We consider XY-spin degrees of freedom on an fcc lattice, such that the system respects some subsystem global symmetry. We then gauge this global symmetry and study the corresponding $U(1)$ gauge theory on the fcc lattice. Surprisingly, this $U(1)$ gauge theory is dual to the original spin system. We also analyze a similar ${\mathbb{Z}}_{N}$ gauge theory on that lattice. All these systems are fractonic. The $U(1)$ theories are gapless and the ${\mathbb{Z}}_{N}$ theories are gapped. We analyze the continuum limits of all these systems and present free continuum Lagrangians for their low-energy physics. Our ${\mathbb{Z}}_{2}$ fcc gauge theory is the continuum limit of the well-known checkerboard model of fractons. Our continuum analysis leads to a straightforward proof of the known fact that this theory is dual to two copies of the ${\mathbb{Z}}_{2}$ X-cube model. We find new models and new relations between known models. The ${\mathbb{Z}}_{N}$ fcc gauge theory can be realized by coupling three copies of an anisotropic model of lineons and planons to a certain exotic ${\mathbb{Z}}_{2}$ gauge theory. Also, although for $N=2$ this model is dual to two copies of the ${\mathbb{Z}}_{2}$ X-cube model, a similar statement is not true for higher $N$ .We consider XY-spin degrees of freedom on an fcc lattice, such that the system respects some subsystem global symmetry. We then gauge this global symmetry and study the corresponding $U(1)$ gauge theory on the fcc lattice. Surprisingly, this $U(1)$ gauge theory is dual to the original spin system. We also analyze a similar ${\mathbb{Z}}_{N}$ gauge theory on that lattice. All these systems are fractonic. The $U(1)$ theories are gapless and the ${\mathbb{Z}}_{N}$ theories are gapped. We analyze the continuum limits of all these systems and present free continuum Lagrangians for their low-energy physics. Our ${\mathbb{Z}}_{2}$ fcc gauge theory is the continuum limit of the well-known checkerboard model of fractons. Our continuum analysis leads to a straightforward proof of the known fact that this theory is dual to two copies of the ${\mathbb{Z}}_{2}$ X-cube model. We find new models and new relations between known models. The ${\mathbb{Z}}_{N}$ fcc gauge theory can be realized by coupling three copies of an anisotropic model of lineons and planons to a certain exotic ${\mathbb{Z}}_{2}$ gauge theory. Also, although for $N=2$ this model is dual to two copies of the ${\mathbb{Z}}_{2}$ X-cube model, a similar statement is not true for higher $N$.

arXiv:2010.16414Physical review. B./Physical review. BMay 7, 202138 citations

Hamiltonian studies of phase diagrams of lattice gauge theories and spin systems

Jay L. Banks

Jan 1, 19800 citations

Kagome Chiral Spin Liquid as a Gauged U ( 1 ) Symmetry Protected Topological Phase

Yin-Chen He, Subhro Bhattacharjee, Frank Pollmann +1 more

While the existence of a chiral spin liquid (CSL) on a class of spin-1/2 kagome antiferromagnets is by now well established numerically, a controlled theoretical path from the lattice model leading to a low-energy topological field theory is still lacking. This we provide via an explicit construction starting from reformulating a microscopic model for a CSL as a lattice gauge theory and deriving the low-energy form of its continuum limit. A crucial ingredient is the realization that the bosonic spinons of the gauge theory exhibit a U(1) symmetry protected topological (SPT) phase, which upon promoting its U(1) global symmetry to a local gauge structure ("gauging"), yields the CSL. We suggest that such an explicit lattice-based construction involving gauging of a SPT phase can be applied more generally to understand topological spin liquids.While the existence of a chiral spin liquid (CSL) on a class of spin-1/2 kagome antiferromagnets is by now well established numerically, a controlled theoretical path from the lattice model leading to a low-energy topological field theory is still lacking. This we provide via an explicit construction starting from reformulating a microscopic model for a CSL as a lattice gauge theory and deriving the low-energy form of its continuum limit. A crucial ingredient is the realization that the bosonic spinons of the gauge theory exhibit a U(1) symmetry protected topological (SPT) phase, which upon promoting its U(1) global symmetry to a local gauge structure ("gauging"), yields the CSL. We suggest that such an explicit lattice-based construction involving gauging of a SPT phase can be applied more generally to understand topological spin liquids.

arXiv:1509.03070Physical Review LettersDec 30, 201531 citations

Hamiltonian Lattice Gauge Theories

Giovanni Cataldi

Graduate texts in physicsJan 1, 20260 citations

Theory of spine latticesand lattice gauge models : 165th WE-Heraeus Seminar, held at Physikzentrum Bad Honnef, Germany, October 14-16, 1996

J. W. Clark, MANFRED L. RISTIG

Ising, Heisenberg and Hubbard models in relation to insulating and metallic ferro- and antiferro-magnets studies of lattice spin systems using series expansions application of linked-cluster expansions to quantum Hamiltonian lattice systems critical properties of 1-D spin 1/2 antiferro-magnetic Heisenberg model the Z(2) lattice gauge vacuum and the transverse Ising model crystallographic point and space group symmetries in correlated many-body wave functions Hamiltonian lattice calculations on gauge and chiral meson field theories.Ising, Heisenberg and Hubbard models in relation to insulating and metallic ferro- and antiferro-magnets studies of lattice spin systems using series expansions application of linked-cluster expansions to quantum Hamiltonian lattice systems critical properties of 1-D spin 1/2 antiferro-magnetic Heisenberg model the Z(2) lattice gauge vacuum and the transverse Ising model crystallographic point and space group symmetries in correlated many-body wave functions Hamiltonian lattice calculations on gauge and chiral meson field theories.

Akademie Verlag eBooksJan 1, 19970 citations

Topics in Lattice Gauge Theories and Spin Systems.

Stephen H. Shenker

Jan 1, 19800 citations

We consider XY-spin degrees of freedom on an fcc lattice, such that the system respects some subsystem global symmetry. We then gauge this global symmetry and study the corresponding

U(1)

gauge theory on the fcc lattice. Surprisingly, this

U(1)

gauge theory is dual to the original spin system. We also analyze a similar

{\mathbb{Z}}_{N}

gauge theory on that lattice. All these systems are fractonic. The

U(1)

theories are gapless and the

{\mathbb{Z}}_{N}

theories are gapped. We analyze the continuum limits of all these systems and present free continuum Lagrangians for their low-energy physics. Our

{\mathbb{Z}}_{2}

fcc gauge theory is the continuum limit of the well-known checkerboard model of fractons. Our continuum analysis leads to a straightforward proof of the known fact that this theory is dual to two copies of the

{\mathbb{Z}}_{2}

X-cube model. We find new models and new relations between known models. The

{\mathbb{Z}}_{N}

fcc gauge theory can be realized by coupling three copies of an anisotropic model of lineons and planons to a certain exotic

{\mathbb{Z}}_{2}

gauge theory. Also, although for

N=2

this model is dual to two copies of the

{\mathbb{Z}}_{2}

X-cube model, a similar statement is not true for higher

N