A detailed study of a model for strongly-interacting fermions with exclusion rules and lattice $\mathcal N=2$ supersymmetry is presented. A submanifold in the space of parameters of the model where it is Bethe-ansatz solvable is identified. The relation between this manifold and the existence of additional, so-called dynamic, supersymmetries is discussed. The ground states are analysed with the help of cohomology techniques, and their exact finite-size Bethe roots are found. Moreover, through analytical and numerical studies it is argued that the model provides a lattice version of the $\mathcal N=1$ super-sine-Gordon model at a particular coupling where an additional $\mathcal N=(2,2)$ supersymmetry is present. The dynamic supersymmetry is shown to allow an exact determination of the gap scaling function of the model.A detailed study of a model for strongly-interacting fermions with exclusion rules and lattice $\mathcal N=2$ supersymmetry is presented. A submanifold in the space of parameters of the model where it is Bethe-ansatz solvable is identified. The relation between this manifold and the existence of additional, so-called dynamic, supersymmetries is discussed. The ground states are analysed with the help of cohomology techniques, and their exact finite-size Bethe roots are found. Moreover, through analytical and numerical studies it is argued that the model provides a lattice version of the $\mathcal N=1$ super-sine-Gordon model at a particular coupling where an additional $\mathcal N=(2,2)$ supersymmetry is present. The dynamic supersymmetry is shown to allow an exact determination of the gap scaling function of the model.

arXiv:1408.4403Journal of Physics A Mathematical and TheoreticalNov 6, 20149 citations

Exact dynamical responses of interacting quantum critical points with emergent supersymmetry

William Witczak‐Krempa, Joseph Maciejko

We obtain exact, nonperturbative results for the zero- and finite-temperature dynamical responses at the semimetal-superconductor quantum critical point (QCP) of two-dimensional Dirac fermions, which can occur on the surface of a topological insulator. This strongly interacting QCP is described by a conformal field theory with emergent $\mathcal{N}=2$ supersymmetry, which imposes strong constraints. At zero temperature, we obtain closed-form results for the optical conductivity, dynamical shear viscosity, and corner entanglement entropy. We also make exact statements for the optical conductivity at finite temperature regarding large-frequency asymptotics and sum rules. Finally, we discuss experimental considerations for the observation of these signatures in topological insulators.We obtain exact, nonperturbative results for the zero- and finite-temperature dynamical responses at the semimetal-superconductor quantum critical point (QCP) of two-dimensional Dirac fermions, which can occur on the surface of a topological insulator. This strongly interacting QCP is described by a conformal field theory with emergent $\mathcal{N}=2$ supersymmetry, which imposes strong constraints. At zero temperature, we obtain closed-form results for the optical conductivity, dynamical shear viscosity, and corner entanglement entropy. We also make exact statements for the optical conductivity at finite temperature regarding large-frequency asymptotics and sum rules. Finally, we discuss experimental considerations for the observation of these signatures in topological insulators.

Oct 21, 20151 citation

Scaling Theory for Finite-Size Effects in the Critical Region

Michael Ellis Fisher, Michael N. Barber

Current physics sources and commentsJan 1, 19882 citations

Supersymmetric quantum spherical spins with short-range interactions

L V T Tavares, L G dos Santos, G T Landi +2 more

Abstract This work is dedicated to the study of a supersymmetric quantum spherical spin system with short-range interactions. We examine the critical properties both a zero and finite temperature. The model undergoes a quantum phase transition at zero temperature without breaking supersymmetry. At finite temperature the supersymmetry is broken and the system exhibits a thermal phase transition. We determine the critical dimensions and compute critical exponents. In particular, we find that the model is characterized by a dynamical critical exponent z = 2. We also investigate properties of correlations in the one-dimensional lattice. Finally, we explore the connection with a nonrelativistic version of the supersymmetric nonlinear sigma model and show that it is equivalent to the system of spherical spins in the large N limit.Abstract This work is dedicated to the study of a supersymmetric quantum spherical spin system with short-range interactions. We examine the critical properties both a zero and finite temperature. The model undergoes a quantum phase transition at zero temperature without breaking supersymmetry. At finite temperature the supersymmetry is broken and the system exhibits a thermal phase transition. We determine the critical dimensions and compute critical exponents. In particular, we find that the model is characterized by a dynamical critical exponent z = 2. We also investigate properties of correlations in the one-dimensional lattice. Finally, we explore the connection with a nonrelativistic version of the supersymmetric nonlinear sigma model and show that it is equivalent to the system of spherical spins in the large N limit.

arXiv:1910.04007Journal of Statistical Mechanics Theory and ExperimentFeb 1, 20200 citations

A detailed study of a model for strongly-interacting fermions with exclusion rules and lattice

\mathcal N=2

supersymmetry is presented. A submanifold in the space of parameters of the model where it is Bethe-ansatz solvable is identified. The relation between this manifold and the existence of additional, so-called dynamic, supersymmetries is discussed. The ground states are analysed with the help of cohomology techniques, and their exact finite-size Bethe roots are found. Moreover, through analytical and numerical studies it is argued that the model provides a lattice version of the

\mathcal N=1

super-sine-Gordon model at a particular coupling where an additional

\mathcal N=(2,2)

supersymmetry is present. The dynamic supersymmetry is shown to allow an exact determination of the gap scaling function of the model.

\mathcal{N}=2

supersymmetry, which imposes strong constraints. At zero temperature, we obtain closed-form results for the optical conductivity, dynamical shear viscosity, and corner entanglement entropy. We also make exact statements for the optical conductivity at finite temperature regarding large-frequency asymptotics and sum rules. Finally, we discuss experimental considerations for the observation of these signatures in topological insulators.