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arXiv:1211.5664 · Physical Review B

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

Vipin Kerala Varma, H. Monien

Published Aug 25, 2014• 2 citations
arXivHTMLPDF

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.

DOI
10.1103/physrevb.90.085138

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We calculate thermodynamic properties of soft-core lattice bosons with on-site nnn-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.
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We employ the numerical linked-cluster expansion to study finite-temperature properties of the uniform cubic lattice Hubbard model in the thermodynamic limit for a wide range of interaction strengths and densities. We carry out the expansion to the 9th order and find that the convergence of the series extends to lower temperatures as the strength of the interaction increases, giving us access to regions of the parameter space that are difficult to reach by most other numerical methods. We study the precise trends in the specific heat, the double occupancy, and magnetic correlations at temperatures as low as 0.2 of the hopping amplitude in the strong-coupling regime. We show that in this regime, accurate estimates for transition temperatures to the N\'eel ordered phase, in agreement with the predicted asymptotic behavior, can be deduced from the low-temperature magnetic structure factor. We also find evidence for possible instability to the magnetically ordered phase away from, but close to, half filling. Our results have important implications for parametrizing fermionic systems in optical lattice experiments and for benchmarking other numerical methods.
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