Detecting a many-body mobility edge with quantum quenches

The many-body localization (MBL) transition is a quantum phase transition involving highly excited eigenstates of a disordered quantum many-body Hamiltonian, which evolve from "extended/ergodic" (exhibiting extensive entanglement entropies and fluctuations) to "localized" (exhibiting area-law scaling of entanglement and fluctuations). The MBL transition can be driven by the strength of disorder in a given spectral range, or by the energy density at fixed disorder - if the system possesses a many-body mobility edge. Here we propose to explore the latter mechanism by using "quantum-quench spectroscopy", namely via quantum quenches of variable width which prepare the state of the system in a superposition of eigenstates of the Hamiltonian within a controllable spectral region. Studying numerically a chain of interacting spinless fermions in a quasi-periodic potential, we argue that this system has a many-body mobility edge; and we show that its existence translates into a clear dynamical transition in the time evolution immediately following a quench in the strength of the quasi-periodic potential, as well as a transition in the scaling properties of the quasi-stationary state at long times. Our results suggest a practical scheme for the experimental observation of many-body mobility edges using cold-atom setups.Comment: v2: references added v3: minor revisions, added reference

Exact results for persistent currents of two bosons in a ring lattice

We study the ground state of two interacting bosonic particles confined in a ring-shaped lattice potential and subjected to a synthetic magnetic flux. The system is described by the Bose-Hubbard model and solved exactly through a plane-wave Ansatz of the wave function. We obtain energies and correlation functions of the system both for repulsive and attractive interactions. In contrast with the one-dimensional continuous theory described by the Lieb-Liniger model, in the lattice case we prove that the center of mass of the two particles is coupled with its relative coordinate. Distinctive features clearly emerge in the persistent current of the system. While for repulsive bosons the persistent current displays a periodicity given by the standard flux quantum for any interaction strength, in the attractive case the flux quantum becomes fractionalized in a manner that depends on the interaction. We also study the density after the long time expansion of the system which provides an experimentally accessible route to detect persistent currents in cold atom settings. Our results can be used to benchmark approximate schemes for the many-body problem

Dynamics of entanglement entropy and entanglement spectrum crossing a quantum phase transition

We study the time evolution of entanglement entropy and entanglement spectrum in a finite-size system which crosses a quantum phase transition at different speeds. We focus on the Ising model with a time-dependent magnetic field, which is linearly tuned on a time scale $\tau$ . The time evolution of the entanglement entropy displays different regimes depending on the value of $\tau$, showing also oscillations which depend on the instantaneous energy spectrum. The entanglement spectrum is characterized by a rich dynamics where multiple crossings take place with a gap-dependent frequency. Moreover, we investigate the Kibble-Zurek scaling of entanglement entropy and Schmidt gap.Comment: Accepted for publication in Phys. Rev.

Time-Dependent Simulations of One-dimensional Quantum Systems: from Thermalization to Localization

In the first part of this thesis we study the Aubry-André model for interacting fermions. We numerically describe its phase diagram at half filling, performing both DMRG and QMC simulations. We show the existence of a localized phase and other three regimes: luttinger liquid, charge density wave and productstate. We study the properties of the excited states of the Hamiltonian, looking for a many-body mobility edge in the spectrum, i.e. an energy threshold that separates localized from ergodic states. Analyzing many indicators we prove its existence. Finally we propose a quench-spectroscopy method for detecting the mobility edge dynamically. In the second part we study the expansion dynamics of two bosons in a one-dimensional lattice as ruled by the Bose-Hubbard model Hamiltonian, both in the attractive and repulsive regime. Using the Bethe Ansatz we identify the bound states effects and how the two-particles state evolves in time. We show that, independently from the initial state, there exists a strong relation between the expansion velocity and the presence of bound states in the spectrum. Moreover, we discuss the role of the lattice in the system expansion. In the third part we study the time evolution of the entanglement entropy in the Ising model, when it is dynamically driven across a quantum phase transition with different velocities. We computed the time-evolution of the half chain entanglement entropy and we found that, depending on the velocity at which the critical point is reached, it displays different regimes: an adiabatic one when the system evolves according to the instantaneous ground state; a a sudden quench regime when the system remains frozen to its initial state; and an intermediate one, where the entropy starts growing linearly but then displays oscillations. Moreover, we discuss the Kibble-Zurek mechanism for the transition between the paramagnetic and the ordered phase

Probing the BCS-BEC crossover with persistent currents

We study the persistent currents of an attractive Fermi gas confined in a tightly-confining ring trap and subjected to an artificial gauge field all through the BCS-BEC crossover. At weak attractions, on the BCS side, fermions display a parity effect in the persistent currents, ie their response to the gauge field is paramagnetic or diamagnetic depending on the number of pairs on the ring. At resonance and on the BEC side of the crossover we find a doubling of the periodicity of the ground-state energy as a function of the artificial gauge field and disappearance of the parity effect, indicating that persistent currents can be used to infer the formation of tightly-bound bosonic pairs. Our predictions can be accessed in ultracold atoms experiments through noise interferograms.Comment: 7 pages, 5 figure

The quantum solitons atomtronic interference device

We study a quantum many-body system of attracting bosons confined in a ring-shaped potential and interrupted by a weak link. With such architecture, the system defines atomtronic quantum interference devices harnessing quantum solitonic currents. We demonstrate that the system is characterized by the specific interplay between the interaction and the strength of the weak link. In particular, we find that, depending on the operating conditions, the current can be a universal function of the relative size between the strength of the impurity and interaction. The low lying many-body states are studied through a quench dynamical protocol that is the atomtronic counterpart of Rabi interferometry. With this approach, we demonstrate how our system defines a two level system of coupled solitonic currents. The current states are addressed through the analysis of the momentum distribution

Raise and fall of a bright soliton in an optical lattice

We study an ultracold atomic gas with attractive interactions in a one-dimensional optical lattice. We find that its excitation spectrum displays a quantum soliton band, corresponding to $N$-particle bound states, and a continuum band of other, mostly extended, states. For a system of a finite size, the two branches are degenerate in energy for weak interactions, while a gap opens above a threshold value for the interaction strength. We find that the interplay between degenerate extended and bound states has important consequences for both static and dynamical properties of the system. In particular, the solitonic states turn out to be protected from spatial perturbations and random disorder. We discuss how such dynamics implies that our system effectively provides an example of a quantum many-body system that, with the variation of the bosonic lattice filling, crosses over from integrable non-ergodic to non-integrable ergodic dynamics, through non-integrable non-ergodic regimes.Comment: To be published in Physical Review Letter

Loschmidt echo singularities as dynamical signatures of strongly localized phases

Quantum localization (single-body or many-body) comes with the emergence of local conserved quantities --- whose conservation is precisely at the heart of the absence of transport through the system. In the case of fermionic systems and S=1/2 spin models, such conserved quantities take the form of effective two-level systems, called l-bits. While their existence is the defining feature of localized phases, their direct experimental observation remains elusive. Here we show that strongly localized l-bits bear a dramatic universal signature, accessible to state-of-the-art quantum simulators, in the form of periodic cusp singularities in the Loschmidt echo following a quantum quench from a Neel/charge-density-wave state. Such singularities are perfectly captured by a simple model of Rabi oscillations of an ensemble of independent two-level systems, which also reproduces the short-time behavior of the entanglement entropy and the imbalance dynamics. In the case of interacting localized phases, the dynamics at longer times shows a sharp crossover to a faster decay of the Loschmidt echo singularities, offering an experimentally accessible signature of the interactions between l-bits