Quantum correlation with sandwiched relative entropies: Advantageous as order parameter in quantum phase transitions

Quantum first order phase transitions

The scaling theory of critical phenomena has been successfully extended for classical first order transitions even though the correlation length does not diverge in these transitions. In this paper we apply the scaling ideas to quantum first order transitions. The usefulness of this approach is illustrated treating the problems of a superconductor coupled to a gauge field and of a biquadratic H...

On Variational Expressions for Quantum Relative Entropies

Distance measures between quantum states like the trace distance and the fidelity can naturally be defined by optimizing a classical distance measure over all measurement statistics that can be obtained from the respective quantum states. In contrast, Petz showed that the measured relative entropy, defined as a maximization of the Kullback-Leibler divergence over projective measurement statisti...

A family of monotone quantum relative entropies

We study here the elementary properties of the relative entropyH(A,B) = Tr[φ(A)−φ(B)−φ(B)(A−B)] for φ a convex function and A,B bounded self-adjoint operators. In particular, we prove that this relative entropy is monotone if and only if φ is operator monotone. We use this to appropriately define H(A,B) in infinite dimension. In this paper we introduce a relative entropy H(A,B) of two bounded o...

Quantum Phase Transitions in 2d Quantum Liquids∗

Entanglement as a quantum order parameter

We show that the quantum order parameters (QOP) associated with the transitions between a normal conductor and a superconductor in the BCS and η-pairing models and between a Mott-insulator and a superfluid in the Bose-Hubbard model are directly related to the amount of entanglement existent in the ground state of each system. This connection gives a physical meaningful interpretation to these Q...