Two-dimensional quantum spin-1/2 Heisenberg model with competing interactions

TL;DR

This paper investigates the phase transitions in a two-dimensional quantum spin-1/2 Heisenberg model with competing interactions, analyzing how the transition temperature varies with interaction ratio and identifying a quantum critical point.

Contribution

It introduces a detailed analysis of the phase diagram for a 2D Heisenberg model with both antiferromagnetic and ferromagnetic interactions using Green's function methods, including quantum phase transition insights.

Findings

Transition temperature decreases with frustration parameter 

Transition temperature drops to zero at =_c= 8

Quantum critical point identified at =_c for varying interaction decay exponent

Abstract

We study the quantum spin-1/2 Heisenberg model in two dimensions, interacting through a nearest-neighbor antiferromagnetic exchange ($J$) and a ferromagnetic dipolar-like interaction ($J_d$), using double-time Green's function, decoupled within the random phase approximation (RPA). We obtain the dependence of $k_B T_c/J_d$ as a function of frustration parameter $\delta$, where $T_c$ is the ferromagnetic (F) transition temperature and $\delta$ is the ratio between the strengths of the exchange and dipolar interaction (i.e., $\delta = J/J_d$). The transition temperature between the F and paramagnetic phases decreases with $\delta$, as expected, but goes to zero at a finite value of this parameter, namely $\delta = \delta_c = \pi /8$. At T=0 (quantum phase transition), we analyze the critical parameter $\delta_c(p)$ for the general case of an exchange interaction in the form $J_{ij}=J_d/r_{ij}^{p}$, where ferromagnetic and antiferromagnetic phases are present.