Fractonlike phases from subsystem symmetries

Ibieta-Jimenez, J. P.; Xavier, L. N. Queiroz; Petrucci, M.; Teotonio-Sobrinho, P.

doi:10.1103/physrevb.102.045104

Cited by 9 publications

(7 citation statements)

References 66 publications

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“…codimension invertibility topologicalness ordinary symmetry = 1 ✓ ✓ higher-form/group sym [1, ≥ 1 ✓ ✓ non-invertible/categorical sym = 1 ✗ ✓ higher categorical sym ≥ 1 ✗ ✓ subsystem sym [75][76][77][78][79][80][81][82][83][84][85][86][87][88][89][90][91] = 1 ✓ ✗ higher subsystem sym [141][142][143][144][145][146][147][148][149][150][151][152] ≥ 1 ✓ ✗ subsystem non-invertible sym = 1 ✗ ✗ higher subsystem non-invertible sym ≥ 1 ✗ ✗…”

Section: Symmetrymentioning

confidence: 99%

“…The remaining symmetries differ in one or multiple properties. For instance, higher-form symmetries relax the condition of codimension being one [1,; 1 non-invertible symmetries in (1 + 1)d relax the invertibility ; subsystem symmetries in (2 + 1)d relax the topologicalness or the mobility of the symmetry generators/defects 2 [75][76][77][78][79][80][81][82][83][84][85][86][87][88][89][90][91]. 3 Here and in Tab.…”

Section: Introduction 1subsystem Non-invertible Symmetrymentioning

confidence: 99%

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Subsystem non-invertible symmetry operators and defects

Cao,

Li,

Yamazaki

et al. 2023

SciPost Phys.

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We explore non-invertible symmetries in two-dimensional lattice models with subsystem \mathbb Z_2ℤ2 symmetry. We introduce a subsystem \mathbb Z_2ℤ2-gauging procedure, called the subsystem Kramers-Wannier transformation, which generalizes the ordinary Kramers-Wannier transformation. The corresponding duality operators and defects are constructed by gaugings on the whole or half of the Hilbert space. By gauging twice, we derive fusion rules of duality operators and defects, which enriches ordinary Ising fusion rules with subsystem features. Subsystem Kramers-Wannier duality defects are mobile in both spatial directions, unlike the defects of invertible subsystem symmetries. We finally comment on the anomaly of the subsystem Kramers-Wannier duality symmetry, and discuss its subtleties.

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Section: Symmetrymentioning

confidence: 99%

Section: Introduction 1subsystem Non-invertible Symmetrymentioning

confidence: 99%

Subsystem non-invertible symmetry operators and defects

Cao,

Li,

Yamazaki

et al. 2023

SciPost Phys.

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“…More details can be found in the reviews [12,13]. A significant portion of the fracton topological ordered systems can be obtained from gauging subsystem symmetries [3,14,15]. Thus it is equally interesting and important to study subsystem-symmetric theories.…”

Section: Introductionmentioning

confidence: 99%

Boson-fermion duality with subsystem symmetry

Cao,

Yamazaki,

Zheng

2022

Preprint

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We explore an exact duality in (2 + 1)d between the fermionization of a bosonic theory with a Z 2 subsystem symmetry and a fermionic theory with a Z 2 subsystem fermion parity symmetry. A typical example is the duality between the fermionization of the plaquette Ising model and the plaquette fermion model. We first revisit the standard boson-fermion duality in (1 + 1)d with a Z 2 0-from symmetry, presenting in a way generalizable to (2 + 1)d. We proceed to (2 + 1)d with a Z 2 subsystem symmetry and establish the exact duality on the lattice by using the generalized Jordan-Wigner map, with a careful discussion on the mapping of the twist and symmetry sectors. This motivates us to introduce the subsystem Arf invariant, which exhibits a foliation structure.

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“…We built a class of models within this framework in 2 and 3 dimensions. This work is to be published on PRLB [37].…”

Section: Further Achievementsmentioning

confidence: 99%

“…• J. P. Ibieta-Jimenez and L. N. Queiroz Xavier and M. Petrucci and P. Teotonio-Sobrinho, Fracton-like Phases from Subsystem Symmetries, Physical Review B [37].…”

Section: Publicationsmentioning

confidence: 99%

Modelo duplo quântico de grupo

Petrucci¹

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I would like to thank my supervisor for the possibility to engage in this path, for the patient presence and professional assistance. I deeply enjoyed the journey. Journey worth pursuing even more for the companions I met in my research group, especially Pablo. I am grateful to Stuart, Ciça, Carlos, Kris and Jenifer for assistance in my inner work. I owe to the love found here in Brazil: Marcinha and Roba, Renata and Ananda, Cata, as Gumietes, Marcos, Rubens. To the strong family that made this possible. And finally to my chosen family, my friends spread all over. All of you make my life truly rich and prosperous. I dedicate this work to Rossella: "Domani é un altro giorno." This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior-Brasil (CAPES)-Finance Code 001. I would like to thank the CPG and FISMAT secretary, all the caretakers and workers at USP.

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Fractonlike phases from subsystem symmetries

Cited by 9 publications

References 66 publications

Subsystem non-invertible symmetry operators and defects

Subsystem non-invertible symmetry operators and defects

Boson-fermion duality with subsystem symmetry

Modelo duplo quântico de grupo

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