The Ising phase in the J1-J2 Heisenberg Model

TL;DR

This paper investigates the phase diagram of the J1-J2 Heisenberg model on a square lattice, revealing an Ising transition and a possible non-magnetic ground state with orientational order through theoretical and numerical methods.

Contribution

It introduces a new effective field theory for the model and combines it with Lanczos diagonalizations to identify a non-magnetic phase with orientational order.

Findings

Support for an Ising phase transition at finite temperature

Identification of a non-magnetic ground state breaking rotational symmetry

Correlation functions show size independence indicating a stable phase

Abstract

The two dimensional Heisenberg antiferromagnet on the square lattice with nearest (J1) and next-nearest (J2) neighbor couplings is investigated in the strong frustration regime (J2/J1>1/2). A new effective field theory describing the long wavelength physics of the model is derived from the quantum hamiltonian. The structure of the resulting non linear sigma model allows to recover the known spin wave results in the collinear regime, supports the presence of an Ising phase transition at finite temperature and suggests the possible occurrence of a non-magnetic ground state breaking rotational symmetry. By means of Lanczos diagonalizations we investigate the spin system at T=0, focusing our attention on the region where the collinear order parameter is strongly suppressed by quantum fluctuations and a transition to a non-magnetic state occurs. Correlation functions display a remarkable size independence and allow to identify the transition between the magnetic and non-magnetic region of the phase diagram. The numerical results support the presence of a non-magnetic phase with orientational ordering.