Replica symmetry breaking in the Bose glass

Abstract

We investigate the nature of the Bose glass phase of the disordered Bose-Hubbard model in $d>2$ and demonstrate the existence of a glass-like replica symmetry breaking (RSB) order parameter in terms of particle number fluctuations. Starting from a strong-coupling expansion around the atomic limit, we study the instability of the Mott insulator towards the formation of a Bose glass. We add some infinitesimal RSB, following the Parisi hierarchical approach in the most general form, and observe its flow under the momentum-shell renormalization group scheme. We find a new fixed point with one-step RSB, corresponding to the transition between the Mott insulator and a Bose glass phase with hitherto unseen RSB. The susceptibility associated to infinitesimal RSB perturbation in the Mott insulator is found to diverge at the transition with an exponent of $\gamma =1/d$. Our findings are consistent with the expectation of glassy behavior and the established breakdown of self-averaging. We discuss the possibility of measuring the glass-like order parameter in optical lattice experiments as well as in certain spin systems that are in the same universality class as the Bose-Hubbard model.

6 pages, 3 figures, improved version with additional references

References in corpus (13)

• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• Single-Spin Addressing in an Atomic Mott Insulator
• Bose-Einstein Condensation in Magnetic Insulators
• Strongly interacting bosons in a disordered optical lattice
• A high-accuracy algorithm for designing arbitrary holographic atom traps
• Mott insulator to superfluid transition in the Bose-Hubbard model: a strong-coupling approach
• Quantum Griffiths effects and smeared phase transitions in metals: theory and experiment
• Particle-hole symmetry and the dirty boson problem
• Superfluid clusters, percolation and phase transitions in the disordered, two dimensional Bose-Hubbard model
• Stochastic Mean-Field Theory for the Disordered Bose-Hubbard Model
• Physical replicas and the Bose-glass in cold atomic gases
• Super-Rough Glassy Phase of the Random Field XY Model in Two Dimensions

Cited by in corpus (8)

• Enhancement of the Bose glass phase in the presence of an artificial gauge field
• Measuring the Edwards-Anderson order parameter of the Bose glass: a quantum gas microscope approach
• Finding the phase diagram of strongly-correlated disordered bosons using quantum quenches
• Bose and Mott Glass Phases in Dimerized Quantum Antiferromagnets
• Local Density of the Bose Glass Phase
• Stability of the replica-symmetric solution in the off-diagonally-disordered Bose-Hubbard model
• Self-consistent T-matrix approach to Bose-glass in one dimension
• Emergence of a superglass phase in the random hopping Bose-Hubbard model