  We explore the finite temperature phase diagram of the anisotropic XY spin
chain using the Quantum Chernoff Bound metric on thermal states. The analysis
of the metric elements allows to easily identify, in terms of different scaling
with temperature, quasi-classical and quantum-critical regions. These results
extend recent ones obtained using the Bures metric and show that different
information-theoretic notions of distance can carry the same sophisticated
information about the phase diagram of an interacting many-body system
featuring quantum-critical points.
