Superfluid–insulator transition in strongly disordered one-dimensional systems

Abstract

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...

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

“…We now go beyond this weak disorder limit, and turn to an investigation of the effects of varying the disorder strength ∆ such that it becomes comparable to the on-site interaction U . We consider fixed commensurate filling n = 1, a situation commonly studied in numerical works [115][116][117][118][119][120], and we demonstrate that in this regime quench spectroscopy also performs well in distinguishing all three phases, with the qualitative features in line with those discussed in Sec. IV.…”

Kosterlitz-Thouless scaling at many-body localization phase transitions

“…32 and 33 and our KT flow equations. Separately, many KT transitions have been observed in the study of disordered ground states, [77][78][79][80] although the physics in those cases are different. Exploring the connections between the KT scaling of the highly excited states in the MBL phase presented here and in the ground state is an open direction.…”

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

“…While early work established the existence of such a phase [29][30][31][32][33][60][61][62], there is an ongoing discussion on the nature of the transition between the delocalized superfluid and the localized phase (which, in the language of bosons, is a Bose-glass phase [63]). This question is not at the focus of our work and we refer the reader to the pertinent literature for details [46,[64][65][66][67][68][69][70][71][72]. …”