibrium statistical mechanics. The ultrashort time nonequilibrium dynamics, revealing the role of high-energy excitations, is also of interest as well as the stationary state that is reached after long time evolution. The latter can be described by the diagonal ensemble, which is roughly the time averaged density matrix. The results of local measurements can be described by simpler ensembles, i.e., by the thermal Gibbs ensemble for nonintegrable (ergodic) systems [11] and by the generalized Gibbs ensemble for integrable ones [12]. The Loschmidt overlap (LO), which is the main focus of this Rapid Communication, is a nonlocal expression and is entirely determined by the diagonal ensemble, hence it characterizes the stationary state [13]. Analyzing the LO has proven to be useful in studying quantum chaos, decoherence, and quantum criticality [14][15][16][17]. It is defined as the scalar product of the initial state and the time evolved state following a sudden global quench (SQ) asand can be regarded as the characteristic function of work performed on the system during the quench. In a SQ the parameters of the Hamiltonian are changed suddenly from some initial to final values, and the system, prepared initially in the ground state |ψ of the initial Hamiltonian, is assumed to be well separated from the environmen...

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Quantum quenches in the anisotropic spin-\frac{1}{2} Heisenberg chain: different approaches to many-body dynamics far from equilibrium

Cited by 120 publications

References 193 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

Quantum quenches in the Hubbard model: Time-dependent mean-field theory and the role of quantum fluctuations

Disentangling dynamical phase transitions from equilibrium phase transitions

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