Exploring the many-body localization transition in two dimensions

Choi, Jae-yoon; Hild, Sebastian; Zeiher, Johannes; Schauß, Peter; Rubio-Abadal, Antonio; Yefsah, Tarik; Khemani, Vedika; Huse, David A.; Bloch, Immanuel; Groß, Christian

doi:10.1126/science.aaf8834

Cited by 961 publications

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“…That such questions can be probed experimentally at all is the result of advances in preparing, controlling and measuring such systems in a variety of platforms, including ultracold atomic [14,15], trapped ion systems [16,17], superconducting qubit arrays [18], NV-centers [19] etc. These developments bring the investigation of outof-equilibrium many-body quantum dynamics within experimental reach; and, indeed, both the failure of thermalization in integrable one-dimensional quantum systems [6,20,21] and the presence of MBL regimes have been experimentally demonstrated [22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2017

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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.

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Section: Introductionmentioning

confidence: 99%

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

et al. 2017

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“…Generically, a MIT features a mobility edge separating a metallic phase, where waves are extended and propagate diffusively, from an insulating phase where waves are localized. Recently observed in spinless timereversal invariant systems [6][7][8][9][10], Anderson MITs still remain challenging and elusive in more exotic configurations where time-reversal or spin-rotation is broken, or when interactions are present [11,12]. Furthermore, transport properties near the critical point, affected by the multifractal character of the eigenstates [13], have been little studied in actual experiments [14].…”

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confidence: 99%

Coherent forward scattering as a signature of Anderson metal-insulator transitions

2017

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We show that the coherent forward scattering (CFS) interference peak amplitude sharply jumps from zero to a finite value upon crossing a metal-insulator transition. Extensive numerical simulations reveal that the CFS peak contrast obeys the one-parameter scaling hypothesis and gives access to the critical exponents of the transition. We also discover that the critical CFS peak directly controls the spectral compressibility at the transition where eigenfunctions are multifractal, and we demonstrate the universality of this property with respect to various types of disorder. Related to Anderson localization (AL), coherent forward scattering (CFS) is a robust interference effect which triggers a macroscopic peak in the forward direction of the momentum distribution n(k, t) obtained after an initial plane wave |k 0 has evolved through a bulk disordered system [15][16][17]. While CFS resembles the well-known coherent backscattering (CBS) effect, which is due to the pair interference of time-reversed scattering sequences and yields a peak in the backward direction [18], the two effects turn out to be fundamentally different. Indeed, the CBS peak relies on time-reversal symmetry (TRS) [19] and exists on both sides of the MIT, with no discontinuous behavior as the mobility edge is crossed [20]. In marked contrast, CFS requires Anderson localization to show up (it is absent in the metallic phase) and is present whether or not TRS is broken [21,22]. While the experimental observation of CBS in momentum space has been recently achieved with cold atoms [23], no observation of CFS has been reported so far. On the theoretical side, CFS has been studied in one ) and metallic (bottom, W = 12J) phases of the cubic 3D Anderson model (lattice constant a, tunneling rate J) when an initial plane wave |k0 is numerically propagated up to time t = 8000 /J. The energy is set to E = J and k0 = π/(3a)êx. The CFS and CBS peaks are visible at k0 and −k0 respectively. The solid curve is a cut along kx. Right: time evolution of the normalized CFS contrast Λ in the three phases.dimension and two dimensions [15,17,21], but not in three dimensions where an Anderson MIT takes place. In this article, we numerically demonstrate that the CFS

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“…This includes the observation of genuine nonequilibrium phenonema such as many-body localization [1][2][3], quantum time crystals [4,5], or particle-antiparticle production in the Schwinger model [6]. It remains, however, a major challenge to identify universal properties in these diverse dynamical phenomena on general grounds.…”

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Connecting dynamical quantum phase transitions and topological steady-state transitions by tuning the energy gap

Wang

Xianlong

2018

Phys. Rev. A

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Considerable theoretical and experimental efforts have been devoted to the quench dynamics, in particular, the dynamical quantum phase transition (DQPT) and the steady-state transition. These developments have motivated us to study the quench dynamics of the topological systems, from which we find the connection between these two transitions, that is, the DQPT, accompanied by a nonanalytic behavior as a function of time, always merges into a steady-state transition signaled by the nonanalyticity of observables in the steady limit. As the characteristic time of the DQPT diverges, it exhibits universal scaling behavior, which is related to the scaling behavior at the corresponding steady-state transition.Isolated quantum many-body systems can nowadays be realized in quantum-optical systems such as ultracold atoms or trapped ions which has opened up the perspective to experimentally study properties beyond the thermodynamic equilibrium paradigm. This includes the observation of genuine nonequilibrium phenonema such as many-body localization [1][2][3], quantum time crystals [4,5], or particle-antiparticle production in the Schwinger model [6]. It remains, however, a major challenge to identify universal properties in these diverse dynamical phenomena on general grounds. Considerable effects have been made to the formulation of various notions of nonequilibrium phase transitions [7][8][9][10][11][12][13][14][15][16][17] which are seen as promising attempts to extend elementary equilibrium concepts such as scaling and universality to the nonequilibrium regime. Among these notions there is the concept of a steady-state transition, which is signaled by a nonanalytic change of physical properties as a function of a parameter of the nonequilibrium protocol in the asymptotic long-time state of the system [8,11,12]. An example is the universal logarithmic divergence of the Hall conductance in the steady state of topological insulators after a quench [16,17]. Another important concept is that of dynamical quantum phase transitions (DQPTs) [15], recently observed experimentally [18,19], which occur on transient and intermediate time scales accompanied by a nonanalytic behavior as a function of time instead of a conventional order parameter. In the context of such developments, it is then a natural question to ask, whether and how these two notions of phase transitions are connected.The DQPT and the steady-state transition under the symmetry-breaking picture have been recently connected in the long-range-interacting Ising chain [20] by relating the singularities of Loschmidt echo to the zeros of local order parameters. In this work, we study the connection between the DQPT and the steady-state transition in a topological system where the local order parameters are absent. The connection is schematically displayed in Fig. 1. The characteristic time scale t * associated with DQPTs diverges when tuning the energy gap of the postquench Hamiltonian towards the steady-state transition at the gap-closing point. The steady-state trans...

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Exploring the many-body localization transition in two dimensions

Cited by 961 publications

References 62 publications

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

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

Coherent forward scattering as a signature of Anderson metal-insulator transitions

Connecting dynamical quantum phase transitions and topological steady-state transitions by tuning the energy gap

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