Time evolution of many-body localized systems in two spatial dimensions

Kshetrimayum, Augustine; Goihl, Marcel; Eisert, Jens

doi:10.1103/physrevb.102.235132

Cited by 62 publications

(38 citation statements)

References 70 publications

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“…Our techniques have the added value of directly tackling the thermodynamic limit: Residual finite-size effects are encompassed by the so-called bond dimension of the ansatz and could be accounted for in a rather systematic way [40][41][42][43][44]. These features have made two-dimensional tensor networks a very suitable tool for studying intricate condensed matter problems, not only via their ground states [45][46][47][48] but even beyond [49][50][51][52][53][54], as well as finite temperature properties of both classical and quantum models in two spatial dimensions [33,34,[55][56][57][58][59][60][61][62]. The present work builds upon and develops this substantial technical machinery.…”

Section: Introductionmentioning

confidence: 99%

The classical two-dimensional Heisenberg model revisited: An $SU(2)$-symmetric tensor network study

et al. 2021

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The classical Heisenberg model in two spatial dimensions constitutes one of the most paradigmatic spin models, taking an important role in statistical and condensed matter physics to understand magnetism. Still, despite its paradigmatic character and the widely accepted ban of a (continuous) spontaneous symmetry breaking, controversies remain whether the model exhibits a phase transition at finite temperature. Importantly, the model can be interpreted as a lattice discretization of the O(3)O(3) non-linear sigma model in 1+11+1 dimensions, one of the simplest quantum field theories encompassing crucial features of celebrated higher-dimensional ones (like quantum chromodynamics in 3+13+1 dimensions), namely the phenomenon of asymptotic freedom. This should also exclude finite-temperature transitions, but lattice effects might play a significant role in correcting the mainstream picture. In this work, we make use of state-of-the-art tensor network approaches, representing the classical partition function in the thermodynamic limit over a large range of temperatures, to comprehensively explore the correlation structure for Gibbs states. By implementing an SU(2)SU(2) symmetry in our two-dimensional tensor network contraction scheme, we are able to handle very large effective bond dimensions of the environment up to \chi_E^\text{eff} \sim 1500χEeff∼1500, a feature that is crucial in detecting phase transitions. With decreasing temperatures, we find a rapidly diverging correlation length, whose behaviour is apparently compatible with the two main contradictory hypotheses known in the literature, namely a finite-TT transition and asymptotic freedom, though with a slight preference for the second.

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Section: Introductionmentioning

confidence: 99%

The classical two-dimensional Heisenberg model revisited: An $SU(2)$-symmetric tensor network study

et al. 2021

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“…Since the Liouvillian evolution involves non-Hermitian operators, an issue here is to find a reliable non-Hermitian algorithm that could substitute the alternating least-squares scheme used in the two-site variational minimization in the standard FU algorithm. There are, however, recent works on time evolution in closed systems [39][40][41][42] for which FU presents problems with stability, meaning SU can be more accurate. However, very recent work by McKeever and Szymanska [43] has shown that a variation on full updatefull environment truncation-can indeed improve the stability of iPEPO.…”

Section: Resultsmentioning

confidence: 99%

On the stability of the infinite Projected Entangled Pair Operator ansatz for driven-dissipative 2D lattices

et al. 2021

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We present calculations of the time-evolution of the driven-dissipative XYZ model using the infinite Projected Entangled Pair Operator (iPEPO) method, introduced by [A. Kshetrimayum, H. Weimer and R. Orús, Nat. Commun. 8, 1291 (2017)]. We explore the conditions under which this approach reaches a steady state. In particular, we study the conditions where apparently converged calculations may become unstable with increasing bond dimension of the tensor-network ansatz. We discuss how more reliable results could be obtained.

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“…At the same time, experiments provided strong support for the stability of the MBL phase on long timescales, verified a number of theoretical predictions, and started exploring new regimes where the theoretical understanding is incomplete [10][11][12][13]. In particular, experiments suggested the existence of MBL in higher dimension [14,15] and also probe the so-called many-body mobility edges [16], although theoretically their existence is subject to debate [17][18][19][20][21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 83%

Localization of a mobile impurity interacting with an Anderson insulator

Brighi,

Michailidis,

Kirova

et al. 2021

Preprint

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Time evolution of many-body localized systems in two spatial dimensions

Cited by 62 publications

References 70 publications

The classical two-dimensional Heisenberg model revisited: An $SU(2)$-symmetric tensor network study

The classical two-dimensional Heisenberg model revisited: An $SU(2)$-symmetric tensor network study

On the stability of the infinite Projected Entangled Pair Operator ansatz for driven-dissipative 2D lattices

Localization of a mobile impurity interacting with an Anderson insulator

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