Quantum correlations and coherence in spin-1 Heisenberg chains

Abstract

We explore quantum and classical correlations along with coherence in the ground states of spin-1 Heisenberg chains, namely the one-dimensional XXZ model and the one-dimensional bilinear biquadratic model, with the techniques of density matrix renormalization group theory. Exploiting the tools of quantum information theory, that is, by studying quantum discord, quantum mutual information and three recently introduced coherence measures in the reduced density matrix of two nearest neighbor spins in the bulk, we investigate the quantum phase transitions and special symmetry points in these models. We point out the relative strengths and weaknesses of correlation and coherence measures as figures of merit to witness the quantum phase transitions and symmetry points in the considered spin-1 Heisenberg chains. In particular, we demonstrate that as none of the studied measures can detect the infinite order Kosterlitz-Thouless transition in the XXZ model, they appear to be able to signal the existence of the same type of transition in the biliear biquadratic model. However, we argue that what is actually detected by the measures here is the SU(3) symmetry point of the model rather than the infinite order quantum phase transition. Moreover, we show in the XXZ model that examining even single site coherence can be sufficient to spotlight the second-order phase transition and the SU(2) symmetry point.

Measures and applications of quantum correlations

“…Most of the above works adopted the quantum discord or the one-way quantum deficit as measures of QCs, but other valid and more efficiently computable quantifiers such as the local quantum uncertainty were also proven of use in the characterisation of quantum critical points [303,312,311].…”

“…Other studies then complemented the above ones when either taking symmetry breaking into account [304,305] or considering more sophisticated quantum phase transitions such as the ones in the one-dimensional spin-1/2 XY model with Dzyaloshinskii-Moriya interaction [306], the Dicke model [307], the Castelnovo-Chamon model [308], cluster-like systems [309], as well as spin-1 XXZ and bilinear-biquadratic chains [310,168,311]. Most of the above works adopted the quantum discord or the one-way quantum deficit as measures of QCs, but other valid and more efficiently computable quantifiers such as the local quantum uncertainty were also proven of use in the characterisation of quantum critical points [303,312,311].…”

How to quantify coherence: Distinguishing speakable and unspeakable notions

“…Quantum phase transitions in the ground states of quantum many-body systems, such as a spin chain, can be studied in terms of the degree of coherence contained in local reductions of the state, such as single-spin or two-spin density operators [55,56].…”

Characterizing coherence with quantum observables

“…Since the basis choice is fixed and not optimized such as in quantum discord, we do not expect to get equivalent results using (10) alone [48]. It is tempting to define (10) as a type of coherence as it has been done in numerous past works [9][10][11][12][13][14][15]. However, δ(ρ) does not properly satisfy the coherence properties (see Supplementary Materials), hence it is not strictly appropriate to call it a type of coherence.…”