SymTFT Approach for Mixed States with Non-Invertible Symmetries

Fuente: arXiv
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Autores principales: Schafer-Nameki, Sakura, Tiwari, Apoorv, Warman, Alison, Zhang, Carolyn
Formato: Preprint
Publicado: 2025
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author Schafer-Nameki, Sakura
Tiwari, Apoorv
Warman, Alison
Zhang, Carolyn
author_facet Schafer-Nameki, Sakura
Tiwari, Apoorv
Warman, Alison
Zhang, Carolyn
contents We develop a general framework for studying phases of mixed states with strong and weak symmetries, including non-invertible or categorical symmetries. The central idea is to consider a purification of the mixed state density matrix, which lives in a doubled Hilbert space. We propose a systematic classification of phases in this doubled Hilbert space, relying crucially on the Symmetry Topological Field Theory (SymTFT) approach. This framework applies not only to group symmetries but also, importantly, to non-invertible symmetries. We illustrate the approach in 1+1d to classify phases with strong (non-)invertible symmetries, which include strong-to-weak spontaneous symmetry breaking (SWSSB) phases and mixed strong/weak symmetry-protected topological phases (SPTs). We also develop an approach for studying symmetries that involve a combination of strong and weak symmetries. A noteworthy example of this has weak non-invertible Kramers-Wannier duality symmetry and strong $\mathbb{Z}_2$ symmetry. The continuum description is complemented by a lattice model analysis informed by the SymTFT framework.
format Preprint
id arxiv_https___arxiv_org_abs_2507_05350
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle SymTFT Approach for Mixed States with Non-Invertible Symmetries
Schafer-Nameki, Sakura
Tiwari, Apoorv
Warman, Alison
Zhang, Carolyn
Quantum Physics
Strongly Correlated Electrons
High Energy Physics - Theory
We develop a general framework for studying phases of mixed states with strong and weak symmetries, including non-invertible or categorical symmetries. The central idea is to consider a purification of the mixed state density matrix, which lives in a doubled Hilbert space. We propose a systematic classification of phases in this doubled Hilbert space, relying crucially on the Symmetry Topological Field Theory (SymTFT) approach. This framework applies not only to group symmetries but also, importantly, to non-invertible symmetries. We illustrate the approach in 1+1d to classify phases with strong (non-)invertible symmetries, which include strong-to-weak spontaneous symmetry breaking (SWSSB) phases and mixed strong/weak symmetry-protected topological phases (SPTs). We also develop an approach for studying symmetries that involve a combination of strong and weak symmetries. A noteworthy example of this has weak non-invertible Kramers-Wannier duality symmetry and strong $\mathbb{Z}_2$ symmetry. The continuum description is complemented by a lattice model analysis informed by the SymTFT framework.
title SymTFT Approach for Mixed States with Non-Invertible Symmetries
topic Quantum Physics
Strongly Correlated Electrons
High Energy Physics - Theory
url https://arxiv.org/abs/2507.05350