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

We study a compact U(1) lattice gauge theory using a self-built Hybrid Monte Carlo (HMC) program. The starting point is the parton construction of the Heisenberg spin chain where the spins are fractionalized into spinons coupled to an emergent compact U(1) gauge field. Here we do not impose Gauss's law, such that the Hamiltonian describes an unconstrained lattice gauge theory. We make theoretical calculations of the ground-state phase diagram and identify an emergent SO(4) symmetry in the strong-coupling limit. Furthermore, the weak coupling limit corresponds to frozen gauge fields which results in a free fermionic phase that is unstable in one dimension. The phase diagram is supported by carrying out HMC simulations which also allow us to study the dynamical generation of Gauss's law at low energy scales. We find that the theory accurately predicts the numerical findings and establish that HMC works as a method for simulating unconstrained gauge theories in (1+1)-dimensions.We study a compact U(1) lattice gauge theory using a self-built Hybrid Monte Carlo (HMC) program. The starting point is the parton construction of the Heisenberg spin chain where the spins are fractionalized into spinons coupled to an emergent compact U(1) gauge field. Here we do not impose Gauss's law, such that the Hamiltonian describes an unconstrained lattice gauge theory. We make theoretical calculations of the ground-state phase diagram and identify an emergent SO(4) symmetry in the strong-coupling limit. Furthermore, the weak coupling limit corresponds to frozen gauge fields which results in a free fermionic phase that is unstable in one dimension. The phase diagram is supported by carrying out HMC simulations which also allow us to study the dynamical generation of Gauss's law at low energy scales. We find that the theory accurately predicts the numerical findings and establish that HMC works as a method for simulating unconstrained gauge theories in (1+1)-dimensions.

Jan 1, 20260 citations

Theory of Spin Lattices and Lattice Gauge Models

J. W. Clark, MANFRED L. RISTIG

Springer eBooksJan 1, 19979 citations

Hamiltonian Lattice Gauge Theories

Giovanni Cataldi

Graduate texts in physicsJan 1, 20260 citations

Analytic Approach to Phase Transitions in Lattice Gauge Theories

Rodolfo Gambini, Antoni Trias

The Hamiltonian formulation is analyzed in a basis of gauge-invariant loop states. A natural geometric asymptotic approximation for the eigenstates of the Hamiltonian is developed to identify the phase diagram of the theory. Satisfactory explicit calculations are performed in the case of ${Z}_{2}$ .The Hamiltonian formulation is analyzed in a basis of gauge-invariant loop states. A natural geometric asymptotic approximation for the eigenstates of the Hamiltonian is developed to identify the phase diagram of the theory. Satisfactory explicit calculations are performed in the case of ${Z}_{2}$.

Physical Review LettersDec 17, 198430 citations

A many-body approach to Hamiltonian lattice gauge field theories

R. F. Bishop, Yang Xian

Nuclear Physics B - Proceedings SupplementsApr 1, 19942 citations

Resonating plaquette phases in SU(4) Heisenberg antiferromagnet

Cenke Xu, Congjun Wu

Large spin cold atom systems can exhibit magnetic properties that do not appear in usual spin- $1∕2$ systems. We investigate the SU(4) resonating plaquette state in the three-dimensional cubic optical lattice with spin- $3∕2$ cold fermions. A gauge field formalism is constructed to describe the Rokhsar--Kivelson type of Hamiltonian and a duality transformation is used to study the phase diagram. Due to the proliferation of topological defects, the system is generally gapped for the whole phase diagram of the quantum model, which agrees with the recent numerical studies. The classical plaquette model on the cubic lattice is also studied, and a critical phase is predicted by tuning one parameter in the low energy field theory.Large spin cold atom systems can exhibit magnetic properties that do not appear in usual spin-$1∕2$ systems. We investigate the SU(4) resonating plaquette state in the three-dimensional cubic optical lattice with spin-$3∕2$ cold fermions. A gauge field formalism is constructed to describe the Rokhsar--Kivelson type of Hamiltonian and a duality transformation is used to study the phase diagram. Due to the proliferation of topological defects, the system is generally gapped for the whole phase diagram of the quantum model, which agrees with the recent numerical studies. The classical plaquette model on the cubic lattice is also studied, and a critical phase is predicted by tuning one parameter in the low energy field theory.

arXiv:0801.0744Physical Review BApr 30, 200878 citations

{Z}_{2}

Large spin cold atom systems can exhibit magnetic properties that do not appear in usual spin-

1∕2

systems. We investigate the SU(4) resonating plaquette state in the three-dimensional cubic optical lattice with spin-

3∕2

cold fermions. A gauge field formalism is constructed to describe the Rokhsar--Kivelson type of Hamiltonian and a duality transformation is used to study the phase diagram. Due to the proliferation of topological defects, the system is generally gapped for the whole phase diagram of the quantum model, which agrees with the recent numerical studies. The classical plaquette model on the cubic lattice is also studied, and a critical phase is predicted by tuning one parameter in the low energy field theory.