Spin-1/2 frustrated antiferromagnet on a spatially anisotopic square lattice: contribution of exact diagonalizations

TL;DR

This paper uses exact diagonalizations to explore the phase diagram of a frustrated spin-1/2 model on an anisotropic square lattice, revealing the presence of a resonating valence bond state and columnar dimer order.

Contribution

It provides new insights into the phase diagram of the anisotropic $J-J'-J_2$ model, especially regarding the RVB state and dimer order, extending previous theoretical predictions.

Findings

Resonating valence bond state exists for specific coupling ratios.

Columnar dimer long-range order likely borders the RVB phase.

The RVB state extends beyond small interchain couplings.

Abstract

The phase diagram of a spin-1/2 $J-J'-J_2$ model is investigated by means of exact diagonalizations on finite samples. This model is a generalization of the $J_1-J_2$ model on the square lattice with two different nearest-neighbor couplings $J,J'$ and may be also viewed as an array of coupled Heisenberg chains. The results suggest that the resonnating valence bond state predicted by Nersesyan and Tsvelik [Phys. Rev. B {\bf 67}, 024422 (2003)] for $J_2=0.5J' \ll J$ is realized and extends beyond the limit of small interchain coupling along a curve nearly coincident with the line where the energy per spin is maximum. This line is likely bordered on both side by a columnar dimer long range order. This columnar order could extends for $J'\to J$ which correspond to the $J_1-J_2$ model.