Loschmidt echo in many-body localized phases

Serbyn, Maksym; Abanin, Dmitry A.

doi:10.1103/physrevb.96.014202

Cited by 34 publications

(37 citation statements)

References 60 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…4 (d), we moreover show that the onset of MBL in the spin-1/2 model reflects itself in a concave shape of C(ω) with a distinct peak at ω/ S ≈ 1, consistent with earlier results in Ref. [73] (see also [90]). While such a pronounced feature is absent for S = 3/2 and classical spins, a small double-peak structure around ω/ S = 1 emerges in the case of S = 1.…”

Section: Dynamicssupporting

confidence: 91%

“…7 (a)], where the curves do not collapse anymore (see also Ref. [73] for similar results and further discussion).…”

Section: Finite-size Analysis and Self-averagingmentioning

confidence: 57%

“…As another probe of self-averaging, we also consider the log-averaged correlation function C log (t) [73], defined as…”

Section: Averagingmentioning

confidence: 99%

“…(5) upon replacing C(t) by C log (t). It is easy to see that the log-average C log (t) is in fact equivalent to the geometric mean (whereas C(t) is the "standard" arithmetic mean), which is also the reason why C log (t) is often referred to as typical correlation [41,73].…”

Section: Averagingmentioning

confidence: 99%

See 3 more Smart Citations

Decay of spin-spin correlations in disordered quantum and classical spin chains

Richter

Schubert

Steinigeweg

2020

Phys. Rev. Research

View full text Add to dashboard Cite

The real-time dynamics of equal-site correlation functions is studied for one-dimensional spin models with quenched disorder. Focusing on infinite temperature, we present a comparison between the dynamics of models with different quantum numbers S = 1/2, 1, 3/2, as well as of chains consisting of classical spins. Based on this comparison as well as by analyzing the statistics of energy-level spacings, we show that the putative many-body localization transition is shifted to considerably stronger values of disorder for increasing S. In this context, we introduce an effective disorder strength W eff , which provides a mapping between the dynamics for different spin quantum numbers. For small W eff , we show that the real-time correlations become essentially independent of S, and are moreover very well captured by the dynamics of classical spins. Especially for S = 3/2, the agreement between quantum and classical dynamics is remarkably observed even for very strong values of disorder. This behavior also reflects itself in the corresponding spectral functions, which are obtained via a Fourier transform from the time to the frequency domain. As an aside, we also comment on the self-averaging properties of the correlation function at weak and strong disorder. Our work sheds light on the correspondence between quantum and classical dynamics at high temperatures and extends our understanding of the dynamics in disordered spin chains beyond the well-studied case of S = 1/2.

show abstract

Section: Dynamicssupporting

confidence: 91%

“…7 (a)], where the curves do not collapse anymore (see also Ref. [73] for similar results and further discussion).…”

Section: Finite-size Analysis and Self-averagingmentioning

confidence: 57%

“…As another probe of self-averaging, we also consider the log-averaged correlation function C log (t) [73], defined as…”

Section: Averagingmentioning

confidence: 99%

Section: Averagingmentioning

confidence: 99%

See 2 more Smart Citations

Decay of spin-spin correlations in disordered quantum and classical spin chains

Richter

Schubert

Steinigeweg

2020

Phys. Rev. Research

View full text Add to dashboard Cite

show abstract

“…Quantum-mechanical description of Loschmidt echoes involves OTOCs [16,17,22,23,28,[47][48][49][50][51][52][53][54][55][56]. We now illustrate that the parameter Λ defined in the present work from the relation…”

Section: Relation To Quantum Systemsmentioning

confidence: 90%

Estimating ergodization time of a chaotic many-particle system from a time reversal of equilibrium noise

Tarkhov

Fine

2018

New J. Phys.

View full text Add to dashboard Cite

We propose a method of estimating ergodization time of a chaotic many-particle system by monitoring equilibrium noise before and after time reversal of dynamics(Loschmidt echo). The ergodization time is defined as the characteristic time required to extract the largest Lyapunov exponent from a system's dynamics. We validate the method by numerical simulation of an array of coupled Bose-Einstein condensates in the regime describable by the discrete Gross-Pitaevskii equation. The quantity of interest for the method is a counterpart of out-of-time-order correlators in the quantum regime. Outline of the methodIn figure 1, we outline the method. It consists of the following steps.

show abstract

Fidelity as a marker of topological phase transitions in 2D Dirac materials

Bolívar

Cordero

Nagy

et al. 2018

Int J of Quantum Chemistry

View full text Add to dashboard Cite

Silicene, as other 2D buckled structures, is a gapped Dirac material with intrinsic spin-orbit coupling whose band structure can be controlled by applying a perpendicular electric field. It presents a topological phase transition from a topological insulator to a band insulator at the charge neutrality point. We present in this article a characterization of this phase transition by using fidelity of Loschmidt echoes when a magnetic and two slightly different electric fields are applied by considering the time evolution of two kinds of wave packets, one with a single Gaussian profile and the other with a double Gaussian profile creating a cat state. We also show that Zitterbewegung, classical, and revival Loschmidt periods diverge close to but not exactly at the charge neutrality point and explain this behavior.Silicene is a two dimensional crystal of silicon, belonging to a group of 2D gapped Dirac materials analogous to graphene but with a relevant intrinsic spin-orbit coupling (as compared to graphene) and a buckled structure. It has been studied theoretically [1,2] and experimentally. [3][4][5][6][7] Other gapped Dirac materials are germanene, stannene, and Pb. [8] In the case of silicene, the low energy electronic properties can be described by a Dirac Hamiltonian with a Fermi velocity v F = 4:2 × 10 5 ms − 1 and a value of the spin-orbit coupling Δ so = 4:2 meV. It has a buckling length l = 0:22Å which allows to control the band structure by applying an electric field, ℰ z = Δ z =l, perpendicular to the silicene monolayer generating a tunable band gap jΔ s, ξ j = jðΔ z − sξΔ so Þ=2j (s and ξ denote spin and valley, respectively). Silicene has a topological phase transition (TPT) [9] from a topological insulator (TI, jΔ z j < Δ so ) to a band insulator (BI, jΔ z j > Δ so ), at a charge neutrality point (CNP) Δ ð0Þ z = sξΔ so , with a gap cancellation between the perpendicular electric field and the spin-orbit coupling, thus exhibiting a semimetal behavior.Topological phases are characterized by topological charges like Chern numbers. Theoretical information measures and uncertainty relations have been used to characterize TPTs. [10][11][12][13] Recently, we have studied the time evolution of electron wave packets in silicene under perpendicular magnetic and electric fields to characterize topological-band insulator transitions. [14]

show abstract

Loschmidt echo in many-body localized phases

Cited by 34 publications

References 60 publications

Decay of spin-spin correlations in disordered quantum and classical spin chains

Decay of spin-spin correlations in disordered quantum and classical spin chains

Estimating ergodization time of a chaotic many-particle system from a time reversal of equilibrium noise

Fidelity as a marker of topological phase transitions in 2D Dirac materials

Contact Info

Product

Resources

About