The roles of magnetic and electric perturbations in the quantum Lifshitz model in $2+1$ dimensions are examined in this paper. The quantum Lifshitz model is an effective field theory for quantum multicritical systems, which include generalized two-dimensional (2D) quantum dimer models in bipartite lattices and their generalizations. It describes a class of quantum phase transitions between ordered and topological phases in $2+1$ dimensions. Magnetic perturbations break the dimer conservation law. Electric excitations, the condensation of which leads to ordered phases, have been studied extensively both in the classical three-dimensional model and in the quantum 2D model. The role of magnetic vortex excitations, the condensation of which drives these systems into a ${\mathbb{Z}}_{2}$ topological phase, has been largely ignored. Recent numerical studies claim that the quantum theory has a peculiar feature: the dynamical exponent $z$ flows continuously and the quantum theory is hence unstable to magnetic vortices. To study the interplay of both excitations, we perform a perturbative renormalization group study to one-loop order and study the stability of the theory away from quantum multicriticality. This is done by generalizing the operator-product expansion to anisotropic models. It is found that the dynamical exponent does not appear to flow, in contrast to the classical Monte Carlo study. Possible reasons for this difference are discussed at length.The roles of magnetic and electric perturbations in the quantum Lifshitz model in $2+1$ dimensions are examined in this paper. The quantum Lifshitz model is an effective field theory for quantum multicritical systems, which include generalized two-dimensional (2D) quantum dimer models in bipartite lattices and their generalizations. It describes a class of quantum phase transitions between ordered and topological phases in $2+1$ dimensions. Magnetic perturbations break the dimer conservation law. Electric excitations, the condensation of which leads to ordered phases, have been studied extensively both in the classical three-dimensional model and in the quantum 2D model. The role of magnetic vortex excitations, the condensation of which drives these systems into a ${\mathbb{Z}}_{2}$ topological phase, has been largely ignored. Recent numerical studies claim that the quantum theory has a peculiar feature: the dynamical exponent $z$ flows continuously and the quantum theory is hence unstable to magnetic vortices. To study the interplay of both excitations, we perform a perturbative renormalization group study to one-loop order and study the stability of the theory away from quantum multicriticality. This is done by generalizing the operator-product expansion to anisotropic models. It is found that the dynamical exponent does not appear to flow, in contrast to the classical Monte Carlo study. Possible reasons for this difference are discussed at length.

arXiv:1205.4911Physical Review BFeb 4, 201316 citations

Entanglement entropy in generalised quantum Lifshitz models

J. Angel-Ramelli, Valentina Giangreco M. Puletti, Lárus Thorlacius A

Abstract We compute universal finite corrections to entanglement entropy for generalised quantum Lifshitz models in arbitrary odd spacetime dimensions. These are generalised free field theories with Lifshitz scaling symmetry, where the dynamical critical exponent z equals the number of spatial dimensions d, and which generalise the 2+1-dimensional quantum Lifshitz model to higher dimensions. We analyse two cases: one where the spatial manifold is a d-dimensional sphere and the entanglement entropy is evaluated for a hemisphere, and another where a d-dimensional flat torus is divided into two cylinders. In both examples the finite universal terms in the entanglement entropy are scale invariant and depend on the compactification radius of the scalar field.Abstract We compute universal finite corrections to entanglement entropy for generalised quantum Lifshitz models in arbitrary odd spacetime dimensions. These are generalised free field theories with Lifshitz scaling symmetry, where the dynamical critical exponent z equals the number of spatial dimensions d, and which generalise the 2+1-dimensional quantum Lifshitz model to higher dimensions. We analyse two cases: one where the spatial manifold is a d-dimensional sphere and the entanglement entropy is evaluated for a hemisphere, and another where a d-dimensional flat torus is divided into two cylinders. In both examples the finite universal terms in the entanglement entropy are scale invariant and depend on the compactification radius of the scalar field.

arXiv:1906.08252Journal of High Energy PhysicsAug 1, 201922 citations

Quantum Criticality of the Two-dimensional Bose Gas with the Lifshitz dispersion

Congjun Wu, Jianda Wu

Bulletin of the American Physical SocietyMar 17, 20160 citations

Stability of the Fulde-Ferrell-Larkin-Ovchinnikov states in anisotropic systems and critical behavior at thermal m -axial Lifshitz points

Piotr Zdybel, Mateusz Homenda, Andrzej Chlebicki +1 more

We revisit the question concerning the stability of nonuniform superfluid states of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type to thermal and quantum fluctuations. On general grounds, we argue that the mean-field phase diagram hosting a Lifshitz point cannot be stable to fluctuations for isotropic, continuum systems, at any temperature $T>0$ in any dimensionality $d<4$ . In contrast, in layered unidirectional systems, the lower critical dimension for the onset of FFLO-type long-range order accompanied by a Lifshitz point at $T>0$ is $d=5/2$ . In consequence, its occurrence is excluded in $d=2$ , but not in $d=3$ . We propose a relatively simple method, based on nonperturbative renormalization group, to compute the critical exponents of the thermal $m$ -axial Lifshitz point continuously varying $m$ , spatial dimensionality $d$ , and the number of order parameter components, $N$ . We point out the possibility of a robust, fine-tuning free occurrence of a quantum Lifshitz point in the phase diagram of imbalanced Fermi mixtures.We revisit the question concerning the stability of nonuniform superfluid states of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type to thermal and quantum fluctuations. On general grounds, we argue that the mean-field phase diagram hosting a Lifshitz point cannot be stable to fluctuations for isotropic, continuum systems, at any temperature $T>0$ in any dimensionality $d<4$. In contrast, in layered unidirectional systems, the lower critical dimension for the onset of FFLO-type long-range order accompanied by a Lifshitz point at $T>0$ is $d=5/2$. In consequence, its occurrence is excluded in $d=2$, but not in $d=3$. We propose a relatively simple method, based on nonperturbative renormalization group, to compute the critical exponents of the thermal $m$-axial Lifshitz point continuously varying $m$, spatial dimensionality $d$, and the number of order parameter components, $N$. We point out the possibility of a robust, fine-tuning free occurrence of a quantum Lifshitz point in the phase diagram of imbalanced Fermi mixtures.

arXiv:2109.00631Physical Review ADec 27, 20218 citations

The roles of magnetic and electric perturbations in the quantum Lifshitz model in

2+1

dimensions are examined in this paper. The quantum Lifshitz model is an effective field theory for quantum multicritical systems, which include generalized two-dimensional (2D) quantum dimer models in bipartite lattices and their generalizations. It describes a class of quantum phase transitions between ordered and topological phases in

2+1

dimensions. Magnetic perturbations break the dimer conservation law. Electric excitations, the condensation of which leads to ordered phases, have been studied extensively both in the classical three-dimensional model and in the quantum 2D model. The role of magnetic vortex excitations, the condensation of which drives these systems into a

{\mathbb{Z}}_{2}

topological phase, has been largely ignored. Recent numerical studies claim that the quantum theory has a peculiar feature: the dynamical exponent

z

flows continuously and the quantum theory is hence unstable to magnetic vortices. To study the interplay of both excitations, we perform a perturbative renormalization group study to one-loop order and study the stability of the theory away from quantum multicriticality. This is done by generalizing the operator-product expansion to anisotropic models. It is found that the dynamical exponent does not appear to flow, in contrast to the classical Monte Carlo study. Possible reasons for this difference are discussed at length.

T>0

in any dimensionality

d<4

. In contrast, in layered unidirectional systems, the lower critical dimension for the onset of FFLO-type long-range order accompanied by a Lifshitz point at

T>0

d=5/2

. In consequence, its occurrence is excluded in

d=2

, but not in

d=3

. We propose a relatively simple method, based on nonperturbative renormalization group, to compute the critical exponents of the thermal

m

-axial Lifshitz point continuously varying

m

, spatial dimensionality

d

, and the number of order parameter components,

N

. We point out the possibility of a robust, fine-tuning free occurrence of a quantum Lifshitz point in the phase diagram of imbalanced Fermi mixtures.