Lorenzo Campos Venuti

Quantum critical scaling of the geometric tensors.

Berry phases and the quantum-information theoretic notion of fidelity have been recently used to analyze quantum phase transitions from a geometrical perspective. In this Letter we unify these two approaches showing that the underlying mechanism is the critical singular behavior of a complex tensor over the Hamiltonian parameter space. This is achieved by performing a scaling analysis of this quantum geometric tensor in the vicinity of the critical points. In this way most of the previous results are understood on general grounds and new ones are found. We show that criticality is not a sufficient condition to ensure superextensive divergence of the geometric tensor, and state the conditions under which this is possible. The validity of this analysis is further checked by exact diagonalization of the spin-1/2 XXZ Heisenberg chain.

Bures metric over thermal state manifolds and quantum criticality

We analyze the Bures metric over the manifold of thermal density matrices for systems featuring a zero temperature quantum phase transition. We show that the quantum critical region can be characterized in terms of the temperature scaling behavior of the metric tensor itself. Furthermore, the analysis of the metric tensor when both temperature and an external field are varied, allows one to complement the understanding of the phase diagram including crossover regions which are not characterized by any singular behavior. These results provide a further extension of the scope of the metric approach to quantum criticality.

Adiabaticity in open quantum systems

We provide a rigorous generalization of the quantum adiabatic theorem for open systems described by a Markovian master equation with time-dependent Liouvillian

Coherent Quantum Dynamics in Steady-State Manifolds of Strongly Dissipative Systems

\mathcal{L}(t)

Universality in the equilibration of quantum systems after a small quench

. We focus on the finite system case relevant for adiabatic quantum computing and quantum annealing. Adiabaticity is defined in terms of closeness to the instantaneous steady state. While the general result is conceptually similar to the closed system case, there are important differences. Namely, a system initialized in the zero-eigenvalue eigenspace of

Measures of coherence-generating power for quantum unital operations

\mathcal{L}(t)

Equivalence between XYand dimerized models

will remain in this eigenspace with a deviation that is inversely proportional to the total evolution time

Coherence-generating power of quantum unitary maps and beyond

T

Universal subleading terms in ground-state fidelity from boundary conformal field theory

. In the case of a finite number of level crossings the scaling becomes

Dynamical response theory for driven-dissipative quantum systems

T^{-\eta}