Quantum Double-field Model and Application

Philip Baback Alipour, Thomas Aaron Gulliver

Leander Fiedler, Pieter Naaijkens

We prove Haag duality for cone-like regions in the ground state representation corresponding to the translational invariant ground state of Kitaev’s quantum double model for finite abelian groups. This property says that if an observable commutes with all observables localized outside the cone region, it actually is an element of the von Neumann algebra generated by the local observables inside the cone. This strengthens locality, which says that observables localized in disjoint regions commute. As an application, we consider the superselection structure of the quantum double model for abelian groups on an infinite lattice in the spirit of the Doplicher–Haag–Roberts program in algebraic quantum field theory. We find that, as is the case for the toric code model on an infinite lattice, the superselection structure is given by the category of irreducible representations of the quantum double.

Eduardo C. Marino

Michele Fabrizio, Alexander O. Gogolin, A. A. Nersesyan

We study the properties of the double-frequency sine–Gordon model in the vicinity of the Ising quantum phase transition displayed by this model. Using a mapping onto a generalised lattice quantum Ashkin-Teller model, we obtain critical and nearly-off-critical correlation functions of various operators. We discuss applications of the double-sine-Gordon model to one-dimensional physical systems, like spin chains in a staggered external field and interacting electrons in a staggered potential. PACS: 71.10.Pm; 71.10.Fd; 75.10.Jm

S. De Martino, Silvio De Siena, Pasquale Sodano

We investigate the critical behavior of systems modeled by the quantum double-sine-Gordon theory. We find the existence of a Kosterlitz-Thouless transition in a region of the phase space. For different ranges of the physical parameters, the model is shown to be equivalent to a free massive Dirac field.