A new paradigm for two-dimensional spin-liquids

TL;DR

This paper proposes a new framework for understanding two-dimensional spin liquids by studying a square-lattice Heisenberg antiferromagnet with bond-centered spins, revealing a potential quantum disordered ground state.

Contribution

It introduces a novel model based on bond-centered spins on a square lattice and explores its quantum disordered ground state as a paradigm for 2D spin liquids.

Findings

Quantum fluctuations favor a 4-sublattice order.

The ground state likely remains disordered despite classical degeneracy.

The model provides a new paradigm for 2D spin-liquid behavior.

Abstract

Motivated by the geometry of the materials Na_2 Ti_2 As_2 O and Na_2 Ti_2 Sb_2 O, we study a square-lattice Heisenberg antiferromagnet with spins located at the bond-centers. The largest exchange constant J couples neighboring spins in a given row or column. This leads to a mesh of isolated spin-chains running along the X and Y axes. A weaker exchange constant J' couples the nearest-neighbor spins on the lattice. Classically, J' fails to fix the relative spin orientation for different chains and hence the ground state is highly degenerate. Quantum order by disorder effect is studied by spin-wave theory and numerical methods. It is shown that a 4-sublattice order is favored by quantum fluctuations. However, several arguments are presented that suggest that the ground state of the system remains disordered, thus providing us with a paradigm for a two-dimensional spin-liquid.