Local density of the Bose-glass phase

Abstract

We study the Bose-Hubbard model in the presence of on-site disorder in the canonical ensemble and conclude that the local density of the Bose glass phase behaves differently at incommensurate filling than it does at commensurate one. Scaling of the superfluid density at incommensurate filling of ρ = 1.1 and on-site interaction U = 80t predicts a superfluid-Bose glass transition at disorder strength of ∆c ≈ 30t. At this filling the local density distribution shows skew behavior with increasing disorder strength. Multifractal analysis also suggests a multifractal behavior resembling that of the Anderson localization. Percolation analysis points to a phase transition of percolating non-integer filled sites around the same value of disorder. Our findings support the scenario of percolating superfluid clusters enhancing Anderson localization near the superfluid-Bose glass transition. On the other hand, the behavior of the commensurate filled system is rather different. Close to the tip of the Mott lobe (ρ = 1, U = 22t) we find a Mott insulator-Bose glass transition at disorder strength of ∆c ≈ 16t. An analysis of the local density distribution shows Gaussian like behavior for a wide range of disorders above and below the transition. The behaviors of the superfluid-Bose glass transition call for a thorough finite size scaling analysis of percolation and multifractality to understand the universality of the transition.

Phase Properties of Interacting Bosons in Presence of Quasiperiodic and Random Disorder

“…However, evidence suggests that a direct transition from the MI to the SF phase is ruled out in presence of random disorder, and is always intervened by a BG phase [46]. Apart from such fundamental realizations, various numerical techniques, such as, quantum Monte Carlo (QMC) [47][48][49][50][51][52], stochastic mean-field theory [53,54], Green's function approach and DMRG [55,56] etc have been developed to study the BG phase in the disordered cold atomic gases. Moreover, a site dependent mean field approximation (MFA) employs finding of the SF percolating cluster using a percolation analysis to capture the BG phase.…”

Quantifying fermionic interactions from the violation of Wick's theorem

“…The interaction distance is the trace distance between the reduced density matrix of the system's ground state from the density matrix of the closest possible free system [27]. While the interaction distance is an optimal theoretical way to infer emergent gaussianity, its relation to the Wick's theorem violation provides an intuitive way to understand its properties and to experimentally estimate its value through measurements of quantum correlations [29][30][31][32].…”

Quantifying fermionic interactions from the violation of Wick's theorem

“…While the interaction distance is an optimal theoretical way to infer emergent gaussianity, its relation to the Wick's theorem violation provides an intuitive way to understand its properties and to experimentally estimate its value through measurements of quantum correlations (e.g. [8,11,32,33]), as one can relate the operators of the original and the entanglement Hamiltonian [6,29]. Along these lines, in [17] one can find an example of applying our approach to the XYZ model in the simple case of a system with only two fermionic modes.…”