Local quenches with global effects in interacting quantum systems

Torres-Herrera, E. J.; Santos, Lea F.

doi:10.1103/physreve.89.062110

Cited by 109 publications

(219 citation statements)

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“…We have shown that, while the former retains its power law structure even in the presence of a strong nonequilibrium perturbation the latter is a source of nonlinearity which generates locally an exponential decay in time of the OC correlator. Such a result appears to be consistent with a recent numerical study on Loschmidt echo decay in a 1D spin chain after a local quench starting from a highly excited state [59].We expect the physics of this quench-induced decoherence to be relevant in other contexts as well, most notably in steady-state transport, where it will result in a non-vanishing zero bias conductance in the weak-link limit as well as a non-zero backscattering correction in the dual limit [60], a result which is consistent with the non-vanishing impurity density of states recently found in [61].Acknowledgment -It is a pleasure to thank …”

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confidence: 91%

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: 91%

Transient Orthogonality Catastrophe in a Time-Dependent Nonequilibrium Environment

Schiró

Mitra

2014

Phys. Rev. Lett.

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“…Conclusion.-In general, the dynamics of initial states with energies very close to the edges of the spectrum is much slower than for states with energies closer to the middle of the spectrum [47]. Here, we showed that in an isolated system undergoing an ESQPT, a slow time evolution can occur also for initial states with energy very close to E ESQPT .…”

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confidence: 74%

Structure of eigenstates and quench dynamics at an excited-state quantum phase transition

2015

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We study the structure of the eigenstates and the dynamics of a system that undergoes an excited state quantum phase transition (ESQPT). The analysis is performed for two-level pairing models characterized by a U (n + 1) algebraic structure. They exhibit a second order phase transition between two limiting dynamical symmetries represented by the U (n) and SO(n + 1) subalgebras. They are, or can be mapped onto, models of interacting bosons. We show that the eigenstates with energies very close to the ESQPT critical point, EESQPT, are highly localized in the U (n)-basis. Consequently, the dynamics of a system initially prepared in a U (n)-basis vector with energy E ∼ EESQPT may be extremely slow. Signatures of an ESQPT can therefore be found in the structures of the eigenstates and in the speed of the system evolution after a sudden quench. Our findings can be tested experimentally with trapped ions. Introduction.-Quantum phase transitions (QPTs) occur at zero temperature. They correspond to an abrupt change in the character of the ground state of a system when a control parameter passes a critical point [1]. The subject, which permeates condensed matter and nuclear physics, has become one of the highlights of experiments with cold gases, where transitions from a superfluid to a Mott insulator [2] and from a normal to a superradiant phase [3] have been observed. The investigations are not restricted to the properties of the ground state, but extend also to the dynamics of systems undergoing QPTs. In this context, one finds studies about the quantum analogue of the Kibble-Zurek mechanism [4], as well as the relaxation time [5][6][7][8], revivals [9,10], and temporal fluctuations [11,12] at critical points.Recently, the concept of ground state QPT has been generalized to encompass also QPTs occurring at excited states. These so-called ESQPT refer to a singularity in the energy spectrum caused by the clustering of excited levels at a critical energy [13][14][15][16]. This critical point can be reached either for a constant excited energy by varying the control parameter(s) or by fixing the latter and increasing the energy. ESQPTs have been investigated for a broad class of many-body quantum systems, such as the Lipkin-Meshkov-Glick (LMG) [17][18][19], the molecular vibron [15,20] In terms of dynamics, it has been shown that an ESQPT leads to random oscillations of the survival probability in isolated systems [21], to singularities in the evolution of observables [32], and to maximal decoherence in open systems [18,33]. Despite these works, studies of the effects of ESQPTs on systems' evolutions are still scarce.In this Rapid Communication, we provide insights into the

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“…For example, the energy width of the distribution determines the coefficient of the initial quadratic decay of L(t), as it can be seen by expanding e −iH f t in Eq. (3) to second order in t [46,48]. After a quench, a generic observable O has the following time evolution: …”

Section: Str-el] 15 Sep 2015mentioning

confidence: 99%

“…In the current era of non-equilibrium physics, it has been widely used as a model system to explore and exemplify non-equilibrium phenomena, including studies of the Loschmidt echo (e.g. [22,46,[64][65][66][67][68]), studies of quenches of the anisotropy parameter ∆ (e.g. [99,100]), and of quenches starting from a Néel state (e.g.…”

Section: The Modelmentioning

confidence: 99%

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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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Local quenches with global effects in interacting quantum systems

Cited by 109 publications

References 92 publications

Transient Orthogonality Catastrophe in a Time-Dependent Nonequilibrium Environment

Transient Orthogonality Catastrophe in a Time-Dependent Nonequilibrium Environment

Structure of eigenstates and quench dynamics at an excited-state quantum phase transition

Overlap distributions for quantum quenches in the anisotropic Heisenberg chain

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