Bilinear-biquadratic spin-1 model in the Haldane and dimerized phases

TL;DR

This paper investigates the low-energy spectrum of the spin-1 bilinear-biquadratic model in different phases using tensor renormalization, revealing partial agreement with theoretical predictions and identifying unexpected gaps.

Contribution

It applies tensor renormalization to analyze the spectrum in the Haldane and dimerized phases, highlighting discrepancies with WZW model predictions.

Findings

Partial confirmation of WZW spectrum at critical point

Discovery of a singlet-singlet gap inconsistent with WZW

Comparison with Bethe Ansatz, ED, and DMRG results

Abstract

We study the low-lying spectrum of the bilinear-biquadratic Heisenberg model in the dimerized and Haldane phases using a tensor renormalization method. At the (Takhtajan-Babujian) critical point the finite size spectrum predicted by the Wess-Zumino-Witten (WZW) model can only partly be confirmed. We find a singlet-singlet gap which does not fit into the WZW systematics. The results obtained are compared to Bethe Ansatz, exact diagonalization, and density matrix renormalization group (DMRG) calculations for specific parameters.