Quantum Phase Transitions in the Spin 1 Bilinear-Biquadratic Heisenberg Model Based on Classical and Quantum Correlations

TL;DR

This paper explores how quantum and classical correlations can be used to detect quantum phase transitions in a one-dimensional spin-1 bilinear-biquadratic Heisenberg model, revealing insights into critical points at various temperatures.

Contribution

It introduces the use of generalized quantum correlation measures to identify quantum phase transitions in the spin-1 Heisenberg model, highlighting the effectiveness of partial concurrence and chain size.

Findings

Negativity detects QPTs at low temperatures.

Partial concurrence outperforms total concurrence in identifying critical points.

Odd-length spin chains are more effective for QPT detection.

Abstract

We investigate thermal and nonthermal quantum correlations in the one dimensional spin 1 bilinear-biquadratic Heisenberg model. Using tools from quantum information theory such as generalized concurrence, negativity, and various measures of quantum, classical, and total correlations in bipartite states we demonstrate that these measures effectively identify quantum phase transitions (QPTs) at critical points. Our negativity analysis reveals nearly identical results at zero or very low temperatures. Importantly, we find that partial concurrence, defined with the reduced density matrix, detects more quantum critical points than total concurrence. Additionally, we argue that spin chains with an odd number of spins are more effective than those with an even number in identifying QPTs.