Towards a Holographic Bose-Hubbard Model

TL;DR

This paper constructs a holographic large-N Bose-Hubbard model using Maxwell and scalar fields in AdS2, reproducing key phase features like Mott insulators and phase transitions, including first-order and holographic transitions.

Contribution

It introduces a holographic realization of the Bose-Hubbard model capturing its phase structure and phase transitions, including Mott insulators and inhomogeneous phases.

Findings

Realizes Mott insulator ground states at large Coulomb repulsion.

Identifies first-order level-crossing transitions between Mott phases.

Discovers almost zero modes in the non-homogeneous phase.

Abstract

We present a holographic construction of the large-N Bose-Hubbard model. The model is based on Maxwell fields coupled to charged scalar fields on the AdS2 hard wall. We realize the lobe-shaped phase structure of the Bose-Hubbard model and find that the model admits Mott insulator ground states in the limit of large Coulomb repulsion. In the Mott insulator phases, the bosons are localized on each site. At zero hopping we find that the transitions between Mott insulating phases with different fillings correspond to first order level-crossing phase transitions. At finite hopping we find a holographic phase transition between the Mott phase and a non-homogeneous phase. We then analyze the perturbations of fields around both the Mott insulator phase and inhomogeneous phase. We find almost zero modes in the non-homogeneous phase.