Weak- versus strong-disorder superfluid—Bose glass transition in one dimension

Abstract

Using large-scale simulations based on matrix product state and quantum Monte Carlo techniques, we study the superfluid to Bose glass-transition for one-dimensional attractive hard-core bosons at zero temperature, across the full regime from weak to strong disorder. As a function of interaction and disorder strength, we identify a Berezinskii-Kosterlitz-Thouless critical line with two different regimes. At small attraction where critical disorder is weak compared to the bandwidth, the critical Luttinger parameter Kc takes its universal Giamarchi-Schulz value Kc = 3/2. Conversely, a nonuniversal Kc > 3/2 emerges for stronger attraction where weak-link physics is relevant. In this strong disorder regime, the transition is characterized by self-similar power-law distributed weak links with a continuously varying characteristic exponent α.

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

“…Second, we used functional renormalization group simulations to compute the conductance at zero temperature, which also resolves the delocalized ground-state region. While the FRG simulations for the conductance are computationally cheap and can be pushed to system sizes as large as L ∼ 10 6 , the phase boundaries, in particular, at large negative interaction strengths V −2t, are quantitatively different from the results of other methods (see, e.g., [46]). Thus, improvements in the FRG scheme are necessary to render the method accurate at larger interactions strengths as well, which poses an interesting direction for further method development.…”

“…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]. …”

“…In the ground state, i.e., at ε = 0, and for small system sizes, only the phase boundary at large negative values of V is resolved by a clear maximum in var S vN , while this is not the case for the transition at small negative values. We believe this to be a consequence of (i) the large single-particle localization length on the attractive side and (ii) the different nature of the Luttinger-liquid to localization transition at ε = 0 (see the discussion in [46,67]). By comparison of Fig.…”

“…For the purpose of clarifying the question of an inverted mobility edge on the attractive side, no conclusive picture arises from the existing results for V = 2t: according to Refs. [29,46], V = −2t sits right at the edge of the Luttinger-liquid phase and any finite disorder drives the system into the localized regime in the ground state (see, e.g., the ground-state phase diagram presented in Figs. 3 and 4(a)).…”

From eigenstate to Hamiltonian: Prospects for ergodicity and localization

“…where the first term represents the pairwise spin-spin couplings acting on the L − 1 bonds of the open chain, and the second one is a sum of L on-site random field terms. The above model (2.1) has been intensely studied in the past, owing to its localization properties in the ground-state [6,[20][21][22], as well as more recently as a paradigmatic example for the MBL problem for highly excited states [9][10][11].…”