Neel order in the Hubbard model within spin-charge rotating reference frame approach: crossover from weak to strong coupling

TL;DR

This paper develops a self-consistent SU(2)xU(1) rotor approach to study the antiferromagnetic phase in the Hubbard model, capturing the crossover from weak to strong coupling and respecting symmetry constraints.

Contribution

It introduces a novel spin-charge rotor framework that describes the evolution from Slater to Mott-Heisenberg antiferromagnetism in the Hubbard model.

Findings

Describes the evolution from Slater to Mott-Heisenberg antiferromagnetism.

Provides phase diagrams for 2D and 3D Hubbard models.

Analyzes the role of the spin Berry phase in the crossover.

Abstract

The antiferromagnetic phase of two-dimensional (2D) and three-dimensional (3D) Hubbard model with nearest neighbors hopping is studied on a bipartite cubic lattice by means of the quantum SU(2)xU(1) rotor approach that yields a fully self-consistent treatment of the antiferromagnetic state that respects the symmetry properties the model and satisfy the Mermin-Wagner theorem. The collective variables for charge and spin are isolated in the form of the space-time fluctuating U(1) phase field and rotating spin quantization axis governed by the SU(2) symmetry, respectively. As a result interacting electrons appear as a composite objects consisting of bare fermions with attached U(1) and SU(2) gauge fields. An effective action consisting of a spin-charge rotor and a fermionic fields is derived as a function of the Coulomb repulsion U and hopping parameter t. At zero temperature, our theory describes the evolution from a Slater (U<<t) to a Mott-Heisenberg (U>>t) antiferromagnet. The results for zero-temperature sublatice magnetization (2D) and finite temperature (3D) phase diagram of the antiferromagnetic Hubbard model as a function of the crossover parameter U/t are presented and the role of the spin Berry phase in the interaction driven crossover is analyzed.