Superfluid density and quasi-long-range order in the one-dimensional disordered Bose–Hubbard model

Gerster, Matthias; Rizzi, Matteo; Tschirsich, Ferdinand; Silvi, Pietro; Fazio, Rosario; Montangero, Simone

doi:10.1088/1367-2630/18/1/015015

Cited by 41 publications

(52 citation statements)

References 55 publications

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“…The cyan line shows the gaps of the Mott insulator in the disorder-free system taken from [14], which signals the transition between the Mott insulator and the BG phase in the presence of disorder. We also show the ( ) ¥ = K 3 2 line obtained by the tree tensor network (TTN) method [13] (orange), which agrees with our GS-line within the error bars. As expected, in the weak-link regime, the TTN line ends inside the BG phase.…”

supporting

confidence: 85%

“…Another consequence of the small angle intersection is that the critical value of K on the sXY line is only slightly higher than the GS value of 3/2. Under such circumstances, a brute-force observation of the violation of the GS scenario in the vicinity of the tri-critical point becomes problematic (see [13]) even though our data in figure 2 are not compatible with GS even when done with a brute force analysis.…”

Section: 7mentioning

confidence: 78%

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Superfluid–insulator transition in strongly disordered one-dimensional systems

et al. 2016

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We present an asymptotically exact renormalization-group theory of the superfluid-insulator transition in one-dimensional (1D) disordered systems, with emphasis on an accurate description of the interplay between the Giamarchi-Schulz (instanton-anti-instanton) and weak-link (scratched-XY) criticalities. Combining the theory with extensive quantum Monte Carlo simulations allows us to shed new light on the ground-state phase diagram of the 1D disordered Bose-Hubbard model at unit filling. c KF , a single arbitrarily weak impurity gets renormalized to an infinitely high (in relative low-energy units) barrier; for > K K c KF , by contrast, the link gets progressively healed with increasing length scale and becomes asymptotically transparent.A controlled theory of SF-BG transition in 1D, yielding, in particular, = K 3 2 c , was first developed by Giamarchi and Schulz (GS) using a perturbative RG treatment of disorder [6]. In the same work, the authors conjectured that there might exist an alternative strong-disorder scenario not captured by their theory. Subsequently, some of us demonstrated [3] that the GS result is valid beyond the lowest-order RG equations and is, in fact, a generic answer thanks to the above-mentioned asymptotically exact mechanism of instanton-antiinstanton proliferation, which is tantamount to the arguments presented in the original papers by Kosterlitz and Thouless. A 'strong-disorder' alternative therefore seems unlikely. Nevertheless, Altman et al, inspired by the 1D-specific classical-field mechanism of destroying global SF stiffness by anomalously rare but anomalously weak links, speculated that an alternative strong-disorder scenario does exist [8]. To corroborate their idea, the authors employed a real-space RG treatment. It is important to realize, however, that the treatment of [8] is essentially uncontrolled, abandoning the usual LL paradigm in favor of the 'Coulomb blockade' single-particle nomenclature promoted to macroscopic scales.This, in turn, was countered by the theorem of critical self-averaging, which implies that the LL picture holds at criticality [9]. In combination with the Kane-Fisher result that a single weak link is an irrelevant perturbation at > K 1, this seemed to leave no room for alternatives to the GS scenario because no other asymptotically exact mechanisms for destruction of superfluidity were known. However, recently three of us have realized [10] that previous studies have overlooked the difference in the outcome of the Kane-Fisher renormalization for weak links, which occur with finite probability per unit length, relative to the one for a single link in an infinite system. The difference is in the classical-field mechanism of suppressing the SF stiffness by weak links (for a discussion, see [9,11]): in absolute units, the Kane-Fisher renormalization is always towards making links weaker-and the weaker the link, the stronger its effect on Λ. Despite the fact that at > K 1 a single weak link cannot destroy superfluidity, the combined effect of all anomalously...

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confidence: 85%

Section: 7mentioning

confidence: 78%

Superfluid–insulator transition in strongly disordered one-dimensional systems

et al. 2016

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“…The DBHM have been studied with diverse techniques: mean field [11], projected Gutzwiller method [3], site independent and multisite mean-field method [12,13], stochastic mean field [14], quantum Monte Carlo [15][16][17], density matrix renormalisation group (DMRG) [18,19] for 1D system and numerous others [20][21][22][23][24]. In all the cases the introduction of disorder leads to the emergence of BG phase which is characterized by finite compressibility and zero superfluid stiffness.…”

Section: Introductionmentioning

confidence: 99%

Enhancement of the Bose glass phase in the presence of an artificial gauge field

et al. 2019

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We examine the effects of an artificial gauge field and finite temperature in a two-dimensional disordered Bose-Hubbard model. The disorder considered is diagonal and quenched in nature. A signature of disorder in the Bose-Hubbard model is the Bose glass phase. Our work shows that the introduction of an artificial gauge field enhances the domain of the Bose glass phase in the phase diagram. Most importantly, the size of the domain can be tuned with the strength of the artificial gauge field. The introduction of the finite temperature effects is essential to relate theoretical results with the experimental realizations. For our studies we use the single site and cluster Gutzwiller mean-field theories. The results from the latter are more reliable as it better describes the correlation effects. Our results show that the Bose glass phase has a larger domain with the latter method.arXiv:1807.00269v2 [cond-mat.quant-gas]

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“…particularly well known for the case of bosons with repulsive interactions in the Bose-Hubbard model (see, e.g., [34][35][36]). The reason are the disorder-induced density deviations (or, in other words, fluctuations in the local chemical potential) that drive density locally away from commensurability.…”

Section: Introductionmentioning

confidence: 99%

Many-body localization of spinless fermions with attractive interactions in one dimension

et al. 2018

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We study the finite-energy density phase diagram of spinless fermions with attractive interactions in one dimension in the presence of uncorrelated diagonal disorder. Unlike the case of repulsive interactions, a delocalized Luttinger-liquid phase persists at weak disorder in the ground state, which is a well-known result. We revisit the ground-state phase diagram and show that the recently introduced occupation-spectrum discontinuity computed from the eigenspectrum of the one-particle density matrix is noticeably smaller in the Luttinger liquid compared to the localized regions. Moreover, we use the functional renormalization group scheme to study the finite-size dependence of the conductance, which also resolves the existence of the Luttinger liquid and is computationally cheap. Our main results concern the finite-energy density case. Using exact diagonalization and by computing various established measures of the many-body localization-delocalization transition, we argue that the zero-temperature Luttinger liquid smoothly evolves into a finite-energy density ergodic phase without any intermediate phase transition.

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Superfluid density and quasi-long-range order in the one-dimensional disordered Bose–Hubbard model

Cited by 41 publications

References 55 publications

Superfluid–insulator transition in strongly disordered one-dimensional systems

Superfluid–insulator transition in strongly disordered one-dimensional systems

Enhancement of the Bose glass phase in the presence of an artificial gauge field

Many-body localization of spinless fermions with attractive interactions in one dimension

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