State Space Geometry of the Spin-1 Antiferromagnetic Heisenberg Chain

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 (39)

• Advances in Quantum Metrology
• Area laws for the entanglement entropy - a review
• Quantum metrology
• Entanglement spectrum of a topological phase in one dimension
• The ITensor Software Library for Tensor Network Calculations
• Ground state overlap and quantum phase transitions
• Bose-Einstein Condensation in Magnetic Insulators
• Fisher information and multiparticle entanglement
• Quantum critical scaling of the geometric tensors
• Complete classification of 1D gapped quantum phases in interacting spin systems
• Measuring multipartite entanglement via dynamic susceptibilities
• Direct measurement of the quantum geometric tensor in a two-dimensional continuous medium
• Ground State Phase Diagram of S=1 XXZ Chains with Uniaxial Single-Ion-Type Anisotropy
• Quantum Critical Scaling of Fidelity Susceptibility
• Symmetry-protected phases for measurement-based quantum computation
• Spectral Function for the S=1 Heisenberg Antiferromagetic Chain
• Classifying and measuring the geometry of the quantum ground state manifold
• Large-Scale Numerical Evidence for Bose Condensation in the S=1 Antiferromagnetic Chain in a Strong Field
• 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
• Magnetic Excitations in the Spin-1 Anisotropic Heisenberg Antiferromagnetic Chain System NiCl${}_2$-4SC(NH${}_2$)${}_2$
• Experimental measurement of the quantum geometric tensor using coupled qubits in diamond
• Witnessing entanglement in quantum magnets using neutron scattering
• Revealing tensor monopoles through quantum-metric measurements
• Equal Time Correlations in Haldane Gap Antiferromagnets
• Quantifying and controlling entanglement in the quantum magnet Cs${}_2$CoCl${}_4$
• Multipartite Entanglement at Finite Temperature
• Entanglement entropy of highly degenerate states and fractal dimensions
• The Euler Number of Bloch States Manifold and the Quantum Phases in Gapped Fermionic Systems
• Ground-state fidelity of the spin-1 Heisenberg chain with single ion anisotropy: quantum renormalization group and exact diagonalization approaches
• Information geometry in quantum field theory: lessons from simple examples
• 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-$\frac{1}{2}$ Heisenberg Antiferromagnet
• Nested-sphere description of the N-level Chern number and the generalized Bloch hypersphere
• Estimates of the Quantum Fisher Information in the $S=1$ Anti-Ferromagnetic Heisenberg Spin Chain with Uniaxial Anisotropy
• Entanglement in permutation symmetric states, fractal dimensions, and geometric quantum mechanics
• Revealing divergent length scales using quantum Fisher information in the Kitaev honeycomb model

Cited by in corpus (3)

• From Classical to Quantum Information Geometry: A Guide for Physicists
• Quantum Fisher Information and multipartite entanglement in spin-1 chains
• A Jastrow wave function for the spin-1 Heisenberg chain: the string order revealed by the mapping to the classical Coulomb gas