Ground States for Generalized Gauge Actions on UHF Algebras

Klaus Thomsen

doi:10.1007/s00220-021-04075-1

Ground States for Generalized Gauge Actions on UHF Algebras

^*Corresponding author for this work

Department of Mathematics

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Abstract

We describe the structure of ground states and ceiling states for generalized gauge actions on a UHF algebra. It is shown that both sets are affinely homeomorphic to the state space of a unital AF algebra, and that any pair of unital AF algebras can occur in this way, independently of the field of KMS states. In addition we study the subset of the ground states called KMS _∞-states.

Original language	English
Journal	Communications in Mathematical Physics
Volume	386
Issue	1
Pages (from-to)	57-85
Number of pages	29
ISSN	0010-3616
DOIs	https://doi.org/10.1007/s00220-021-04075-1
Publication status	Published - Aug 2021

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10.1007/s00220-021-04075-1

https://arxiv.org/pdf/1905.11466.pdf

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abstract = "We describe the structure of ground states and ceiling states for generalized gauge actions on a UHF algebra. It is shown that both sets are affinely homeomorphic to the state space of a unital AF algebra, and that any pair of unital AF algebras can occur in this way, independently of the field of KMS states. In addition we study the subset of the ground states called KMS ∞-states.",

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AB - We describe the structure of ground states and ceiling states for generalized gauge actions on a UHF algebra. It is shown that both sets are affinely homeomorphic to the state space of a unital AF algebra, and that any pair of unital AF algebras can occur in this way, independently of the field of KMS states. In addition we study the subset of the ground states called KMS ∞-states.

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Ground States for Generalized Gauge Actions on UHF Algebras

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