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A new signature of quantum phase transitions from the numerical range
Description:  A quantum phase transition is a ground state phenomenon in an infinite lattice model with various defining key properties. We focus on two of them and point out their signatures in finite lattice models: Non-analyticity of the ground state energy and strong variation of the entropy of inferred states.
We study the numerical range W associated with the two energy terms of a one-parameter Hamiltonian (two arbitrary hermitian matrices). We show that parameter values with a C^2 smooth non-analytic ground state energy correspond to C^2 smooth non-analytic points of the boundary of W (viewed as a manifold). At these boundary points, the maximum-entropy inference map, constrained on the expectation values of the energy operators, is discontinuous. We conclude that a C^2 smooth non-analytic boundary point of W is a geometric signature of a quantum phase transition.
On the way, we obtain a classification of the maximal order of differentiability of all boundary points of W.

This is joint work with Ilya M. Spitkovsky (NYU Abu Dhabi, UAE).

Reference: arXiv:1703.00201 [math-ph]

Date:  2017-07-10
Start Time:   14:30
Speaker:  Stephan Weis (Université libre de Bruxelles, Belgium)
Institution:  Centre for Quantum Information and Communication, Université libre de Bruxelles, Belgium
Place:  Room 5.5, Department of Mathematics, U.C.
Research Groups: -Algebra and Combinatorics
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