Effective field theory and integrability in two-dimensional Mott transition

• Autores: Bottesi, Federico L.; Zemba, Guillermo Raúl
• Año de publicación: 2010
• Idioma: inglés
• Tipo de recurso: documento de trabajo
• Materia: TRANSICION DE MOTT; MODELO BIDIMENSIONAL; TEORIA DE CHERN SIMONS; MODELO DE ISING; FISICA
• Institución: Pontificia Universidad Católica Argentina

Fil: Zemba, Guillermo Raúl. Pontificia Universidad Católica Argentina. Facultad de Ciencias Fisicomatemáticas e Ingeniería; Argentina
Fil: Bottesi, Federico L. Pontificia Universidad Católica Argentina. Facultad de Ciencias Fisicomatemáticas e Ingeniería; Argentina
Abstract: We study the Mott transition in a two-dimensional lattice spinless fermion model with nearest neighbors density-density interactions. By means of a two-dimensional Jordan-Wigner transformation, the model is mapped onto the lattice XXZ spin model, which is shown to possess a Quantum Group symmetry as a consequence of a recently found solution of the Zamolodchikov Tetrahedron Equation. A projection (from three to two space-time dimen- sions) property of the solution is used to identify the symmetry of the model at the Mott critical point as Uq([sl(2)) ⊗ Uq([sl(2)), with deformation param- eter q = −1. Based on this result, the low-energy Effective Field theory for the model is obtained and shown to be a lattice double Chern-Simons theory with coupling constant k = 1 (with the standard normalization). By further employing the Effective Filed Theory methods, we show that the Mott transi- tion that arises is of topological nature, with vortices in an antiferromagnetic array and matter currents characterized by a d-density wave order parameter. We also analyze the behavior of the system upon weak coupling, and conclude that it undergoes a quantum gas-liquid transition which belongs to the Ising universality class.