Criticality in coupled quantum spin-chains with competing ladder-like and two-dimensional couplings

TL;DR

This paper investigates a two-layer quantum spin model inspired by CaCu$_2$O$_3$, revealing how interlayer coupling influences magnetic order and demonstrating a square root relationship with in-plane anisotropy.

Contribution

It introduces a detailed analysis of a coupled spin-1/2 Heisenberg model with competing interactions, combining Quantum Monte Carlo and series expansion methods to map the phase diagram.

Findings

Critical interlayer coupling J_ot^c depends on in-plane anisotropy as a square root.

The model exhibits a transition from Néel order to disordered ground state.

Finite-temperature properties align with zero-temperature phase boundaries.

Abstract

Motivated by the geometry of spins in the material CaCu$_2$O$_3$, we study a two-layer, spin-half Heisenberg model, with nearest-neighbor exchange couplings J and \alpha*J along the two axes in the plane and a coupling J_\perp perpendicular to the planes. We study these class of models using the Stochastic Series Expansion (SSE) Quantum Monte Carlo simulations at finite temperatures and series expansion methods at T=0. The critical value of the interlayer coupling, J_\perp^c, separating the N{\'e}el ordered and disordered ground states, is found to follow very closely a square root dependence on $\alpha$. Both T=0 and finite-temperature properties of the model are presented.