Total correlations of the diagonal ensemble as a generic indicator for ergodicity breaking in quantum systems

Pietracaprina, Francesca; Gogolin, Christian; Goold, John

doi:10.1103/physrevb.95.125118

Cited by 9 publications

(9 citation statements)

References 62 publications

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“…Under these conditions, namely, initial ground state and sudden quench, the work distribution is mathematically equivalent to the infinite time average of the quantum state, i.e., the diagonal ensemble. Therefore, we have all the information necessary to determine the entropy of the diagonal ensemble [74,75,82], which is simply given by the Shannon entropy of P W :…”

Section: Model and Key Quantities Of Interestmentioning

confidence: 99%

“…( 9) is experimentally accessible [81]. Remarkably this provides all the information necessary to determine the entropy of the diagonal ensemble [74,75,82], which is simply given by the Shannon entropy of P W ,…”

Section: Model and Key Quantities Of Interestmentioning

confidence: 99%

“…Furthermore, we study the entropy of the diagonal ensemble (i.e. the Shannon entropy of the work distribution) establishing that this accessible quantity [71][72][73][74][75] is very sensitive to the presence of the ESQPT. Finally, we examine the behavior for initially excited states where a qualitatively consistent behavior is found and we consider the case of states initialized in the paramagnetic phase.…”

Section: Introductionmentioning

confidence: 96%

“…[12,70], we find that for quenches exactly to the ESQPT point the work distribution becomes non-Gaussian and further evidence of the effect of symmetry breaking can be seen in a reduction of the probability amplitudes. Furthermore, we study the entropy of the diagonal ensemble (i.e., the Shannon entropy of the work distribution) establishing that this accessible quantity [71][72][73][74][75] is very sensitive to the presence of the ESQPT. Finally, we examine the behavior for initially excited states where a qualitatively consistent behavior is found and we consider the case of states initialized in the paramagnetic phase.…”

Section: Introductionmentioning

confidence: 96%

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Work statistics and symmetry breaking in an excited-state quantum phase transition

et al. 2021

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We examine how the presence of an excited-state quantum phase transition manifests in the dynamics of a many-body system subject to a sudden quench. Focusing on the Lipkin-Meshkov-Glick model initialized in the ground state of the ferromagnetic phase, we demonstrate that the work probability distribution displays non-Gaussian behavior for quenches in the vicinity of the excited-state critical point. Furthermore, we show that the entropy of the diagonal ensemble is highly susceptible to critical regions, making it a robust and practical indicator of the associated spectral characteristics. We assess the role that symmetry breaking has on the ensuing dynamics, highlighting that its effect is only present for quenches beyond the critical point. Finally, we show that similar features persist when the system is initialized in an excited state and briefly explore the behavior for initial states in the paramagnetic phase.

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Section: Model and Key Quantities Of Interestmentioning

confidence: 99%

Section: Model and Key Quantities Of Interestmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 96%

See 2 more Smart Citations

Work statistics and symmetry breaking in an excited-state quantum phase transition

et al. 2021

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“…⊗ ρ L where ρ i := Tr L/i ρ. In our case of a pure state |ψ t it is easy to see that the total correlations T t := T (|ψ t ψ t |) are simply a rescaling of S(t)It was recently shown that the study of the total correlations in the diagonal ensemble can signal the transition from ergodic to the MBL phase [38,41] but since the diagonal ensemble is a mixed state this requires knowledge of the global state. Since the states here are pure the total correlations can be probed dynamically by means of only local operations.…”

mentioning

confidence: 99%

Logarithmic growth of local entropy and total correlations in many-body localized dynamics

Anzà

Pietracaprina

Goold

2020

Quantum

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The characterizing feature of a many-body localized phase is the existence of an extensive set of quasilocal conserved quantities with an exponentially localized support. This structure endows the system with the signature logarithmic in time entanglement growth between spatial partitions. This feature differentiates the phase from Anderson localization, in a non-interacting model. Experimentally measuring the entanglement between large partitions of an interacting many-body system requires highly non-local measurements which are currently beyond the reach of experimental technology. In this work we demonstrate that the defining structure of many-body localization can be detected by the dynamics of a simple quantity from quantum information known as the total correlations which is connected to the local entropies. Central to our finding is the necessity to propagate specific initial states, drawn from the Hamiltonian unbiased basis (HUB). The dynamics of the local entropies and total correlations requires only local measurements in space and therefore is potentially experimentally accessible in a range of platforms.The study of transport properties of quantum systems is a topic of paramount importance in condensed matter physics. A crucial aspect is the presence of disorder due to defects and irregularities in the material under study. In a celebrated work [1] Anderson showed how the presence of strong disorder can completely suppress transport of non-interacting electrons in a tight-binding model. Understanding the fate of this localisation phenomenon in the presence of interactions has seen an unprecedented revival in recent years [2,3]. In a seminal contribution Basko et. al. [4] argued that such phenomenon is stable when interactions between particles are introduced, showing the existence of a new dynamical phase of matter, the Many-Body Localized (MBL) phase [5][6][7][8] which, like its single particle counterpart exhibits a lack of both transport and thermalization [8]. From the experimental perspective, signatures of MBL physics have recently been observed in a number of different laboratories in cold atoms [9-11], ion traps [12] and NMR [13].As the system fails to thermalize, local observables retain memory of their initial conditions. In the last ten years there has been a large amount of effort devoted to the understanding of the MBL phase [2,5,[14][15][16][17][18]. The defining feature of an MBL state (e.g. as opposed to Anderson localization) has been identified in the fact that, while the transport of energy and local quantities is suppressed [19][20][21][22][23][24][25][26], there is transport of quantum information, occurring on a logarithmic time scale manifested in the growth of the half-chain entanglement entropy [27,28]. This behaviour can be explained by the emergence of an extensive set of quasi-local integrals of motions (Q-LIOMs) [18,[28][29][30]. Such objects have a support which is exponentially localized, the localization length being ξ. In the high-disorder regime the tails become more...

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Generalized time-dependent Schrödinger equation in two dimensions under constraints

Sandev

Petreska

Lenzi

2018

Journal of Mathematical Physics

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We investigate a generalized two-dimensional time-dependent Schrödinger equation on a comb with a memory kernel. A Dirac delta term is introduced in the Schrödinger equation so that the quantum motion along the x-direction is constrained at y = 0. The wave function is analyzed by using Green’s function approach for several forms of the memory kernel, which are of particular interest. Closed form solutions for the cases of Dirac delta and power-law memory kernels in terms of Fox H-function, as well as for a distributed order memory kernel, are obtained. Further, a nonlocal term is also introduced and investigated analytically. It is shown that the solution for such a case can be represented in terms of infinite series in Fox H-functions. Green’s functions for each of the considered cases are analyzed and plotted for the most representative ones. Anomalous diffusion signatures are evident from the presence of the power-law tails. The normalized Green’s functions obtained in this work are of broader interest, as they are an important ingredient for further calculations and analyses of some interesting effects in the transport properties in low-dimensional heterogeneous media.

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Total correlations of the diagonal ensemble as a generic indicator for ergodicity breaking in quantum systems

Cited by 9 publications

References 62 publications

Work statistics and symmetry breaking in an excited-state quantum phase transition

Work statistics and symmetry breaking in an excited-state quantum phase transition

Logarithmic growth of local entropy and total correlations in many-body localized dynamics

Generalized time-dependent Schrödinger equation in two dimensions under constraints

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