The full counting statistics encodes the probability distribution of a dynamical observable and is a dynamical analogue of the thermodynamic partition function. It is naturally discussed within the frameworks of the large deviation theory and the Lee-Yang theory of phase transitions, which we briefly review. By combining the two approaches we point out that, in the presence of dynamical critical point, a rich phenomenology of fluctuations is permissible. As an explicit demonstration we introduce an interacting cellular automaton, where an…

Supersolids are phases of matter that spontaneously and simultaneously break both a global U(1) and translational symmetry. In this talk I will show how to derive a phenomenological description -- in the spirit of Ginzburg-Landau theory -- valid near the supersolid transition, and use it to find a few model-independent relationships between quantities of interest around it. Such relationships are then confirmed by performing calculations in the framework of the holographic correspondence, which provides some predictions even away from the…

The nonequilibrium steady states of open quantum many-body systems can undergo phase transitions due to the competition of unitary and dissipative dynamics. We consider translation-invariant systems governed by Lindblad master equations, where the Hamiltonian is quadratic in the ladder operators, and the Lindblad operators are either linear or quadratic and Hermitian. These systems are called quasi-free and quadratic, respectively. Quadratic one-dimensional systems with finite-range interactions necessarily have exponentially decaying Green's functions. For the quasi-free case without quadratic Lindblad operators, we…

Spatiotemporal correlation functions provide the key diagnostic tool for studying spatially extended complex quantum many-body systems. In ergodic systems scrambling causes initially local observables to spread uniformly over the whole available Hilbert space and causes exponential suppression of correlation functions with the spatial size of the system. In this talk, we present a perturbed free quantum circuit model, in which ergodicity is induced by a unitary impurity placed on the system's boundary. We refer to this setting as boundary chaos.…

Ongoing development of quantum simulators allows for a progressively finer degree of control of quantum many-body systems. This motivates the development of efficient approaches to facilitate the control of such systems and enable the preparation of non-trivial quantum states using a  limited set of available controls. In this talk I will present a new approach which can be used to find the locally optimal driving protocol for trajectories within an MPS manifold. I will then focus on a specific example,…

One of the most general results of non-equilibrium statistical physics is the fluctuation symmetry, which relates the probabilities of forwards and backward fluctuations even far away from equilibrium. We present a novel mechanism that generates dynamical phase transitions, which spontaneously break the fluctuation symmetry. Moreover, the same mechanism leads to universal non-Gaussian typical fluctuations in equilibrium. An attempt at a pedagogical presentation will be made.

Especially in one dimension, models with discrete and continuous symmetries display different physical properties, starting from the existence of long-range order. Introducing topological frustration in spin chains characterized by a discrete local symmetry, they develop a region in parameter space which mimics the features of models with continuous symmetries. After discussing the emergence and the characterization of this novel region, I will show how these effects of frustration can be exploited for the development of efficient quantum technologies such as quantum…

The operator space entanglement entropy, or simply ‘operator entanglement’ (OE), is an indicator of the complexity of quantum operators and of their approximability by Matrix Product Operators (MPO). In this talk I will present the study of OE of the density matrix of a 1D spin chain undergoing dissipative evolution. While it is expected that, after an initial linear growth the OE should be supressed by dissipative processes as the system evolves to a simple stationary state, we find that…