An Exactly Solvable Gauge Theory Model for Correlated Fermions in 3+1 Dimensions

We propose a Hamiltonian framework for constructing chiral gauge theories on the lattice based on symmetry disentanglers: constant-depth circuits of local unitaries that transform not-on-site symmetries into on-site ones. When chiral symmetry can be realized not-on-site and such a disentangler exists, the symmetry can be implemented in a strictly local Hamiltonian and gauged by standard lattice methods. Using lattice rotor models, we realize this idea in 1+1 and 3+1 spacetime dimensions for $U(1)$ symmetries with mixed 't Hooft anomalies, and show that symmetry disentanglers can be constructed when anomalies cancel. As an example, we present an exactly solvable Hamiltonian lattice model of the (1+1)-dimensional "3450" chiral gauge theory, and we argue that a related construction applies to the $U(1)$ hypercharge symmetry of the Standard Model fermions in 3+1 dimensions. Our results open a new route toward fully local, nonperturbative formulations of chiral gauge theories.We propose a Hamiltonian framework for constructing chiral gauge theories on the lattice based on symmetry disentanglers: constant-depth circuits of local unitaries that transform not-on-site symmetries into on-site ones. When chiral symmetry can be realized not-on-site and such a disentangler exists, the symmetry can be implemented in a strictly local Hamiltonian and gauged by standard lattice methods. Using lattice rotor models, we realize this idea in 1+1 and 3+1 spacetime dimensions for $U(1)$ symmetries with mixed 't Hooft anomalies, and show that symmetry disentanglers can be constructed when anomalies cancel. As an example, we present an exactly solvable Hamiltonian lattice model of the (1+1)-dimensional "3450" chiral gauge theory, and we argue that a related construction applies to the $U(1)$ hypercharge symmetry of the Standard Model fermions in 3+1 dimensions. Our results open a new route toward fully local, nonperturbative formulations of chiral gauge theories.

hep-thCross-listedarXiv:2601.04304Jan 9, 20260 citations

Fractonic order and emergent fermionic gauge theory

Wilbur E. Shirley

We consider fermionic systems in which fermion parity is conserved within rigid subsystems, and describe an explicit procedure for gauging such subsystem fermion parity symmetries to obtain bosonic spin Hamiltonians. We show that gauging planar or fractal subsystem fermion parity symmetry in three spatial dimensions gives rise to a plethora of exactly solvable spin models exhibiting novel gapped fractonic orders characterized by emergent fermionic gauge theory. The low energy excitations of these models include fractional quasiparticles with constrained mobility and emergent fermionic statistics. We illustrate this phenomenon through a series of examples including fermionic analogs of both foliated fracton phases and fractal spin liquids. We find that the foliated analogs actually exhibit the same fractonic order as their bosonic counterparts, while this is not generally the case for fermionic fractal spin liquids.We consider fermionic systems in which fermion parity is conserved within rigid subsystems, and describe an explicit procedure for gauging such subsystem fermion parity symmetries to obtain bosonic spin Hamiltonians. We show that gauging planar or fractal subsystem fermion parity symmetry in three spatial dimensions gives rise to a plethora of exactly solvable spin models exhibiting novel gapped fractonic orders characterized by emergent fermionic gauge theory. The low energy excitations of these models include fractional quasiparticles with constrained mobility and emergent fermionic statistics. We illustrate this phenomenon through a series of examples including fermionic analogs of both foliated fracton phases and fractal spin liquids. We find that the foliated analogs actually exhibit the same fractonic order as their bosonic counterparts, while this is not generally the case for fermionic fractal spin liquids.

arXiv:2002.12026Feb 27, 202015 citations

Gauge Invariance, Correlated Fermions, and Photon Mass in 2+1 Dimensions

Jonas de Woul, Edwin Langmann A

arXiv:1107.0891Journal of Statistical PhysicsJan 16, 20142 citations

Chiral lattice gauge theories from symmetry disentanglers

Ryan Thorngren, John P. Preskill, Lukasz Fidkowski

A bstract We propose a Hamiltonian framework for constructing chiral gauge theories on the lattice based on symmetry disentanglers : constant-depth circuits of local unitaries that transform not-on-site symmetries into on-site ones. When chiral symmetry can be realized not-on-site and such a disentangler exists, the symmetry can be implemented in a strictly local Hamiltonian and gauged by standard lattice methods. Using lattice rotor models, we realize this idea in 1+1 and 3+1 spacetime dimensions for U(1) symmetries with mixed ’t Hooft anomalies, and show that symmetry disentanglers can be constructed when anomalies cancel. As an example, we present an exactly solvable Hamiltonian lattice model of the (1+1)-dimensional “3450” chiral gauge theory, and we argue that a related construction applies to the U(1) hypercharge symmetry of the Standard Model fermions in 3+1 dimensions. Our results open a new route toward fully local, nonperturbative formulations of chiral gauge theories.A bstract We propose a Hamiltonian framework for constructing chiral gauge theories on the lattice based on symmetry disentanglers : constant-depth circuits of local unitaries that transform not-on-site symmetries into on-site ones. When chiral symmetry can be realized not-on-site and such a disentangler exists, the symmetry can be implemented in a strictly local Hamiltonian and gauged by standard lattice methods. Using lattice rotor models, we realize this idea in 1+1 and 3+1 spacetime dimensions for U(1) symmetries with mixed ’t Hooft anomalies, and show that symmetry disentanglers can be constructed when anomalies cancel. As an example, we present an exactly solvable Hamiltonian lattice model of the (1+1)-dimensional “3450” chiral gauge theory, and we argue that a related construction applies to the U(1) hypercharge symmetry of the Standard Model fermions in 3+1 dimensions. Our results open a new route toward fully local, nonperturbative formulations of chiral gauge theories.

Journal of High Energy PhysicsJul 29, 20261 citation

New soluble model of interacting fermions in one-dimension

Seth Grable, Noah Kamm, Harsh Mathur

Bulletin of the American Physical SocietyMar 16, 20210 citations

U(1)

symmetries with mixed 't Hooft anomalies, and show that symmetry disentanglers can be constructed when anomalies cancel. As an example, we present an exactly solvable Hamiltonian lattice model of the (1+1)-dimensional "3450" chiral gauge theory, and we argue that a related construction applies to the

U(1)

hypercharge symmetry of the Standard Model fermions in 3+1 dimensions. Our results open a new route toward fully local, nonperturbative formulations of chiral gauge theories.