Bifurcating subsystem symmetric entanglement renormalization in two dimensions

Miguel, Jonathan F. San; Dua, Arpit; Williamson, Dominic J.

doi:10.1103/physrevb.103.035148

“…4) To what extent can the bifurcating entanglement renormalization group flows of gapped fracton phases [51,[120][121][122] be generalized to their subdimensional critical points, including those studied here? We plan to report some progress in this direction in a forthcoming work [123].…”

Section: Discussionmentioning

confidence: 99%

Higher-form subsystem symmetry breaking: Subdimensional criticality and fracton phase transitions

Rayhaun

¹

,

Williamson

²

2023

SciPost Phys.

15

0

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Subsystem symmetry has emerged as a powerful organizing principle for unconventional quantum phases of matter, most prominently fracton topological orders. Here, we focus on a special subclass of such symmetries, known as higher-form subsystem symmetries, which allow us to adapt tools from the study of conventional topological phases to the fracton setting. We demonstrate that certain transitions out of familiar fracton phases, including the X-cube model, can be understood in terms of the spontaneous breaking of higher-form subsystem symmetries. We find simple pictures for these seemingly complicated fracton topological phase transitions by relating them in an exact manner, via gauging, to spontaneous higher-form subsystem symmetry breaking phase transitions of decoupled stacks of lower-dimensional models. We harness this perspective to construct a sequence of unconventional subdimensional critical points in two and three spatial dimensions based on the stacking and gauging of canonical models with higher-form symmetry. Through numerous examples, we illustrate the ubiquity of coupled layer constructions in theories with higher-form subsystem symmetries.

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“…4) To what extent can the bifurcating entanglement renormalization group flows of gapped fracton phases [50,[115][116][117] be generalized to their subdimensional critical points, including those studied here? We plan to report some progress in this direction in a forthcoming work [118].…”

Section: Discussionmentioning

confidence: 99%

Higher-Form Subsystem Symmetry Breaking: Subdimensional Criticality and Fracton Phase Transitions

Rayhaun¹,

Williamson²

2021

Preprint

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Subsystem symmetry has emerged as a powerful organizing principle for unconventional quantum phases of matter, most prominently fracton topological orders. Here, we focus on a special subclass of such symmetries, known as higher-form subsystem symmetries, which allow us to adapt tools from the study of conventional topological phases to the fracton setting. We demonstrate that certain transitions out of familiar fracton phases, including the X-cube model, can be understood in terms of the spontaneous breaking of higher-form subsystem symmetries. We find simple pictures for these seemingly complicated fracton topological phase transitions by relating them in an exact manner, via gauging, to spontaneous higher-form subsystem symmetry breaking phase transitions of decoupled stacks of lower-dimensional models. We harness this perspective to construct a sequence of unconventional subdimensional critical points in two and three spatial dimensions based on the stacking and gauging of canonical models with higher-form symmetry. Through numerous examples, we illustrate the ubiquity of coupled layer constructions in theories with higher-form subsystem symmetries. Contents2 This symmetry motivates our choice of notation 2 H (0,1) Z 2 for the Hamiltonian of the plaquette Ising model: the (0, 1) in the superscript indicates that the model has a Z (0,1) 2 (F x , F y ) ∼ symmetry, and the 2 denotes its spatial dimension. We define an infinite family d H (q,k) Z 2 of similar models in §2.1.

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“…In the present paper, we are interested in the role that subsystem symmetries play in the classification of topological phases of matter. Subsystem symmetry-protected topological (SSPT) phases of matter-those, which are trivial in the absence of symmetry-have by now received considerable attention [13,[17][18][19][20][21][22], due in part to their aforementioned ability to perform universal MBQC and their unique entanglement properties [23][24][25][26]. On the other hand, subsystem symmetryenriched topological (SSET) phases, where the symmetry fractionalizes on nontrivial bulk excitations of a topologically ordered system, remain largely unexplored.…”

Section: Introductionmentioning

confidence: 99%