Breakdown of self-averaging in the Bose glass

Hegg, Anthony; Krüger, Frank; Phillips, Philip

doi:10.1103/physrevb.88.134206

Cited by 11 publications

(10 citation statements)

References 39 publications

(75 reference statements)

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“…Then the inhomogeneous nature of the SF and BG phases is addressed through the study of the probability distribution of the SF response which shows strikingly different proper ties when increasing lattice sizes. Shrinking in the SF phase, it clearly broadens in the BG regime, thus indicating the absence of self-averaging [52], We also demonstrate that all sites remain compressible, ruling out a percolation picture. Our conclusions are supported by careful groundstate (GS) simulations through the so-called /^-doubling scheme, disorder averaging over a very large number of realizations, detailed error bar evaluation, and systematic finite-size scaling analysis.…”

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confidence: 57%

Critical Properties of the Superfluid—Bose-Glass Transition in Two Dimensions

et al. 2015

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We investigate the superfluid (SF) to Bose-glass (BG) quantum phase transition using extensive quantum Monte Carlo simulations of two-dimensional hard-core bosons in a random box potential. T=0 critical properties are studied by thorough finite-size scaling of condensate and SF densities, both vanishing at the same critical disorder Wc=4.80(5). Our results give the following estimates for the critical exponents: z=1.85(15), ν=1.20(12), η=-0.40(15). Furthermore, the probability distribution of the SF response P(lnρSF) displays striking differences across the transition: while it narrows with increasing system sizes L in the SF phase, it broadens in the BG regime, indicating an absence of self-averaging, and at the critical point P(lnρSF+zlnL) is scale invariant. Finally, high-precision measurements of the local density rule out a percolation picture for the SF-BG transition.

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confidence: 57%

Critical Properties of the Superfluid—Bose-Glass Transition in Two Dimensions

et al. 2015

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“…It has been argued by various authors [1,13,20,21] that the BG is a Griffiths phase [34], with the behavior dominated by the existence of rare SF regions. As pointed out recently [35,36], the existence of rare SF regions is intimately related to a breakdown of self-averaging. Although the lack of ergodicity and selfaveraging are common features of conventional spin glasses [37,38] and despite the fact that the BG is dubbed a 'glass', an Edwards-Anderson-like glassy order parameter has not yet been shown to exist in this phase.…”

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confidence: 89%

Replica symmetry breaking in the Bose glass

Thomson

Krüger

2014

EPL

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We investigate the nature of the Bose glass phase of the disordered Bose-Hubbard model in d > 2 and demonstrate the existence of a glass-like replica symmetry breaking (RSB) order parameter in terms of particle number fluctuations. Starting from a strong-coupling expansion around the atomic limit, we study the instability of the Mott insulator towards the formation of a Bose glass. We add some infinitesimal RSB, following the Parisi hierarchical approach in the most general form, and observe its flow under the momentum-shell renormalization group scheme. We find a new fixed point with one-step RSB, corresponding to the transition between the Mott insulator and a Bose glass phase with hitherto unseen RSB. The susceptibility associated to infinitesimal RSB perturbation in the Mott insulator is found to diverge at the transition with an exponent of γ = 1/d. Our findings are consistent with the expectation of glassy behavior and the established breakdown of self-averaging. We discuss the possibility of measuring the glass-like order parameter in optical lattice experiments as well as in certain spin systems that are in the same universality class as the Bose-Hubbard model.

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“…Despite intense analytical [56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72] and numerical [73][74][75][76][77][78][79][80][81][82][83][84] study, many questions as to the nature of the BG remain. Various theoretical proposals have been put forward suggesting ways to observe the BG in experiments [70,[83][84][85][86][87][88][89].…”

Section: The Disordered Bose-hubbard Modelmentioning

confidence: 99%

Finding the phase diagram of strongly correlated disordered bosons using quantum quenches

2021

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The question of how the low-energy properties of disordered quantum systems may be connected to exotic localization phenomena at high energy is a key open question in the context of quantum glasses and many-body localization. In Ref.[1], we have shown that key features of the excitation spectrum of a disordered system can be efficiently probed from out-of-equilibrium dynamics following a quantum quench, providing distinctive signatures of the various phases. Here, we extend this work by providing a more in-depth study of the behavior of the quench spectral functions associated to different observables and investigating an extended parameter regime. We provide a detailed introduction to quench spectroscopy for disordered systems and show how spectral properties can be probed using both local operators and two-point correlation functions. We benchmark the technique using the one-dimensional Bose-Hubbard model in the presence of a random external potential, focusing on the low-lying excitations, and demonstrate that quench spectroscopy can distinguish the Mott insulator, superfluid, and Bose glass phases. We then explicitly reconstruct the zero-temperature phase diagram of the disordered Bose-Hubbard at fixed filling using two independent methods, both experimentally accessible via time-of-flight imaging and quantum gas microscopy respectively, and demonstrate that quench spectroscopy can give valuable insights as to the distribution of rare regions within disordered systems.

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Breakdown of self-averaging in the Bose glass

Cited by 11 publications

References 39 publications

Critical Properties of the Superfluid—Bose-Glass Transition in Two Dimensions

Critical Properties of the Superfluid—Bose-Glass Transition in Two Dimensions

Replica symmetry breaking in the Bose glass

Finding the phase diagram of strongly correlated disordered bosons using quantum quenches

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