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.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.

arXiv:2112.12735SciPost PhysicsJul 19, 202336 citations

Chern-Simons-like theories for fracton phases

Weslei Bernardino Fontana

May 6, 20210 citations

A symmetry principle for gauge theories with fractons

Yuji Hirono, Minyoung You, Stephen Angus +1 more

Fractonic phases are new phases of matter that host excitations with restricted mobility. We show that a certain class of gapless fractonic phases are realized as a result of spontaneous breaking of continuous higher-form symmetries whose conserved charges do not commute with spatial translations. We refer to such symmetries as nonuniform higher-form symmetries. These symmetries fall within the standard definition of higher-form symmetries in quantum field theory, and the corresponding symmetry generators are topological. Worldlines of particles are regarded as the charged objects of 1-form symmetries, and mobility restrictions can be implemented by introducing additional 1-form symmetries whose generators do not commute with spatial translations. These features are realized by effective field theories associated with spontaneously broken nonuniform 1-form symmetries. At low energies, the theories reduce to known higher-rank gauge theories such as scalar/vector charge gauge theories, and the gapless excitations in these theories are interpreted as Nambu-Goldstone modes for higher-form symmetries. Due to the nonuniformity of the symmetry, some of the modes acquire a gap, which is the higher-form analogue of the inverse Higgs mechanism of spacetime symmetries. The gauge theories have emergent nonuniform magnetic symmetries, and some of the magnetic monopoles become fractonic. We identify the ’t Hooft anomalies of the nonuniform higher-form symmetries and the corresponding bulk symmetry-protected topological phases. By this method, the mobility restrictions are fully determined by the choice of the commutation relations of charges with translations. This approach allows us to view existing (gapless) fracton models such as the scalar/vector charge gauge theories and their variants from a unified perspective and enables us to engineer theories with desired mobility restrictions.Fractonic phases are new phases of matter that host excitations with restricted mobility. We show that a certain class of gapless fractonic phases are realized as a result of spontaneous breaking of continuous higher-form symmetries whose conserved charges do not commute with spatial translations. We refer to such symmetries as nonuniform higher-form symmetries. These symmetries fall within the standard definition of higher-form symmetries in quantum field theory, and the corresponding symmetry generators are topological. Worldlines of particles are regarded as the charged objects of 1-form symmetries, and mobility restrictions can be implemented by introducing additional 1-form symmetries whose generators do not commute with spatial translations. These features are realized by effective field theories associated with spontaneously broken nonuniform 1-form symmetries. At low energies, the theories reduce to known higher-rank gauge theories such as scalar/vector charge gauge theories, and the gapless excitations in these theories are interpreted as Nambu-Goldstone modes for higher-form symmetries. Due to the nonuniformity of the symmetry, some of the modes acquire a gap, which is the higher-form analogue of the inverse Higgs mechanism of spacetime symmetries. The gauge theories have emergent nonuniform magnetic symmetries, and some of the magnetic monopoles become fractonic. We identify the ’t Hooft anomalies of the nonuniform higher-form symmetries and the corresponding bulk symmetry-protected topological phases. By this method, the mobility restrictions are fully determined by the choice of the commutation relations of charges with translations. This approach allows us to view existing (gapless) fracton models such as the scalar/vector charge gauge theories and their variants from a unified perspective and enables us to engineer theories with desired mobility restrictions.

arXiv:2207.00854SciPost PhysicsFeb 20, 202426 citations

Symmetric fracton matter: Twisted and enriched

Yizhi You, Trithep Devakul, F. J. Burnell +1 more

arXiv:1805.09800Annals of PhysicsMar 19, 202094 citations

String membrane nets from higher-form gauging: An alternate route to p -string condensation

Pranay Gorantla, Abhinav Prem, Nathanan Tantivasadakarn +1 more

We present a unique perspective on the $p$ -string condensation procedure for constructing (3+1)-dimensional [(3+1)D] fracton phases by implementing this process via the gauging of higher-form symmetries. Specifically, we show that gauging a 1-form symmetry in (3+1)D that is generated by Abelian anyons in isotropic stacks of (2+1)-dimensional [(2+1)D] topological orders naturally results in a (3+1)D $p$ -string condensed phase, providing a controlled nonperturbative construction that realizes fracton orders. This approach clarifies the symmetry principles underlying $p$ -string condensation and generalizes the familiar connection between anyon condensation and 1-form gauging in two spatial dimensions. We demonstrate this correspondence explicitly in both field theories and lattice models: In field theory, we derive the foliated field theory description of the ${\mathbb{Z}}_{N}$ X-cube model by gauging a higher-form symmetry in stacks of (2+1)D ${\mathbb{Z}}_{N}$ gauge theories; on the lattice, we show how gauging a diagonal 1-form symmetry in isotropic stacks of $G$ -graded string-net models leads to string membrane nets hosting restricted mobility excitations. This perspective naturally generalizes to spatial dimensions $d\ensuremath{\ge}2$ and provides a step towards building an algebraic theory of $p$ -string condensation.We present a unique perspective on the $p$-string condensation procedure for constructing (3+1)-dimensional [(3+1)D] fracton phases by implementing this process via the gauging of higher-form symmetries. Specifically, we show that gauging a 1-form symmetry in (3+1)D that is generated by Abelian anyons in isotropic stacks of (2+1)-dimensional [(2+1)D] topological orders naturally results in a (3+1)D $p$-string condensed phase, providing a controlled nonperturbative construction that realizes fracton orders. This approach clarifies the symmetry principles underlying $p$-string condensation and generalizes the familiar connection between anyon condensation and 1-form gauging in two spatial dimensions. We demonstrate this correspondence explicitly in both field theories and lattice models: In field theory, we derive the foliated field theory description of the ${\mathbb{Z}}_{N}$ X-cube model by gauging a higher-form symmetry in stacks of (2+1)D ${\mathbb{Z}}_{N}$ gauge theories; on the lattice, we show how gauging a diagonal 1-form symmetry in isotropic stacks of $G$-graded string-net models leads to string membrane nets hosting restricted mobility excitations. This perspective naturally generalizes to spatial dimensions $d\ensuremath{\ge}2$ and provides a step towards building an algebraic theory of $p$-string condensation.

arXiv:2505.13604Physical review. B./Physical review. BAug 29, 20253 citations

We present a unique perspective on the

p

-string condensation procedure for constructing (3+1)-dimensional [(3+1)D] fracton phases by implementing this process via the gauging of higher-form symmetries. Specifically, we show that gauging a 1-form symmetry in (3+1)D that is generated by Abelian anyons in isotropic stacks of (2+1)-dimensional [(2+1)D] topological orders naturally results in a (3+1)D

p

-string condensed phase, providing a controlled nonperturbative construction that realizes fracton orders. This approach clarifies the symmetry principles underlying

p

-string condensation and generalizes the familiar connection between anyon condensation and 1-form gauging in two spatial dimensions. We demonstrate this correspondence explicitly in both field theories and lattice models: In field theory, we derive the foliated field theory description of the

{\mathbb{Z}}_{N}

X-cube model by gauging a higher-form symmetry in stacks of (2+1)D

{\mathbb{Z}}_{N}

gauge theories; on the lattice, we show how gauging a diagonal 1-form symmetry in isotropic stacks of

G

-graded string-net models leads to string membrane nets hosting restricted mobility excitations. This perspective naturally generalizes to spatial dimensions $d\ensuremath{\ge}2$ and provides a step towards building an algebraic theory of

p

-string condensation.