Quantum Chernoff Bound metric for the XY model at finite temperature

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.