Renormalization of two-body interactions due to higher-body interactions of lattice bosons

TL;DR

This paper develops a method to exactly renormalize two-body interactions in lattice bosons by resumming higher-body interactions, simplifying the analysis of thermodynamic properties in such systems.

Contribution

It introduces a renormalization technique that resums three- and four-body interactions into two-body terms using linked cluster methods, applicable across various many-body systems.

Findings

Exact renormalization of two-body interactions achieved

Universality observed at different three-body interaction strengths

Method applicable to a broad class of systems with linked cluster expansions

Abstract

We calculate thermodynamic properties of soft-core lattice bosons with on-site $n$-body interactions using up to twelfth and tenth order strong coupling expansion in one and two dimensional cubic lattices at zero temperature. Using linked cluster techniques, we show that it is possible to exactly renormalize the two-body interactions for quasiparticle excitations and ground-state energy by resumming the three and four body terms in the system, which suggests that all higher-body on-site interactions may be exactly and perturbatively resummed into the two-body terms for similar system observables. The renormalization procedure that we develop is applicable to a broad range of systems analyzable by linked cluster expansions, ranging from perturbative quantum chromodynamics to spin models, giving either an exact or approximate resummation depending on the specific system and properties. Universality at various three-body interaction strengths for the two dimensional boson Hubbard model is checked numerically.