Haldane phases and phase diagrams of the S = 3/2, 1 bilinear-biquadratic Heisenberg model on the orthogonal dimer chain

TL;DR

This paper explores the complex quantum phases of higher-spin orthogonal dimer chains, revealing multiple Haldane and gapless phases, and shows how higher-order interactions influence these phases using advanced numerical methods.

Contribution

It provides a systematic numerical analysis of the S=3/2, 1 orthogonal dimer chains, identifying new Haldane phases and their connection to AKLT states under higher-order interactions.

Findings

Biquadratic interactions expand Haldane phase regions.

S=3/2 Haldane phase connects to AKLT point with bicubic term.

Multiple quantum phases including gapless and ordered states identified.

Abstract

We systematically study the effects of higher-order interactions on the S = 3/2, 1 orthogonal dimer chains using exact diagonalization and density matrix renormalization group. Due to frustration and higher spin, there are rich quantum phases, including three Haldane phases, two gapless phases and several magnetically ordered phases. To characterize these phases and their phase transitions, we study various physical quantities such as energy gap, energy level crossing, fidelity susceptibility, spin correlation, entanglement spectrum and central charge. According to our calculations, the biquadratic term can enhance the Haldane phase regions. In particular, we numerically identify that a Haldane phase in S = 3/2 case is adiabatically connected to the exact AKLT point when adding bicubic term. Our study on the orthogonal dimer model, which is a 1D version of Shastry-Sutherland model, provides insights into understanding the possible S = 3/2, 1 Haldane phases in quasi-1D and 2D frustrated magnetic materials.