Quench echo and work statistics in integrable quantum field theories

Palmai, Tamas; Sotiriadis, Spyros

doi:10.1103/physreve.90.052102

Cited by 35 publications

(51 citation statements)

References 119 publications

(113 reference statements)

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“…P (W ) is the probability distribution of the work done, starting from a non-equilibrium state described by the diagonal ensemble ρ nn , and suddenly switching on the local potential. This extends to the non-equilibrium case the connection between the OC correlator and work statistics and represents an interesting result on its own, in view of recent theoretical interest in characterizing the work statistics and its universal properties in non-thermal ensembles [38,39]. While it is known that in equilibrium the work statistics of local quenches shows zero-temperature edge singularities[9, 32], we will see below how this is modified in the presence of bulk excitations.…”

supporting

confidence: 52%

Transient Orthogonality Catastrophe in a Time-Dependent Nonequilibrium Environment

Schiró

Mitra

2014

Phys. Rev. Lett.

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We study the response of a highly-excited time dependent quantum many-body state to a sudden local perturbation, a sort of orthogonality catastrophe problem in a transient non-equilibrium environment. To this extent we consider, as key quantity, the overlap between time dependent wavefunctions, that we write in terms of a novel two-time correlator generalizing the standard Loschmidt Echo. We discuss its physical meaning, general properties, and its connection with experimentally measurable quantities probed through non-equilibrium Ramsey interferometry schemes. Then we present explicit calculations for a one dimensional interacting Fermi system brought out of equilibrium by a sudden change of the interaction, and perturbed by the switching on of a local static potential. We show that different scattering processes give rise to remarkably different behaviors at long times, quite opposite from the equilibrium situation. In particular, while the forward scattering contribution retains its power law structure even in the presence of a large non-equilibrium perturbation, with an exponent that is strongly affected by the transient nature of the bath, the backscattering term is a source of non-linearity which generates an exponential decay in time of the Loschmidt Echo, reminiscent of an effective thermal behavior.PACS numbers: 72.10. Pm,05.70.Ln,72.15.Qm Introduction -The response of gapless quantum manybody systems to sudden local perturbations is a remarkably non-linear phenomenon, even a weak disturbance substantially changes the structure of the many-body state. Signatures of this orthogonality catastrophe (OC) emerge in various condensed matter settings [1], from Xray spectra in metals [2] and Luttinger Liquids (LL) [3][4][5][6] to the physics of the Kondo Effect [7][8][9][10][11] and typically results in power-law decays of dynamical correlations. Recently, impressive experimental developments with ultracold atomic gases [12], have made possible to create and probe local excitations in a quantum many-body system with single-site and real-time resolution [13,14], bringing fresh new input to this venerable problem [15]. While most of the attention has been traditionally devoted to perturbations acting on systems in their ground state or, more recently, in driven stationary non-equilibrium conditions [16][17][18][19][20][21][22], much less is known about the response of explicitly time dependent quantum states, such as, for example, those obtained by rapidly changing in time some parameter of an otherwise isolated system. The problem is of current experimental relevance since ultracold gases have proven to be natural laboratories where dynamical quantum correlations can be probed in the time domain. In addition, it also raises a number of intriguing theoretical questions. A coherent time dependent excitation, such as a sudden global quench, creates an effective nonequilibrium time-dependent bath for the local degrees of freedom. What is the effect of such an environment on the OC phenomenon and its associated p...

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supporting

confidence: 52%

Transient Orthogonality Catastrophe in a Time-Dependent Nonequilibrium Environment

Schiró

Mitra

2014

Phys. Rev. Lett.

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“…Following common practice, we will refer to this quantity simply as the Loschmidt echo. The behavior of the Loschmidt echo after a quantum quench has been studied in a large body of recent literature, see, e.g., [18,22,25,34,. In particular, the Loschmidt echo is central to the study of so-called dynamical phase transitions [67][68][69][70][71][72][73][74][75][76].…”

Section: Str-el] 15 Sep 2015mentioning

confidence: 99%

“…The work distribution is thus simply a continuous version of the distribution of squared overlaps, with the zero of the energy shifted by E i . The work statistics in non-equilibrium processes in various quantum many-body systems is a topic of much recent interest [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. Another quantity of wide current interest, closely related to the overlap distribution and work distribution, is the return probability,…”

Section: Str-el] 15 Sep 2015mentioning

confidence: 99%

Overlap distributions for quantum quenches in the anisotropic Heisenberg chain

et al. 2016

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The dynamics after a quantum quench is determined by the weights of the initial state in the eigenspectrum of the final Hamiltonian, i.e., by the distribution of overlaps in the energy spectrum. We present an analysis of such overlap distributions for quenches of the anisotropy parameter in the one-dimensional anisotropic spin-1/2 Heisenberg model (XXZ chain). We provide an overview of the form of the overlap distribution for quenches from various initial anisotropies to various final ones, using numerical exact diagonalization. We show that if the system is prepared in the antiferromagnetic Néel state (infinite anisotropy) and released into a non-interacting setup (zero anisotropy, XX point) only a small fraction of the final eigenstates gives contributions to the post-quench dynamics, and that these eigenstates have identical overlap magnitudes. We derive expressions for the overlaps, and present the selection rules that determine the final eigenstates having nonzero overlap. We use these results to derive concise expressions for time-dependent quantities (Loschmidt echo, longitudinal and transverse correlators) after the quench. We use perturbative analyses to understand the overlap distribution for quenches from infinite to small nonzero anisotropies, and for quenches from large to zero anisotropy.

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“…where ) and (49). As discussed in the main text, the traversal time is retarded and larger than L 2vmax , where the vmax the maximum quasi-particle velocity.…”

Section: B Return Amplitude For the Néel Initial Statementioning

confidence: 87%

Return amplitude after a quantum quench in the XY chain

Najafi¹,

Rajabpour²,

Viti³

2019

J. Stat. Mech.

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We determine an exact formula for the transition amplitude between any two arbitrary eigenstates of the local z-magnetization operators in the quantum XY chain. We further use this formula to obtain an analytical expression for the return amplitude of fully polarized states and the Néel state on a ring of length L. Then, we investigate finite-size effects in the return amplitude: in particular quasi-particle interference halfway along the ring, a phenomenon that has been dubbed traversal [33]. We show that the traversal time and the features of the return amplitude at the traversal time depend on the initial state and on the parity of L. Finally, we briefly discuss nonanalyticities in time of the decay rates in the thermodynamic limit L → ∞, which are known as dynamical phase transitions. arXiv:1905.01272v3 [cond-mat.stat-mech]

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Quench echo and work statistics in integrable quantum field theories

Cited by 35 publications

References 119 publications

Transient Orthogonality Catastrophe in a Time-Dependent Nonequilibrium Environment

Transient Orthogonality Catastrophe in a Time-Dependent Nonequilibrium Environment

Overlap distributions for quantum quenches in the anisotropic Heisenberg chain

Return amplitude after a quantum quench in the XY chain

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