Ground-state phases of the spin-1/2 J_1-J_2 Heisenberg antiferromagnet on the square lattice: A high-order coupled cluster treatment

TL;DR

This study uses high-order coupled cluster and exact diagonalization methods to analyze the ground state phases of the spin-1/2 J1-J2 Heisenberg antiferromagnet on a square lattice, identifying quantum critical points and phase transition nature.

Contribution

The paper provides a high-order coupled cluster analysis of the J1-J2 model, offering new insights into quantum critical points and the nature of phase transitions.

Findings

Quantum critical points at J2c1≈0.44J1 and J2c2≈0.59J1.

No evidence for first-order transition from Néel to valence-bond solid.

Supports deconfinement scenario for the phase transition.

Abstract

Using the coupled cluster method for high orders of approximation and complementary exact diagonalization studies we investigate the ground state properties of the spin-1/2 $J_1$--$J_2$ frustrated Heisenberg antiferromagnet on the square lattice. We have calculated the ground-state energy, the magnetic order parameter, the spin stiffness, and several generalized susceptibilities to probe magnetically disordered quantum valence-bond phases. We have found that the quantum critical points for both the N\'eel and collinear orders are $J_2^{c1}\approx (0.44 \pm 0.01)J_1$ and $J_2^{c2}\approx (0.59 \pm 0.01)J_1$ respectively, which are in good agreement with the results obtained by other approximations. In contrast to the recent study by [Sirker et al. Phys. Rev. B {\bf 73}, 184420 (2006)], our data do not provide evidence for the transition from the N\'{e}el to the valence-bond solid state to be first order. Moreover, our results are in favor of the deconfinement scenario for that phase transition. We also discuss the nature of the magnetically disordered quantum phase.