# Stability of Insulating Phases in the Hubbard Model: a Cluster Expansion

Source: [Stability of Insulating Phases in the Hubbard Model: a Cluster Expansion](<https://www.sota2.com/research/paper/68fa1e8c7a2b558e29323037>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-23T15:21:59.528Z

Authors: K. Ziegler

Published: 1993-10-14T15:12:14.000Z

## Abstract

The stability of the insulating regime of the Hubbard model on a $d$-dimensional lattice, which is characterized by an exponential decay of the Green's functions, is investigated in terms of a cluster expansion. This expansion for the Green's function is organized in terms of connected clustered transfer matrices. An upper bound for the expansion terms is derived for the hopping rate ${\\bar t}$ depending on the coupling constant $U$ as ${\\bar t}\<U/4d$. This implies an upper bound for the decay length of the Green's function.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/9310031>)

[PDF](<https://arxiv.org/pdf/cond-mat/9310031.pdf>)