Dynamical correlations and a quantum glass phase in a random hopping Bose–Hubbard model

Abstract

We investigate a system of interacting bosons with random intersite tunnelling amplitudes. We describe these by introducing Gaussian-distributed hopping integrals into the standard Bose-Hubbard model. This system has been recently shown to exhibit a quantum phase transition to a glassy state. The latter is characterized by a quenched disorder of boson wave-function phases. In this aspect, the system resembles quantum spin-glass systems that attracted much attention. By exploiting this analogy, we employ the wellestablished methodology originated by Sherrington and Kirkpatrick, which bases on the replica trick and the Trotter-Suzuki expansion. This treatment transforms the original quantum problem into an eective classical one with an additional time-like dimension. Here, we focus on autocorrelation functions of canonical variables of the eective system in the time-like domain. Deep in the disordered phase, we find a highly dynamical nature of correlations in agreement with the expected short memory of the system. This behaviour weakens while approaching and passing the phase boundary, where in the glassy phase asymptotically non-vanishing correlations are encountered. Thus, the state features infinite memory, which is consistent with the quenched nature of glassy disorder with random but frozen boson phases.

Stability of the replica-symmetric solution in the off-diagonally-disordered Bose–Hubbard model

“…where R kk are dynamic self-correlations [27] we introduce the replica symmetry by further simplifying the static part Q αα = q. We treat λ P Q kαk α analogously, while ν kα just drops the α index in the replica symmetric case.…”

“…In this section, we are only interested in the dependence on Trotter indices, so we consider replica-indexed matrices [G uv ] (k,k+Δk),(k+l,k+l+Δl) as a whole. Combining rules (24) and (27), one can see that when two expressions are indexed with different replicas, the average of their product does not depend on the relative difference of their Trotter indices. Thus, among the elements of a matrix [G uv ] (k,k+Δk),(k+l,k+l+Δl) , those with the most repeated replica indices (so diagonal elements) will depend on at least as many Trotter indices as other elements of the same matrix.…”

“…From rule (27), one can see that the third term in equation ( 21) will always contain at least the same dependence on Trotter indices as the second term. Therefore, out of the two, focusing on the third term only captures the dependence of both.…”

Emergence of a superglass phase in the random hopping Bose-Hubbard model

“…It was found that in such a case there is no direct transition between superfluid and Mott insulator phases, as a Bose glass phase emerges between them upon introduction of disorder [15]. The case discussed in this work is the less explored one of random interactions [16][17][18][19][20], called the off-diagonal disorder. Such a system is frustrated and thus the glassy phase that emerges in it differs from the Bose glass [21].…”

Reentrant phase transitions involving glassy and superfluid orders in the random hopping Bose–Hubbard model

“…Next to the widely studied diagonally-disordered ones [12,13,14,9], the off-diagonal disorder class offers a connection to the spin-glass [15,16] realm -the paradigmatic foundation for understanding disordered systems. While the diagonal disorder, i.e., the one present in the potential energy, leads to the emergence of the amorphic Bose glass (BG) phase [14], the off-diagonal one, meaning randomness of the kinetic energy, has been recently shown [17,18,19] to result in a different kind of glassiness involving complex phases of bosons in analogy to spin orientation in spin-glass systems.…”