Effective field theory and integrability in two-dimensional Mott transition

Journal Article · Mon Aug 15 00:00:00 EDT 2011 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2011.04.010· OSTI ID:21583321

Bottesi, Federico L ^[1]

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1. Facultad de Ingenieria Pontificia Universidad Catolica Argentina, Av. Alicia Moreau de Justo 1500, 1428 Buenos Aires (Argentina)

Highlights: > Mott transition in 2d lattice fermion model. > 3D integrability out of 2D. > Effective field theory for Mott transition in 2d. > Double Chern-Simons. > d-Density waves. - 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 dimensions) property of the solution is used to identify the symmetry of the model at the Mott critical point as U{sub q}(sl(2)-circumflex)xU{sub q}(sl(2)-circumflex), with deformation parameter 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 transition 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.

• OSTI ID: 21583321
• Journal Information: Annals of Physics (New York), Vol. 326, Issue 8; Other Information: DOI: 10.1016/j.aop.2011.04.010; PII: S0003-4916(11)00069-8; Copyright (c) 2011 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANTIFERROMAGNETISM
COUPLING
COUPLING CONSTANTS
DEFORMATION
DENSITY
FERMIONS
FIELD THEORIES
INTERACTIONS
LIQUIDS
MATHEMATICAL SOLUTIONS
MATTER
ORDER PARAMETERS
QUANTUM GROUPS
SPACE-TIME
SPIN
SYMMETRY
TOPOLOGY
TRANSFORMATIONS
TWO-DIMENSIONAL CALCULATIONS
VORTICES
ANGULAR MOMENTUM
DIMENSIONLESS NUMBERS
FLUIDS
MAGNETISM
MATHEMATICS
PARTICLE PROPERTIES
PHYSICAL PROPERTIES
SYMMETRY GROUPS