The low-energy theory for the Bose-Hubbard model and the normal ground state of bosons

TL;DR

This paper develops a low-energy effective theory for the Bose-Hubbard model using a bosonic SU(2) algebra realization, exploring the potential for a normal bosonic phase without crystalline or superfluid order.

Contribution

It introduces a novel anisotropic quantum rotor theory for the Bose-Hubbard model and investigates the existence of a non-ordered bosonic phase at specific fillings.

Findings

Constructed a bosonic SU(2) algebra realization.

Proposed an anisotropic low-energy theory for the Bose-Hubbard model.

Examined the possibility of a normal bosonic phase at half-integer fillings.

Abstract

A bosonic realization of the SU(2) Lie algebra and of its vector representation is constructed, and an effective low-energy description of the Bose-Hubbard model in the form of anisotropic theory of quantum rotors is proposed and discussed. A possibility of a normal zero-temperature bosonic phase with neither crystalline nor superfluid order around the tip of the checkerboard-solid lobe at half-integer fillings is examined.