State Space Geometry of the Spin-1 Antiferromagnetic Heisenberg Chain
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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.
