Spin transport of weakly disordered Heisenberg chain at infinite temperature

Khait, Ilia; Gazit, Snir; Yao, Norman Y.; Auerbach, Assa

doi:10.1103/physrevb.93.224205

Cited by 77 publications

(88 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Most notably, however, the time dependence of σ(t) is inconsistent with diffusion, as can be seen easiest from the non-constant D(t). In fact, σ(t) points to superdiffusion [37,40], contrary to [46]. Now, we turn to the untypical initial state |ψ(0) , i.e., the case of equal c k .…”

Section: Numerical Methods and Resultsmentioning

confidence: 99%

Real-time broadening of nonequilibrium density profiles and the role of the specific initial-state realization

et al. 2017

View full text Add to dashboard Cite

The real-time broadening of density profiles starting from non-equilibrium states is at the center of transport in condensed-matter systems and dynamics in ultracold atomic gases. Initial profiles close to equilibrium are expected to evolve according to linear response, e.g., as given by the current correlator evaluated exactly at equilibrium. Significantly off equilibrium, linear response is expected to break down and even a description in terms of canonical ensembles is questionable. We unveil that single pure states with density profiles of maximum amplitude yield a broadening in perfect agreement with linear response, if the structure of these states involves randomness in terms of decoherent off-diagonal density-matrix elements. While these states allow for spin diffusion in the XXZ spin-1/2 chain at large exchange anisotropies, coherences yield entirely different behavior.

show abstract

Section: Numerical Methods and Resultsmentioning

confidence: 99%

Real-time broadening of nonequilibrium density profiles and the role of the specific initial-state realization

et al. 2017

View full text Add to dashboard Cite

show abstract

“…[58], provided the interpretation of these results in terms of Griffiths physics. These numerical studies, as well as subsequent work using exact diagonalization [89,90], and approximate memory-matrix approaches [91] found anomalous diffusion at essentially all values of disorder. (In Ref.…”

Section: Numerical Evidencementioning

confidence: 99%

Rare‐region effects and dynamics near the many‐body localization transition

et al. 2017

View full text Add to dashboard Cite

The low-frequency response of systems near the many-body localization phase transition, on either side of the transition, is dominated by contributions from rare regions that are locally "in the other phase", i.e., rare localized regions in a system that is typically thermal, or rare thermal regions in a system that is typically localized. Rare localized regions affect the properties of the thermal phase, especially in one dimension, by acting as bottlenecks for transport and the growth of entanglement, whereas rare thermal regions in the localized phase act as local "baths" and dominate the low-frequency response of the MBL phase. We review recent progress in understanding these rare-region effects, and discuss some of the open questions associated with them: in particular, whether and in what circumstances a single rare thermal region can destabilize the many-body localized phase.

show abstract

“…is the most studied Many-Body-Localization model where numerical results for many observables are available [42][43][44][45][46][47][48][49][50][51][52][53] As explained in the Introduction, besides the usual periodic boundary conditions σ L+1 = σ 1 , it is interesting to consider twisted boundary conditions with some angle φ for the spin operators [21] …”

Section: Many-body-localization Models With Twisted Boundary Condmentioning

confidence: 99%

Many-body-localization transition: sensitivity to twisted boundary conditions

Monthus¹

2017

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

For disordered interacting quantum systems, the sensitivity of the spectrum to twisted boundary conditions depending on an infinitesimal angle φ can be used to analyze the Many-Body-Localization Transition. The sensitivity of the energy levels En(φ) is measured by the level curvature Kn = E ′′ n (0), or more precisely by the Thouless dimensionless curvature kn = Kn/∆n, where ∆n is the level spacing that decays exponentially with the size L of the system. For instance ∆n ∝ 2 −L in the middle of the spectrum of quantum spin chains of L spins, while the Drude weight Dn = LKn studied recently by M. Filippone, P.W. Brouwer, J. Eisert and F. von Oppen [arXiv:1606.07291v1] involves a different rescaling. The sensitivity of the eigenstates |ψn(φ) > is characterized by the susceptibility χn = −F ′′ n (0) of the fidelity Fn = | < ψn(0)|ψn(φ) > |. Both observables are distributed with probability distributions displaying power-law tails2 , where β is the level repulsion index taking the values β GOE = 1 in the ergodic phase and β loc = 0 in the localized phase. The amplitudes A β and B β of these two heavy tails are given by some moments of the off-diagonal matrix element of the local current operator between two nearby energy levels, whose probability distribution has been proposed as a criterion for the Many-Body-Localization transition by M. Serbyn, Z. Papic and D.A. Abanin [Phys. Rev. X 5, 041047 (2015)].

show abstract

Spin transport of weakly disordered Heisenberg chain at infinite temperature

Cited by 77 publications

References 38 publications

Real-time broadening of nonequilibrium density profiles and the role of the specific initial-state realization

Real-time broadening of nonequilibrium density profiles and the role of the specific initial-state realization

Rare‐region effects and dynamics near the many‐body localization transition

Many-body-localization transition: sensitivity to twisted boundary conditions

Contact Info

Product

Resources

About