Mott glass to superfluid transition for random bosons in two dimensions

Abstract

We study the zero temperature superfluid-insulator transition for a two-dimensional model of interacting, lattice bosons in the presence of quenched disorder and particle-hole symmetry. We follow the approach of a recent series of papers by Altman, Kafri, Polkovnikov, and Refael, in which the strong disorder renormalization group is used to study disordered bosons in one dimension. Adapting this method to two dimensions, we study several different species of disorder and uncover universal features of the superfluid-insulator transition. In particular, we locate an unstable finite disorder fixed point that governs the transition between the superfluid and a gapless, glassy insulator. We present numerical evidence that this glassy phase is the incompressible Mott glass and that the transition from this phase to the superfluid is driven by percolation-type process. Finally, we provide estimates of the critical exponents governing this transition.

Dynamical Conductivity across the Disorder-Tuned Superconductor-Insulator Transition

“…5) with a critical value of σ Ã ≈ 0.5σ Q . For a detailed comparison of the critical exponents and σ Ã with previous results [42], see Appendix C.…”

Anomalous Quantum Glass of Bosons in a Random Potential in Two Dimensions

“…This state has been the subject of numerous studies [1][2][3][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] but many of its properties are still not well understood. Two types of glass states are known; the compressible Bose glass (BG) and the incompressible Mott glass (MG), with the latter commonly believed to appear only at commensurate filling fractions in systems with particle-hole symmetry [18][19][20][26][27][28][29]. The currently prevailing notion is that the glass state in the 2D BHM with random potentials is always of the compressible BG type [20][21][22]25].…”

“…This form has previously been found in random quantum spin systems [29,35], where κ corresponds to the magnetic susceptibility and one expects it to vanish as T → 0 because of spin-inversion symmetry (corresponding to particle-hole symmetry for bosons). Such an incompressible and insulating quantum glass is called an MG [13] and has also been shown to exist in variants of the 2D random BHM where particle-hole symmetry is explicitly built in [27,28] (and Ref.…”

Breakdown of self-averaging in the Bose glass

“…It is in the difficult intermediate parameter space where the BG phase obtains. It has been argued by various authors 1,[3][4][5][6][7] that the BG is a quantum Griffiths phase dominated by arbitrarily large SF regions that are, however, exponentially suppressed. Despite the abundance of numerical 3,[8][9][10][11][12][13] and analytical [14][15][16][17][18][19][20][21][22][23] work on the subject, it is only recently that several aspects of this model have been fully understood.…”