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arXiv:cond-mat/0605378

Entanglements in Systems with Multiple Degrees of Freedom

Dongmeng Chen, Wang, Wei-Hua, Liang‐Jian Zou

Published May 15, 2006• 0 citations
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Abstract

We present the entanglement properties of the spin-orbital coupling systems with multiple degrees of freedom. After constructing the maximally entangled spin-orbital basis of bipartite, we find that the quantum entanglement length in the noninteracting itinerant Fermion system with spin and orbit is considerably larger than that in the system with only spin. In the SU(2)$\otimes$SU(2) spin-orbital interacting system, the entanglement, expressed in terms of the spin-orbital correlation functions, clearly manifests the close relationship with the quantum phases in strongly correlated systems; and the entanglement phase diagram of the finite-size systems is in agreement with the magnetic and orbital phase diagram of the infinite systems. The application of the present theory on nucleon systems is suggested.

DOI
10.48550/arxiv.cond-mat/0605378

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We investigate the phase diagram and the spin-orbital entanglement of a one-dimensional $\mathrm{SU}(2)\phantom{\rule{0.16em}{0ex}}\ensuremath{\bigotimes}\phantom{\rule{0.16em}{0ex}}\text{XXZ}$ model with SU(2) spin exchange and anisotropic XXZ\text{XXZ}XXZ orbital exchange interactions and negative exchange coupling constant. 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 $\mathrm{SU}(2)\phantom{\rule{0.16em}{0ex}}\ensuremath{\bigotimes}\phantom{\rule{0.16em}{0ex}}\text{SU}$(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.
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The concept of entanglement in many‑body physics has traditionally focused on spin or particle‑number degrees of freedom. Here we introduce a novel class of fermionic quantum phases in which orbital degrees of freedom of identical particles become entangled across spatially distinct sites. We construct the general form of the many‑body wavefunction for a system of N fermions occupying L orbitals per site, and show that the ground state of certain interacting Hamiltonians can be written as |\Psi> = \sum_{i,j} c_{ij} | \phi_i \phi_j >, where | \phi_i > and | \phi_j > denote single‑particle orbital states localized at different lattice sites. This entangled orbital structure leads to emergent properties distinct from conventional band insulators, Mott insulators, or spin liquids. We discuss the symmetry constraints, the role of fermionic statistics, and the topological aspects that arise when the orbital entanglement is global. Theoretical analysis predicts that FOEPs can host protected edge modes, exotic quasiparticles, and non‑Abelian statistics in two‑dimensional lattices. We also outline experimental signatures that could be observed in engineered cold‑atom systems, photonic lattices, or layered transition‑metal dichalcogenides, and argue that the discovery of FOEPs would open a new frontier in the search for quantum materials with high‑temperature superconductivity or quantum information processing capabilities.
We study the evolution of spin-orbital correlations in an inhomogeneous quantum system with an impurity replacing a doublon by a holon orbital degree of freedom. Spin-orbital entanglement is large when spin correlations are antiferromagnetic, while for a ferromagnetic host we obtain a chain with only orbital interactions. In this regime, the orbital model can be mapped on spinless fermions and we uncover topological phases with zero energy modes at the edge or at the domain between magnetically inequivalent regions.