Quantum Glass of Interacting Bosons with Off-Diagonal Disorder

Abstract

We study disordered interacting bosons described by the Bose-Hubbard model with Gaussian-distributed random tunneling amplitudes. It is shown that the off-diagonal disorder induces a spin-glass-like ground state, characterized by randomly frozen quantum-mechanical U(1) phases of bosons. To access criticality, we employ the "n-replica trick," as in the spin-glass theory, and the Trotter-Suzuki method for decomposition of the statistical density operator, along with numerical calculations. The interplay between disorder, quantum, and thermal fluctuations leads to phase diagrams exhibiting a glassy state of bosons, which are studied as a function of model parameters. The considered system may be relevant for quantum simulators of optical-lattice bosons, where the randomness can be introduced in a controlled way. The latter is supported by a proposition of experimental realization of the system in question.

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

“…From rule (23), one can see that the third term in Eq. ( 17) will always contain at least the same dependence on Trotter indices as the second term.…”

“…It has been found that frustrated Coulomb interactions lead to the emergence of a superglass [11], again with the EA order parameter defined based on local boson density. In the case of frustrated hopping [21][22][23][24], the EA order parameter of the resulting glassy phase is based on the complex (1) phase of bosons. Here, we focus on the latter.…”

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].…”

“…In this paper, we consider a system of strongly correlated bosons with normal-distributed random hopping of nonzero mean. The model is fully connected, however, experimental realization with optical lattices is possible [19]. We study the competition between the glassy and superfluid orders, which leads to the emergence of the superglass phase, apart from the usual glass and superfluid ones.…”

“…[21]. We obtain the phase diagrams by solving numerically self-consistent equations that arise after a derivation that follows a similar scheme as our previous work [19] and its spin-glass and quantum-spin-glass predecessors [24,44]. First, we use the replica method [24] and the Trotter-Suzuki formula [45] to map the problem onto an effective classical model, to which we then apply the saddle-point method in the thermodynamic limit.…”