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

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.

5 + epsilon pages, 2 figures. Difference from v1: extra explanatory section (IIIA) on procedure + cosmetic changes

References in corpus (5)

• Mott-Hubbard Transition of Bosons in Optical Lattices with Three-body Interactions
• Exact diagonalization of the one dimensional Bose-Hubbard model with local 3-body interactions
• Three body on-site interactions in ultracold bosonic atoms in optical lattices and superlattices
• First order phase transitions in optical lattices with tunable three-body onsite interaction
• Strong coupling expansion for bosons on the kagome lattice

Cited by in corpus (2)

• Mott lobes of the $S=1$ Bose-Hubbard model with three-body interactions
• Emergent Phases in an Extended Bose-Hubbard Model with Three-body On-site Interaction