Real-time Dynamics in Strongly Correlated Quantum Matter

I explain how in many one-dimensional spin chains with open boundary conditions, the edge spins retain memory of their initial state for very long times. The long coherence times do not require disorder, only an ordered phase. In the integrable Ising and XYZ chains, the presence of a strong zero mode means the coherence time is infinite, even at infinite temperature. When Ising is perturbed by interactions breaking the integrability, the coherence time remains exponentially long in the perturbing couplings. This behavior is a consequence of an edge "almost" strong zero mode, guaranteed by a theorem requiring a single almost conservation law.

Confinement is a ubiquitous mechanism in nature, whereby particles feel an attractive force that increases without bound as they separate. A prominent example is color confinement in particle physics, in which baryons and mesons are produced by quark confinement. Analogously, confinement can also occur in low-energy quantum many-body systems when elementary excitations are confined into bound quasiparticles. Here, we report the first observation of magnetic domain wall confinement in interacting spin chains with a trapped-ion quantum simulator. By measuring how correlations spread, we show that confinement can dramatically suppress information propagation and thermalization in such many-body systems. We are able to quantitatively determine the excitation energy of domain wall bound states from non-equilibrium quench dynamics. Furthermore, we study the number of domain wall excitations created for different quench parameters, in a regime that is difficult to model with classical computers.

Despite tremendous theoretical efforts to understand subtleties of the many-body localization (MBL) transition, many questions remain open, in particular concerning its critical properties. Here we make the key observation that MBL in one dimension is accompanied by a spin freezing mechanism which implies a chain breaking in the thermodynamic limit. Using analytical and numerical approaches, we show that such chain breakings directly probe the typical localization length, and that their scaling properties at the MBL transition agree with the Kosterlitz-Thouless scenario predicted by phenomenological renormalization group approaches.

Gauge theories are the cornerstone of our understanding of fundamental interactions among particles. Their properties are often probed in dynamical experiments, such as those performed at ion colliders and high-intensity laser facilities. Describing the evolution of these strongly coupled systems is a formidable challenge for classical computers, and represents one of the key open quests for quantum simulation approaches to particle physics phenomena. In our work, we show how recent experiments done on Rydberg atom chains naturally realize the real-time dynamics of a lattice gauge theory at system sizes at the boundary of classical computational methods.

At its most fundamental level the calculation of real-time transition amplitudes requires, in the spirit of Feynman, an integration over the space of histories. In the limit of large actions, after a non-trivial asymptotic analysis, Gutzwiller showed that the Feynman path integral is reduced to a coherent sum over interfering classical trajectories, the starting point of modern semiclassical methods. The extension of this ideas into the realm of many-body (bosonic systems) allows for a precise separation between incoherent (classical) and coherent (interference-related) contributions in the dynamics of transition probabilities, where the first can be shown to be exactly given by the celebrated Truncated Wigner method (TWM). In non-localized phases, however, although quantum effects due to interference of many-body paths are extremely well described by semiclassical methods, they posse a challenge due to both their fragility and the non-trivial dependence on classical but unfamiliar objects like stabilities and topological indexes. In this talk we report a robust enhancement of many-body transition amplitudes due to path interference in non-integrable systems with discrete symmetries that produces macroscopic deviations from the TWM and, moreover, we show how this enhancement is successfully described by a minimal extension of the TWM.

An accepted definition of quantum chaos is based on emergence of the random matrix description of the spectrum and the eigenstates of chaotic Hamiltonians. Standard measures of chaos in quantum systems are level statistics and the spectral form factor. In this talk I will argue that the norm of the adiabatic gauge potential, the generator of adiabatic deformations between eigenstates, serves as much more sensitive probe of quantum chaos. Using this measure one can detect transitions from non-ergodic to ergodic behavior at perturbation strengths orders of magnitude smaller than those required for standard measures. I will present numerical analysis of the effect of integrability breaking perturbations on various spin chains leading to some interesting observations: (i) the chaotic threshold decreases exponentially with system size, (ii) integrability-breaking perturbations can be detected already in the integrable systems, i.e. at zero perturbation strength, (iii) small integrability-breaking can lead to anomalously slow dynamics with exponentially long in the system size relaxation times.