Spin-1/2 $J_{1}$-$J_{2}$ Heisenberg model on a cross-striped square lattice

TL;DR

This study uses the coupled cluster method to map the zero-temperature ground-state phase diagram of a quantum spin-1/2 $J_1$-$J_2$ Heisenberg model on a cross-striped square lattice, revealing five distinct phases including a novel plaquette VBC phase.

Contribution

First detailed quantum phase diagram of the spin-1/2 $J_1$-$J_2$ model on a cross-striped lattice, identifying a new quantum phase and characterizing the nature of phase transitions.

Findings

Identification of five quantum phases including a new plaquette VBC phase.

High-accuracy determination of quantum critical points.

Evidence for deconfined quantum phase transitions.

Abstract

Using the coupled cluster method (CCM) we study the full (zero-temperature) ground-state (GS) phase diagram of a spin-half ($s=1/2$) $J_{1}$-$J_{2}$ Heisenberg model on a cross-striped square lattice. Each site of the square lattice has 4 nearest-neighbour exchange bonds of strength $J_{1}$ and 2 next-nearest-neighbour (diagonal) bonds of strength $J_{2}$. The $J_{2}$ bonds are arranged so that the basic square plaquettes in alternating columns have either both or no $J_{2}$ bonds included. The classical ($s \rightarrow \infty$) version of the model has 4 collinear phases when $J_{1}$ and $J_{2}$ can take either sign. Three phases are antiferromagnetic (AFM), showing so-called N\'{e}el, double N\'{e}el and double columnar striped order respectively, while the fourth is ferromagnetic. For the quantum $s=1/2$ model we use the 3 classical AFM phases as CCM reference states, on top of which the multispin-flip configurations arising from quantum fluctuations are incorporated in a systematic truncation hierarchy. Calculations of the corresponding GS energy, magnetic order parameter and the susceptibilities of the states to various forms of valence-bond crystalline (VBC) order are thus carried out numerically to high orders of approximation and then extrapolated to the (exact) physical limit. We find that the $s=1/2$ model has 5 phases, which correspond to the four classical phases plus a new quantum phase with plaquette VBC order. The positions of the 5 quantum critical points are determined with high accuracy. While all 4 phase transitions in the classical model are first order, we find strong evidence that 3 of the 5 quantum phase transitions in the $s=1/2$ model are of continuous deconfined type.