Composite Boson Mapping for Lattice Boson Systems

TL;DR

This paper introduces a composite boson mapping technique for lattice boson systems that accurately reproduces phase diagrams and excitations with reduced computational effort, applicable to complex frustrated systems.

Contribution

A novel canonical mapping of boson operators into composite bosons that preserves operator matrix elements and simplifies the analysis of lattice boson systems.

Findings

Reproduces quantum Monte Carlo phase diagrams accurately

Unravels Higgs boson behavior consistent with experiments

Achieves competitive results with lower computational cost

Abstract

We present a canonical mapping transforming physical boson operators into quadratic products of cluster composite bosons that preserves matrix elements of operators when a physical constraint is enforced. We map the 2D lattice Bose-Hubbard Hamiltonian into $2\times 2$ composite bosons and solve it at mean field. The resulting Mott insulator-superfluid phase diagram reproduces well Quantum Monte Carlo results. The Higgs boson behavior along the particle-hole symmetry line is unraveled and in remarkable agreement with experiment. Results for the properties of the ground and excited states are competitive with other state-of-the-art approaches, but at a fraction of their computational cost. The composite boson mapping here introduced can be readily applied to frustrated many-body systems where most methodologies face significant hurdles.