Factorization, coherence and asymmetry in the Heisenberg spin-1/2 XXZ chain a transverse magnetic field and with Dzyaloshinskii-Moriya interaction

TL;DR

This paper explores how Dzyaloshinskii-Moriya interactions and magnetic fields influence quantum coherence, entanglement, and symmetry properties in the 1D Heisenberg XXZ spin chain, revealing conditions for factorization and phase coherence.

Contribution

It demonstrates the differential effects of longitudinal and transverse DMI on factorizability, identifies a pseudofactorizing field with minimal entanglement, and links symmetry breaking to chiral currents in the system.

Findings

Longitudinal DMI destroys factorizability, transverse DMI preserves it.

A pseudofactorizing field minimizes entanglement and symmetry breaking.

Chiral current and local magnetization specify the phase reference at the pseudofactorizing field.

Abstract

We investigate the factorization, coherence and asymmetry properties of the 1d Heisenberg spin-1/2 XXZ chain with Dzyaloshinskii-Moriya interaction (DMI) and a transverse magnetic field using quantum information measures. Both longitudinal and transverse DM vectors are considered. Using numerical DMRG, we compute the one-tangle, two-spin concurrence and the Wigner-Yananse-skew information. We show that a longitudinal DMI destroys the factorizability property while a transverse DMI preserves it. We relate the absence of factorizability to the breaking of the $U(1)$ rotation symmetry about the local magnetization axis at each lattice site. Physically, breaking of the symmetry manifests in the existence of a chiral current. Although the longitudinal DMI destroys factorizability, we obtain a `pseudofactorizing' field ($h_{pf}$) at which entanglement and hence violation of the $U(1)$ symmetry is minimal. Our calculations indicate a phase coherent ground state at $h_{pf}$. An entanglement transition (ET) occurs across this field which is characterized by an enhanced but finite range of two-spin concurrence in its vicinity in contrast with the diverging range of the concurrence for the ET across the factorizing field ($h_{f}$). We relate the asymmetry to the `frameness' or the ability for the state to act as a reference frame for some measurement. In absence of longitudinal DMI (or in presence of transverse DMI), at $h_{f}$, the single site magnetization axis specifies the common $z$-axis for the full system but not the full Cartesian reference frame due to a lack of phase reference. On the other hand, in the presence of a longitudinal DMI, our results indicate that at $h_{pf}$, the local magnetization and the chiral current are sufficient to specify the full Cartesian reference frame, with the chiral current being the macroscopic quantity to determine the phase reference.