Replica symmetry breaking in the Bose glass

¹ SUPA, School of Physics and Astronomy, University of St Andrews, North Haugh - St Andrews, KY16 9SS, UK
² ISIS Facility, Rutherford Appleton Laboratory - Chilton, Didcot, Oxfordshire OX11 0QX, UK
³ London Centre for Nanotechnology, University College London - Gordon St., London, WC1H 0AH, UK

Received: 4 April 2014
Accepted: 17 October 2014

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 . 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.