Mean-field theory for Heisenberg zigzag ladder: Ground state energy and spontaneous symmetry breaking

TL;DR

This paper develops a mean-field theoretical approach to analyze the ground state energy and symmetry-breaking phenomena in the spin-1/2 zig-zag Heisenberg ladder, revealing phase transitions at specific coupling ratios.

Contribution

A novel representation and saddle point approximation for the J_1-J_2 model are introduced, providing analytical insights into phase transitions and symmetry breaking.

Findings

Identification of phase transitions at J_2/J_1=0.231 and 1/2

Analytical derivation of effective action for the model

Observation of spontaneous symmetry breaking phenomena

Abstract

The spin-1/2 zig-zag Heisenberg ladder (J_1 - J_2 model) is considered. A new representation for the model is found and a saddle point approximation over the spin-liquid order parameter < \vec \sigma_{n-1}(\vec \sigma_{n}\times \vec \sigma_{n+1}) > is performed. Corresponding effective action is derived and analytically analyzed. We observe the presence of phase transitions at values J_2/J_1=0.231 and J_2/J_1=1/2.