Quantum entanglement in the one-dimensional spin-orbitalSU(2)⊗XXZmodel

Abstract

We investigate the phase diagram and the spin-orbital entanglement of a one-dimensional SU(2)⊗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)⊗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. We demonstrate that spin-orbital excitons can be experimentally explored using resonant inelastic x-ray scattering, where the strongly entangled exciton states can be easily distinguished from the spin-orbital continuum.

Spin, orbital and topological order in models of strongly correlated electrons

“…Even more exotic order is present in one-dimensional (1D) spin-orbital SU(2) ⊗ XY model introduced by Kumar [108] in the context of spin-orbital separation found in 1D TMO [109]. Such models are challenging in low dimension as they often exhibit strong spinorbital entanglement [110] and quantum critical points [111]. The model has a generic form of equation ( 3) with spins S = 1/2 and orbital pseudospins T = 1/2, so we will use notions spins up and down but also orbitals 'up' and 'down'.…”

Quantum entanglement, local indicators, and the effect of external fields in the Kugel-Khomskii model

“…Later on, the entanglement was sought in various other related models: of SU (2) × XY [29], SU (2) × XXZ [30], and SU (2)×SU (2) with additional spin-orbit anisotropy [25]. Briefly, the results of this analysis come to detection and characterization of the significant entanglement area, the degree of the entanglement (mainly through the von Neumann entropy), and sometimes indication of possible complex entangled excitations [31].…”

“…There are several quantitative criteria divided into two main courses. One is based on the calculation of von Neumann entropy [20,25,28,30,31], while the second one requires a partial trace of the density matrix by the degrees of freedom of one of the subsystems. We note right away that qualitatively all criteria give the same result.…”

Phase Diagram of the Spin-1/2 Heisenberg Alternating Chain in a Magnetic Field*

“…Fortunately, with the development of quantum information, various information measures, e.g., quantum coherence, entanglement entropy, and fidelity, can help us to study quantum critical phenomena in spin chains. It is found that the quantum critical points can be well characterized by both the ground-state entanglement and fidelity on large system [27][28][29][30][31][32][33][34]. In this paper we study the entanglement, coherence and fidelity of the spin-1/2 Heisenberg alternating chain under a transverse magnetic field, and finally the phase diagram will be given.…”