A nonvanishing spectral gap for AKLT models on generalized decorated graphs

We consider the spectral gap question for Affleck, Kennedy, Lieb, and Tasaki models defined on decorated versions of simple, connected graphs G. This class of decorated graphs, which are defined by replacing all edges of G with a chain of n sites, in particular includes any decorated multi-dimension...

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Detalles Bibliográficos
Autores: Young, Amanda, Lucia, Angelo
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/96130
Acceso en línea:https://hdl.handle.net/20.500.14352/96130
Access Level:acceso abierto
Palabra clave:Física matemática
Teoría de los quanta
2210.23 Teoría Cuántica
Descripción
Sumario:We consider the spectral gap question for Affleck, Kennedy, Lieb, and Tasaki models defined on decorated versions of simple, connected graphs G. This class of decorated graphs, which are defined by replacing all edges of G with a chain of n sites, in particular includes any decorated multi-dimensional lattice. Using the Tensor Network States approach from [Abdul-Rahman et al., Analytic Trends in Mathematical Physics, Contemporary Mathematics (American Mathematical Society, 2020), Vol. 741, p. 1.], we prove that if the decoration parameter is larger than a linear function of the maximal vertex degree, then the decorated model has a nonvanishing spectral gap above the ground state energy.