Microscopic Origin of the Quantum Mpemba Effect in Integrable Systems.

The highly complicated nature of far from equilibrium systems can lead to a complete breakdown of the physical intuition developed in equilibrium. A famous example of this is the Mpemba effect, which states that nonequilibrium states may relax faster when they are further from equilibrium or, put another way, hot water can freeze faster than warm water. Despite possessing a storied history, the precise criteria and mechanisms underpinning this phenomenon are still not known.

Quantum Information Spreading in Generalized Dual-Unitary Circuits.

We study the spreading of quantum information in a recently introduced family of brickwork quantum circuits that generalizes the dual-unitary class. These circuits are unitary in time, while their spatial dynamics is unitary only in a restricted subspace. First, we show that local operators spread at the speed of light as in dual-unitary circuits, i.

Exact Quench Dynamics of the Floquet Quantum East Model at the Deterministic Point.

We study the nonequilibrium dynamics of the Floquet quantum East model (a Trotterized version of the kinetically constrained quantum East spin chain) at its "deterministic point," where evolution is defined in terms of CNOT permutation gates. We solve exactly the thermalization dynamics for a broad class of initial product states by means of "space evolution." We prove: (i) the entanglement of a block of spins grows at most at one-half the maximal speed allowed by locality (i.

Localized Dynamics in the Floquet Quantum East Model.

We introduce and study the discrete-time version of the quantum East model, an interacting quantum spin chain inspired by simple kinetically constrained models of classical glasses. Previous work has established that its continuous-time counterpart displays a disorder-free localization transition signaled by the appearance of an exponentially large (in the volume) family of nonthermal, localized eigenstates. Here we combine analytical and numerical approaches to show that (i) the transition persists for discrete times, in fact, it is present for any finite value of the time step apart from a zero measure set; (ii) it is directly detected by following the nonequilibrium dynamics of the fully polarized state.

Nonequilibrium Full Counting Statistics and Symmetry-Resolved Entanglement from Space-Time Duality.

Owing to its probabilistic nature, a measurement process in quantum mechanics produces a distribution of possible outcomes. This distribution-or its Fourier transform known as full counting statistics (FCS)-contains much more information than say the mean value of the measured observable, and accessing it is sometimes the only way to obtain relevant information about the system. In fact, the FCS is the limit of an even more general family of observables-the charged moments-that characterize how quantum entanglement is split in different symmetry sectors in the presence of a global symmetry.

Integrable Digital Quantum Simulation: Generalized Gibbs Ensembles and Trotter Transitions.

The Trotter-Suzuki decomposition is a promising avenue for digital quantum simulation (DQS), approximating continuous-time dynamics by discrete Trotter steps of duration τ. Recent work suggested that DQS is typically characterized by a sharp Trotter transition: when τ is increased beyond a threshold value, approximation errors become uncontrolled at large times due to the onset of quantum chaos. Here, we contrast this picture with the case of integrable DQS.

Solution of the BEC to BCS Quench in One Dimension.

A gas of interacting fermions confined in a quasi one-dimensional geometry shows a BEC to BCS crossover upon slowly driving its coupling constant through a confinement-induced resonance. On one side of the crossover the fermions form tightly bound bosonic molecules behaving as a repulsive Bose gas, while on the other they form Cooper pairs, whose size is much larger than the average interparticle distance. Here we consider the situation arising when the coupling constant is varied suddenly from the BEC to the BCS value.

Entanglement Negativity and Mutual Information after a Quantum Quench: Exact Link from Space-Time Duality.

We study the growth of entanglement between two adjacent regions in a tripartite, one-dimensional many-body system after a quantum quench. Combining a replica trick with a space-time duality transformation, we derive an exact, universal relation between the entanglement negativity and Rényi-1/2 mutual information that holds at times shorter than the sizes of all subsystems. Our proof is directly applicable to any local quantum circuit, i.

Bogoliubov-Born-Green-Kirkwood-Yvon Hierarchy and Generalized Hydrodynamics.

We consider fermions defined on a continuous one-dimensional interval and subject to weak repulsive two-body interactions. We show that it is possible to perturbatively construct an extensive number of mutually compatible conserved charges for any interaction potential. However, the contributions to the densities of these charges at second order and higher are generally nonlocal and become spatially localized only if the potential fulfils certain compatibility conditions.

Duality between Weak and Strong Interactions in Quantum Gases.

In one-dimensional quantum gases there is a well known "duality" between hard core bosons and noninteracting fermions. However, at the field theory level, no exact duality connecting strongly interacting bosons to weakly interacting fermions is known. Here we propose a solution to this long-standing problem.

Chaos and Ergodicity in Extended Quantum Systems with Noisy Driving.

We study the time-evolution operator in a family of local quantum circuits with random fields in a fixed direction. We argue that the presence of quantum chaos implies that at large times the time-evolution operator becomes effectively a random matrix in the many-body Hilbert space. To quantify this phenomenon, we compute analytically the squared magnitude of the trace of the evolution operator-the generalized spectral form factor-and compare it with the prediction of random matrix theory.

Exact Thermalization Dynamics in the "Rule 54" Quantum Cellular Automaton.

We study the out-of-equilibrium dynamics of the quantum cellular automaton known as "Rule 54." For a class of low-entangled initial states, we provide an analytic description of the effect of the global evolution on finite subsystems in terms of simple quantum channels, which gives access to the full thermalization dynamics at the microscopic level. As an example, we provide analytic formulas for the evolution of local observables and Rényi entropies.

Exact Correlation Functions for Dual-Unitary Lattice Models in 1+1 Dimensions.

We consider a class of quantum lattice models in 1+1 dimensions represented as local quantum circuits that enjoy a particular dual-unitarity property. In essence, this property ensures that both the evolution in time and that in space are given in terms of unitary transfer matrices. We show that for this class of circuits, generically nonintegrable, one can compute explicitly all dynamical correlations of local observables.

Exact Spectral Form Factor in a Minimal Model of Many-Body Quantum Chaos.

The most general and versatile defining feature of quantum chaotic systems is that they possess an energy spectrum with correlations universally described by random matrix theory (RMT). This feature can be exhibited by systems with a well-defined classical limit as well as by systems with no classical correspondence, such as locally interacting spins or fermions. Despite great phenomenological success, a general mechanism explaining the emergence of RMT without reference to semiclassical concepts is still missing.

Universal Broadening of the Light Cone in Low-Temperature Transport.

We consider the low-temperature transport properties of critical one-dimensional systems that can be described, at equilibrium, by a Luttinger liquid. We focus on the prototypical setting where two semi-infinite chains are prepared in two thermal states at small but different temperatures and suddenly joined together. At large distances x and times t, conformal field theory characterizes the energy transport in terms of a single light cone spreading at the sound velocity v.

Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents.

We consider the nonequilibrium time evolution of piecewise homogeneous states in the XXZ spin-1/2 chain, a paradigmatic example of an interacting integrable model. The initial state can be thought of as the result of joining chains with different global properties. Through dephasing, at late times, the state becomes locally equivalent to a stationary state which explicitly depends on position and time.

Determination of the Nonequilibrium Steady State Emerging from a Defect.

We consider the nonequilibrium time evolution of a translationally invariant state under a Hamiltonian with a localized defect. We discern the situations where a light cone spreads out from the defect and separates the system into regions with macroscopically different properties. We identify the light cone and propose a procedure to obtain a (quasi)stationary state describing the late time dynamics of local observables.

Prethermalization and Thermalization in Models with Weak Integrability Breaking.

We study the effects of integrability-breaking perturbations on the nonequilibrium evolution of many-particle quantum systems. We focus on a class of spinless fermion models with weak interactions. We employ equation of motion techniques that can be viewed as generalizations of quantum Boltzmann equations.