Quantum Melting of Spin-1 Dimer Solid Induced by Inter-chain Couplings

TL;DR

This study investigates the stability of dimerized valence bond solids in spin-1 systems on an anisotropic square lattice, revealing that quantum fluctuations cause the dimer phase to melt at weaker interchain couplings than previously predicted.

Contribution

The paper combines numerical and analytical methods to show that the dimer phase in spin-1 systems is less stable against interchain coupling than mean-field theories suggest.

Findings

Dimer phase melts at interchain coupling ratio r ≈ 0.15

Transition to magnetic order is first order with hysteresis

Quantum fluctuations strongly destabilize the dimer phase

Abstract

Dimerized valence bond solids appear naturally in spin-1/2 systems on bipartite lattices, with the geometric frustrations playing a key role both in their stability and the eventual `melting' due to quantum fluctuations. Here, we ask the question of the stability of such dimerized solids in spin-1 systems, taking the anisotropic square lattice with bilinear and biquadratic spin-spin interactions as a paradigmatic model. The lattice can be viewed as a set of coupled spin-1 chains, which in the limit of vanishing inter-chain coupling are known to possess a stable dimer phase. We study this model using the density matrix renormalization group (DMRG) and infinite projected entangled-pair states (iPEPS) techniques, supplemented by the analytical mean-field and linear flavor wave theory calculations. While the latter predicts the dimer phase to remain stable up to a reasonably large interchain-to-intrachain coupling ratio $r \lesssim 0.6$, the DMRG and iPEPS find that the dimer solid melts for much weaker interchain coupling not exceeding $r\lesssim 0.15$. We find the transition into a magnetically ordered state to be first order, manifested by a hysteresis and order parameter jump, precluding the deconfined quantum critical scenario. The apparent lack of stability of dimerized phases in 2D spin-1 systems is indicative of strong quantum fluctuations that melt the dimer solid.