A Plane of Weakly Coupled Heisenberg Chains: Theoretical Arguments and Numerical Calculations

TL;DR

This paper investigates whether Nel order in a quantum Heisenberg antiferromagnet on a square lattice with anisotropic couplings develops at infinitesimal interchain coupling, using theoretical arguments and numerical calculations.

Contribution

It challenges previous assumptions by suggesting the critical interchain coupling is zero or very small, depending on microscopic details, supported by numerical series expansion results.

Findings

Critical interchain coupling ratio R_c is likely zero or very close to zero.

Numerical results support the absence of a finite critical coupling.

Theoretical arguments indicate non-universality of the critical coupling.

Abstract

The $S=1/2$, nearest-neighbor, quantum Heisenberg antiferromagnet on the square lattice with spatially anisotropic couplings is reconsidered, with particular attention to the following question: at T=0, does N\'eel orderdevelop at infinitesimal interchain coupling, or is there a nonzero critical coupling? A heuristic renormalization group argument is presented which suggests that previous theoretical answers to that question are incorrect or at least incomplete, and that the answer is not universal but rather depends on the microscopic details of the model under consideration. Numerical investigations of the nearest-neighbor model are carried out {\it via} zero-temperature series expansions about Ising and dimer Hamiltonians. The results are entirely consistent with a vanishing critical interchain coupling ratio $R_c$; if $R_c$ is finite, it is unlikely to substantially exceed 0.02.