Quantum entanglement in the one-dimensional spin-orbital SU(2)$\otimes XXZ$ model

TL;DR

This paper explores the phase diagram and spin-orbital entanglement in a one-dimensional SU(2)$\otimes$XXZ model, revealing unique long-range entanglement, emergent dimer phases, and exciton bound states with distinct entanglement properties.

Contribution

It uncovers novel long-range entangled phases and excitations in a negative coupling SU(2)$\otimes$XXZ model, expanding understanding of quantum entanglement in spin-orbital systems.

Findings

Entanglement entropy increases linearly with system size in ground states.

Identification of a long-range spin-singlet dimer phase with finite entanglement.

Discovery of exciton bound states with unique entanglement scaling.

Abstract

We investigate the phase diagram and the spin-orbital entanglement of a one-dimensional SU(2)$\otimes XXZ$ model with SU(2) spin exchange and anisotropic $XXZ$ orbital exchange interactions and negative exchange coupling. As a unique feature, the spin-orbital entanglement entropy in the entangled ground states increases here linearly with system size. In the case of Ising orbital interactions we identify an emergent phase with long-range spin-singlet dimer correlations triggered by a quadrupling of correlations in the orbital sector. The peculiar translational invariant spin-singlet dimer phase has finite von Neumann entanglement entropy and survives when orbital quantum fluctuations are included. It even persists in the isotropic SU(2)$\otimes$SU(2) limit. Surprisingly, for finite transverse orbital coupling the long-range spin singlet correlations also coexist in the antiferromagnetic spin and alternating orbital phase making this phase also unconventional. Moreover we also find a complementary orbital singlet phase that exists in the isotropic case but does not extend to the Ising limit. The nature of entanglement appears essentially different from that found in the frequently discussed model with positive coupling. Furthermore we investigate the collective spin and orbital wave excitations of the disentangled ferromagnetic-spin/ferro-orbital ground state and explore the continuum of spin-orbital excitations. Interestingly one finds among the latter excitations two modes of exciton bound states. Their spin-orbital correlations differ from the remaining continuum states and exhibit logarithmic scaling of the von Neumann entropy with increasing system size.