One dimensionalization in the spin-1 Heisenberg model on the anisotropic triangular lattice

TL;DR

This paper explores how quantum fluctuations induce a transition from a spiral magnetic order to a disordered, one-dimensional-like phase in a frustrated spin-1 Heisenberg model on an anisotropic triangular lattice, using DMRG and Schwinger boson methods.

Contribution

It provides the first combined DMRG and Schwinger boson analysis of the dimensional crossover and quantum phase transition in the spin-1 Heisenberg model on an anisotropic triangular lattice.

Findings

Abrupt transition at (J'/J)_c ≈ 0.42 from spin chains to spiral order.

Predicted instability of spiral order toward a disordered phase at (J'/J)_c ≈ 0.43.

Strong difference in intra- and interchain correlations indicating one-dimensionalization.

Abstract

We investigate the effect of dimensional crossover in the ground state of the antiferromagnetic spin-$1$ Heisenberg model on the anisotropic triangular lattice that interpolates between the regime of weakly coupled Haldane chains ($J^{\prime}\! \!\ll\!\! J$) and the isotropic triangular lattice ($J^{\prime}\!\!=\!\!J$). We use the density-matrix renormalization group (DMRG) and Schwinger boson theory performed at the Gaussian correction level above the saddle-point solution. Our DMRG results show an abrupt transition between decoupled spin chains and the spirally ordered regime at $(J^{\prime}/J)_c\sim 0.42$, signaled by the sudden closing of the spin gap. Coming from the magnetically ordered side, the computation of the spin stiffness within Schwinger boson theory predicts the instability of the spiral magnetic order toward a magnetically disordered phase with one-dimensional features at $(J^{\prime}/J)_c \sim 0.43$. The agreement of these complementary methods, along with the strong difference found between the intra- and the interchain DMRG short spin-spin correlations; for sufficiently large values of the interchain coupling, suggests that the interplay between the quantum fluctuations and the dimensional crossover effects gives rise to the one-dimensionalization phenomenon in this frustrated spin-$1$ Hamiltonian.