We will discuss the effective Hamiltonian that generates time evolution of states on intermediate time scales in the strong-coupling limit of the spin-1/2 XXZ model. To leading order, such an effective Hamiltonian describes an integrable model with local interactions. I will present a full coordinate Bethe Ansatz solution that manifestly breaks the translational symmetry of the model, and describe its quasi-particle content. The corresponding Bethe equations are completely solvable, allowing for exact characterisation of degeneracies, as well as specification of…

Emergence of anomalous transport laws in deterministic interacting many-body systems has become a subject of intense study in the past few years, a prominent example of which is the unexpected discovery of superdiffusive spin dynamics in the isotropic Heisenberg quantum spin chain, conjectured to belong to the Kardar-Parisi-Zhang universality class. In this seminar, we will argue and theoretically justify why the observed anomalous transport of the Noether charges with fractional dynamical exponent z=3/2 is superuniversal, namely a feature of all integrable…

The investigation of nonequilibrium properties of models with many degrees of freedom is a formidable analytical challenge that has recently aroused renewed interest. While many free theories display ballistic behaviour, generic interacting theories give rise to diffusive behaviour, a first-principles derivation of which remains elusive. Further, the role of space-time and internal symmetries in determining transport properties remains unsettled. With these questions in mind I will discuss some recent work on the classification of dynamical correlators in generic (chaotic) theories…

Local quantum circuits have become an important paradigm of many-body physics as, in particular, they allow for the simulation of  complex quantum systems in emerging quantum computing facilities. While much is already known about unitary and projective-measurement circuits, it is also of interest to extend their study to open and nonequilibrium quantum setups. With this goal, we consider quantum circuits in the Kraus map representation of completely positive quantum dynamics and discuss the first exactly-solvable, yet strongly-interacting, non-unitary open quantum…

Open quantum systems are ubiquitous in the contexts of atomic and molecular physics, circuit QED and optomechanics. Couplings to an environment can also have very interesting effects on the dynamics of many-particle quantum systems. In order to arrive at a tractable description of such problems, it is customary to work within the Markovian approximation with the dynamics averaged over the environment, whereby the system is described by a Lindblad master equation. While much progress has been made in analysing Lindblad…

The recent decade has witnessed several breakthroughs in the description of relaxation of local observables in quantum many-body systems prepared far from equilibrium. In contrast, the time evolution on time scales that precede relaxation towards the stationary state  has remained much less explored. Strong coupling expansions offer a good starting point for investigation of such problems, since they provide  a natural time scale, on which prerelaxation can occur. I will discuss the microscopic and ballistic-scale mesoscopic dynamics, described by the…

We study random quantum circuits and their rate of producing bipartite entanglement, specifically with respect to the choice of 2-qubit gates and the order (protocol) in which these are applied. The problem is mapped to a Markovian process and proved that there are large spectral equivalence classes. The optimal gate and the protocol that generates entanglement the fastest is identified. Relaxation towards the asymptotic thermal entanglement proceeds via a series of phase transitions in the local relaxation rate, which are…