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

Abstract

We study a disordered system of interacting bosons described by the Bose–Hubbard Hamiltonian with random tunneling amplitudes. We derive the condition for the stability of the replica-symmetric solution for this model. Following the scheme of de Almeida and Thouless, we determine if the solution corresponds to the minimum of free energy by building the respective Hessian matrix and checking its positive semidefiniteness. Thus, we find the eigenvalues by postulating the set of eigenvectors based on their expected symmetry, and require the eigenvalues to be non-negative. We evaluate the spectrum numerically and identify matrix blocks that give rise to eigenvalues that are always non-negative. Thus, we find a subset of eigenvalues coming from decoupled subspaces that is sufficient to be checked as the stability criterion. We also determine the stability of the phases present in the system, finding that the disordered phase is stable, the glass phase is unstable, while the superfluid phase has both stable and unstable parts.

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

“…The appropriate condition can be found in Ref. [32]. These conditions give us a clear distinction between the phases, nevertheless, we can also characterize the phases by directly checking the values of order parameters.…”

Viewpoints on the 11th International Meeting on Atomic and Molecular Physics and Chemistry

“…Anna Piekarska presented a theoretical study of strongly correlated disordered bosons, which can be simulated using an optical lattice. The system was modeled using the Bose-Hubbard Hamiltonian with Gaussian-distributed random tunneling terms, employing the replica trick and Trotter-Suzuki expansion to arrive at a set of self-consistent equations, which were solved numerically to find the phase diagrams of the system . The poster of Gabriel Schöpfer reported on combining DFT and RRKM theory to model the reaction kinetics of false[ Mg normaln false( SO 4 false) normaln − 1 false( normalH 2 normalO false) normalm false] 2 + ions upon excitation with blackbody radiation in an ion trap, with implications for the production of sea salt aerosols and climate change models.…”