Many body localization in Heisenberg XXZ magnet in a random field

Znidaric, Marko; Prosen, Tomaz; Prelovsek, Peter

doi:10.48550/arxiv.0706.2539

Cited by 8 publications

(16 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In conclusion, our results of numerical simulations on the interplay of disorder and correlations in the spin and thermal transport within Heisenberg spin chains can be summarized by the following scenario: (a) finite randomfield disorder W > 0 induces localization and vanishing dc transport at any T in the XY limit, corresponding to noninteracting fermions 1 , and as well generally at T = 8,9 (for ∆ > 0 considered here); (b) apart from the latter two limits the system appears to behave as a normal conductor with finite σ dc > 0, κ dc > 0 both for various ∆ > 0 and T > 0; in particular, we do not find any evidence for a phase transition by varying T or W ; (c) dynamical transport (at least for larger disorder) reveals a generic cusp-like nonanalytic behavior for ω, analogous to long-time tails in classical dynamical systems in low-dimensional 23 or 2D strongly disordered systems; (d) with increasing disorder the system reveals a crossover from the Drude-like to a pseudo-localized dynamics with very low dc σ dc , κ dc 11 ; and (e) similar conclusions seem to hold for the bond disorder.…”

mentioning

confidence: 97%

“…Even if the system remains localized at T = 0, an arbitrary low temperature could delocalize it or a finite critical temperature 4,5 might be needed to drive it to a normal state at high temperatures. There are also indications that in the presence of large disorder even at high T many body states can appear effectively localized 6,11 .…”

mentioning

confidence: 99%

“…Nevertheless, due to the large disorder W the dynamics is non Drude-like, since the maximum of σ(ω) as well as of κ(ω) appears at a finite ω * > 0, in analogy with the localization at ∆ = 0. Hence, at ∆ > 0 and large W we are dealing with pseudo-localized dynamics 6,11 . Another novel feature of this regime appears to be a generic (nonanalytic) cusp-like behavior at low frequencies, σ(ω) ≃ σ dc + α|ω|, κ(ω) ≃ κ dc + γ|ω|, for which so far we cannot offer an analysis.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Finite-temperature transport in disordered Heisenberg chains

et al. 2009

View full text Add to dashboard Cite

We investigate real-space localization in the few-particle regime of the XXZ spin-1/2 chain with a random magnetic field. Our investigation focuses on the time evolution of the spatial variance of non-equilibrium densities, as resulting for a specific class of initial states, namely, pure product states of densely packed particles. Varying the strength of both particle-particle interactions and disorder, we numerically calculate the long-time evolution of the spatial variance σ(t). For the two-particle case, the saturation of this variance yields an increased but finite localization length, with a parameter scaling different to known results for bosons. We find that this interaction-induced increase is the stronger the more particles are taken into account in the initial condition. We further find that our non-equilibrium dynamics are clearly inconsistent with normal diffusion and instead point to subdiffusive dynamics with σ(t) ∝ t 1/4 .

show abstract

mentioning

confidence: 97%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Finite-temperature transport in disordered Heisenberg chains

et al. 2009

View full text Add to dashboard Cite

show abstract

“…If one adds interactions, the system can find itself in the thermal or MBL phase, usually dependent on disorder strength. Starting with some information in a specific position, in the thermal phase it will flow away and cannot be recovered locally, and in the MBL phase there will still be traces present at the same position after arbitrarily long times, despite some information slowly flowing away [7][8][9].…”

mentioning

confidence: 99%

Localization with random time-periodic quantum circuits

et al. 2018

View full text Add to dashboard Cite

We consider a random time evolution operator composed of a circuit of random unitaries coupling even and odd neighboring spins on a chain in turn. In spirit of Floquet evolution, the circuit is timeperiodic; each timestep is repeated with the same random instances. We obtain analytical results for arbitrary local Hilbert space dimension d: On a single site, average time evolution acts as a depolarising channel. In the spin 1/2 (d = 2) case, this is further quantified numerically. For that, we develop a new numerical method that reduces complexity by an exponential factor. Haardistributed unitaries lead to full depolarization after many timesteps, i.e. local thermalization. A unitary probability distribution with tunable coupling strength allows us to observe a many-body localization transition. In addition to a spin chain under a unitary circuit, we consider the analogous problem with Gaussian circuits. We can make stronger statements about the entire covariance matrix instead of single sites only, and find that the dynamics is localising. For a random time evolution operator homogeneous in space, however, the system delocalizes. CONTENTS 15A. Gaussian circuits: Uncoupled case 15 B. Spins: Uncoupled case 15 C. Spins: Simplification for numerical calculations 16 References 16 arXiv:1805.08487v2 [cond-mat.stat-mech]

show abstract

“…Many-body localization (MBL) [1][2][3][4][5][6][7][8][9][10] has become a subject of intense theoretical and experimental [60][61][62][63][64][65][66][67][68][69][70] interest in recent years as an example of a mechanism by which an interacting many-body system can violate the ergodic hypothesis. In localized phases, the system retains a memory of its initial conditions in local observables at infinitely long times, thereby failing to reach thermal equilibrium.…”

mentioning

confidence: 99%

ac conductivity crossover in localized superconductors

2018

View full text Add to dashboard Cite

An important experimental signature of localization is the low-frequency AC conductivity, which typically vanishes as ω φ . The exponent φ = 2 for Anderson insulators, whereas for many body localized insulators φ is a continuously varying exponent 1 ≤ φ ≤ 2. In this work, we study the low-frequency AC conductivity of localized superconductors, in which disorder is strong enough to localize all quasiparticles, while remaining weak enough to leave superconductivity intact. We find that while the ac conductivity still follows the general form σ(ω) ∼ ω φ , the exponent φ can be markedly different from the characteristic value for localized insulators. This difference occurs due to singularities in the low-energy density of states, permitted by the effective particle-hole symmetry around the Fermi level. In particular, in certain symmetry classes at zero temperature, we obtain φ > 2. We further identify an interesting temperature dependent crossover in the scaling form of the AC conductivity, which could be useful for the experimental characterization of localized superconductors. CONTENTS

show abstract

Many body localization in Heisenberg XXZ magnet in a random field

Cited by 8 publications

References 12 publications

Finite-temperature transport in disordered Heisenberg chains

Finite-temperature transport in disordered Heisenberg chains

Localization with random time-periodic quantum circuits

ac conductivity crossover in localized superconductors

Contact Info

Product

Resources

About