Spontaneous dimerization, critical lines, and short-range correlations in a frustrated spin-1 chain

TL;DR

This paper thoroughly investigates a frustrated spin-1 chain model, identifying phase boundaries, critical behaviors, and correlation changes using advanced numerical methods, revealing complex phase structures and universality classes.

Contribution

It provides a detailed phase diagram of the spin-1 $J_1-J_2-J_3$ model, including precise boundary determination and analysis of critical lines and correlation properties.

Findings

Phase boundaries accurately determined using multiple indicators.

Transition between NNN Haldane and dimerized phases is in the Ising universality class.

Short-range correlations exhibit disorder and Lifshitz lines, indicating rich phase behavior.

Abstract

We report on a detailed investigation of the spin-1 $J_1-J_2-J_3$ Heisenberg model, a frustrated model with nearest-neighbor coupling $J_1$, next-nearest neighbor coupling $J_2$, and a three site interaction $J_3\left[({\bf S}_{i-1}\cdot {\bf S}_i)({\bf S}_i\cdot {\bf S}_{i+1})+{\mathrm H.c.}\right]$ previously studied in [Phys. Rev. B 93, 241108(R) (2016)]. Using DMRG and exact diagonalizations, we show that the phase boundaries between the Haldane phase, the next-nearest neighbor Haldane phase and the dimerized phase can be very accurately determined by combining the information deduced from the dimerization, the ground-state energy, the entanglement spectrum and the Berry phase. By a careful investigation of the finite-size spectrum, we also show that the transition between the next-nearest neighbor Haldane phase and the dimerized phase is in the Ising universality class all along the critical line. Furthermore, we justify the conformal embedding of the $SU(2)_2$ Wess-Zumino-Witten conformal field theory in terms of a boson and an Ising field, and we explicitly derive a number of consequences of this embedding for the spectrum along the $SU(2)_2$ transition line between the Haldane phase and the dimerized phase. We also show that the solitons along the first-order transition line between the Haldane phase and the dimerized phase carry a spin-1/2, while those between different dimerization domains inside the dimerized phase carry a spin 1. Finally, we show that short-range correlations change character in the Haldane and dimerized phases through disorder and Lifshitz lines, as well as through the development of short-range dimer correlations in the Haldane phase, leading to a remarkably rich phase diagram.