Riccardo Senese

Abstract:

We demonstrate the existence of a universal phase diagram of quantum chains with range- $k$ interactions subject to the conservation of a total charge and its dipole moment. These systems exhibit “freezing” transitions between strongly and weakly Hilbert-space-fragmented phases as the charge filling $\nu$ is varied. We show that these continuous phase transitions occur at a critical charge filling of ${\nu }_c={(k-2)}^{-1}$ of the on-site Hilbert-space dimension $d$ . To this end, we analytically prove that, for any $d$ , any state with $\nu <{\nu }_c$ hosts a finite density of sites belonging to “blockages,” which we define as subregions of the chain across which transport of charge and dipole moment cannot occur. Some blockages arise from sequences of frozen sites, i.e., sites with an unchanging on-site charge, while others do not involve frozen sites at all. We prove that the presence of blockages implies strong fragmentation of typical symmetry sectors into Krylov subspaces, each of which forms an exponentially vanishing fraction of the total sector. By studying the distribution of blockages we analytically characterize how typical states are subdivided into dynamically disconnected local “active bubbles” and prove that typical eigenstates at these charge fillings exhibit area-law entanglement entropy, while there exist rare eigenstates featuring non-area-law scaling. We also numerically show that for $\nu >{\nu }_c$ and arbitrary $d$ , typical symmetry sectors are weakly fragmented, with their dominant Krylov sectors constituted of states that are free of blockages. We analytically derive some critical exponents characterizing the transition and numerically determine the density of blockages at $\nu ={\nu }_c$ , with clear implications for transport at the critical point. Finally, we investigate the properties of special-case models for which no phase transitions occur.

Abstract:

The presence of long-lived oscillations in the expectation values of local observables after quantum quenches has recently attracted considerable attention in relation to weak ergodicity breaking. Here, we focus on an alternative mechanism that gives rise to such oscillations in a class of systems that support kinematically protected gapped excitations at zero temperature. An open question in this context is whether such oscillations will ultimately decay. We provide strong support for the decay hypothesis by considering spin models that can be mapped to systems of weakly interacting fermions, which in turn are amenable to an analysis by standard methods based on the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. We find that there is a time scale beyond which the oscillations start to decay that grows as the strength of the quench is made small.

Abstract:

Transverse plasma polaritons and longitudinal plasmons describe the propagation of light-matter modes in an isotropic metal. However, in a layered metal the anisotropy of the bare electromagnetic response mixes the longitudinal and transverse excitations, making the distinction between polariton and plasmon blurred at small wave vectors, where retardation effects of the electromagnetic interactions become quantitatively relevant. In the usual Kubo approach for the linear response, this effect appears as a mixing between the density and the transverse current fluctuations, that requires to revise the standard random phase approximation (RPA) approach for density correlations where only the instantaneous Coulomb potential is included. In this paper we derive the general expression for the density and current correlation functions at long wavelength in a layered metal, showing that below a crossover scale set by the anisotropy of the plasma frequencies retardation effects make the dispersion of the generalized plasma modes different from the standard RPA result. In addition, the mixed longitudinal and transverse nature of these excitations reflects in a double-peak structure for the density response, that can be eventually accessed by means of high-momentum resolution electron-energy-loss or x-ray spectroscopies.