A new signature of quantum phase transitions from the numerical range

Understand

The ground state energy of a finite-dimensional one-parameter Hamiltonian and the continuity of a maximum-entropy inference map are discussed in the context of quantum critical phenomena.

• The domain of the inference map is a convex compact set in the plane, called the numerical range.
• We study the differential geometry of its boundary in relation to the ground state energy.
• We prove that discontinuities of the inference map correspond to $C^1$-smooth crossings of the ground state energy with a higher energy level.