Entanglement in XYZ model on a spin-star system: Anisotropy vs. field-induced dynamics

• Published in: arXiv.org 2023-07
• Main Authors: Krishnan, Jithin G, Harikrishnan, K J, Pal, Amit Kumar
• Format: Article
• Language: English
• Subjects: Anisotropy; Energy gap; Entanglement; Logarithms; Particle spin; Spin dynamics
• ISSN: 2331-8422

We consider a star-network of \(n=n_0+n_p\) spin-\(\frac{1}{2}\) particles, where interaction between \(n_0\) central spins and \(n_p\) peripheral spins are of the XYZ-type. In the limit \(n_0/n_p\ll 1\), we show that for odd \(n\), the ground state is doubly degenerate, while for even \(n\), the energy gap becomes negligible when \(n\) is large, inducing an \emph{effective} double degeneracy. In the same limit, we show that for vanishing \(xy\)-anisotropy \(\gamma\), bipartite entanglement on the peripheral spins computed using either a partial trace-based, or a measurement-based approach exhibits a logarithmic growth with \(n_p\), where the sizes of the partitions are typically \(\sim n_p/2\). This feature disappears for \(\gamma\neq 0\), which we refer to as the \emph{anisotropy effect}. Interestingly, when the system is taken out of equilibrium by the introduction of a magnetic field of constant strength on all spins, the time-averaged bipartite entanglement on the periphery at the long-time limit exhibits a logarithmic growth with \(n_p\) irrespective of the value of \(\gamma\). We further study the \(n_0/n_p\gg 1\) and \(n_0/n_p\rightarrow 1\) limits of the model, and show that the behaviour of bipartite peripheral entanglement is qualitatively different from that of the \(n_0/n_p\ll 1\) limit.