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Perturbation Expansions for Quantum Many-Body Systems

Simon Trebst

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

The linked cluster method is one of the most ecient ways to generate per-turbation series expansions for quantum lattice models. For the ground state energy and related properties, a linked cluster approach was rst discussed in unpublished work by Nickel, followed by work of Marland [1], Irving and Hamer

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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.