In this article we provide a review of geometrical methods employed in the analysis of
quantum phase transitions and non-equilibrium dissipative phase transitions. After a …

This Colloquium gives an overview of recent theoretical and experimental progress in the
area of nonequilibrium dynamics of isolated quantum systems. There is particularly a focus …

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The transverse field Ising and XY models (the simplest quantum spin models) provide the
organising principle for the rich variety of interconnected subjects which are covered in this …

Quantum criticality, as a fascinating quantum phenomenon, may provide significant
advantages for quantum sensing. Here we propose a dynamic framework for quantum …

We review the quantum fidelity approach to quantum phase transitions in a pedagogical
manner. We try to relate all established but scattered results on the leading term of the …

The dynamics of a quantum phase transition is inextricably woven with the formation of
excitations, as a result of critical slowing down in the neighborhood of the critical point. We …

The many-body physics at quantum phase transitions shows a subtle interplay between
quantum and thermal fluctuations, emerging in the low-temperature limit. In this review, we …

We investigate critical quantum metrology, that is, the estimation of parameters in many-
body systems close to a quantum critical point, through the lens of Bayesian inference …

We address the question of whether the super-Heisenberg scaling for quantum estimation is
indeed realizable. We unify the results of two approaches. In the first one, the original system …