State Space Geometry of the Spin-1 Antiferromagnetic Heisenberg Chain
arXiv:2209.05005 · doi:10.1103/PhysRevB.107.174427
Abstract
We study the phase diagram of the spin-1 antiferromagnetic Heisenberg chain with uniaxial anisotropy and applied magnetic field in terms of the genuine multipartite entanglement as witnessed by the mean quantum Fisher information density. By generalizing the manifold studied in [1, 2] to the many body case for spin 1, we connect the state space curvature in the vicinity of the ground state of the Heisenberg chain to the genuine multipartite entanglement. Our analysis demonstrates that the quantum critical points and symmetry protected topological (SPT) phase exhibit large state space curvature, while the separable phases are completely flat, offering insight into the physical interpretation of state space curvature. We further show that the entanglement in the SPT phase is enhanced by the presence of uniaxial anisotropy, and undiminished in the presence of uniform magnetic fields. The magnon condensate phase induced by large fields is shown to emanate from the Gaussian critical point, and exhibits massive multipartite entanglement over a robust region of the parameter space.
References in corpus (10)
- Bose-Einstein Condensation in Magnetic Insulators
- Quantum critical scaling of the geometric tensors
- Spectral Function for the S=1 Heisenberg Antiferromagetic Chain
- Fidelity susceptibility and long-range correlation in the Kitaev honeycomb model
- Bures metric over thermal state manifolds and quantum criticality
- Multipartite entanglement in topological quantum phases
- Spin-1 Heisenberg antiferromagnetic chain with exchange and single-ion anisotropies
- Quantum geometric tensor and quantum phase transitions in the Lipkin-Meshkov-Glick model
- Multipartite entanglement in the 1-D spin- Heisenberg Antiferromagnet
- Nested-sphere description of the N-level Chern number and the generalized Bloch hypersphere