Sam Genway

Signatures of many-body localisation in a system without disorder and the relation to a glass transition

We study a quantum spin system with local bilinear interactions and without quenched disorder which seems to display characteristic signatures of a many-body localisation (MBL) transition. From direct diagonalisation of small systems, we find a change in certain dynamical and spectral properties at a critical value of a coupling, from those characteristic of a thermalising phase to those characteristic of a MBL phase. The system we consider is known to have a quantum phase transition in its ground-state in the limit of large size, related to a first-order active-to-inactive phase transition in the stochastic trajectories of an associated classical model of glasses. Our results here suggest that this transition is present throughout the spectrum of the system in the large size limit. These findings may help understand the connection between MBL and structural glass transitions.

Generalized Dicke nonequilibrium dynamics in trapped ions.

We explore trapped ions as a setting to investigate nonequilibrium phases in a generalized Dicke model of dissipative spins coupled to phonon modes. We find a rich dynamical phase diagram including superradiantlike regimes, dynamical phase coexistence, and phonon-lasing behavior. A particular advantage of trapped ions is that these phases and transitions among them can be probed in situ through fluorescence. We demonstrate that the main physical insights are captured by a minimal model and consider an experimental realization with Ca+ ions trapped in a linear Paul trap with a dressing scheme to create effective two-level systems with a tunable dissipation rate.

Phase transitions in trajectories of a superconducting single-electron transistor coupled to a resonator.

Recent progress in the study of dynamical phase transitions has been made with a large-deviation approach to study trajectories of stochastic jumps using a thermodynamic formalism. We study this method applied to an open quantum system consisting of a superconducting single-electron transistor, near the Josephson quasiparticle resonance, coupled to a resonator. We find that the dynamical behavior shown in rare trajectories can be rich even when the mean dynamical activity is small, and thus the formalism gives insights into the form of fluctuations. The structure of the dynamical phase diagram found from the quantum-jump trajectories of the resonator is studied, and we see that sharp transitions in the dynamical activity may be related to the appearance and disappearance of bistabilities in the state of the resonator as system parameters are changed. We also demonstrate that for a fast resonator, the trajectories of quasiparticles are similar to the resonator trajectories.

Dynamical phase transitions, time-integrated observables, and geometry of states

We show that there exist dynamical phase transitions (DPTs), as defined by Heyl et al. [Phys. Rev. Lett. 110, 135704 (2013)], in the transverse-field Ising model (TFIM) away from the static quantum critical points. We study a class of special states associated with singularities in the generating functions of time-integrated observables as found by Hickey et al. [Phys. Rev. B 87, 184303 (2013)]. Studying the dynamics of these special states under the evolution of the TFIM Hamiltonian, we find temporal nonanalyticities in the initial-state return probability associated with dynamical phase transitions. By calculating the Berry phase and Chern number we show the set of special states have interesting geometric features similar to those associated with static quantum critical points.

Time-integrated observables as order parameters for full counting statistics transitions in closed quantum systems

The dynamical behaviour of many-body systems is often richer than what can be anticipated from their static properties. Here we show that in closed quantum systems this becomes evident by considering time-integrated observables as order parameters. In particular, the analytic properties of their generating functions, as estimated by full-counting statistics, allow to identify dynamical phases, i.e. phases with specific fluctuation properties of time-integrated observables, and to locate the transitions between these phases. We discuss in detail the case of the quantum Ising chain in a transverse field. We show that this model displays a continuum of quantum dynamical transitions, of which the static transition is just an end point. These singularities are not a consequence of particular choices of initial conditions or other external non-equilibrium protocols such as quenches in coupling constants. They can be probed generically through quantum jump statistics of an associated open problem, and for the case of the quantum Ising chain we outline a possible experimental realisation of this scheme by digital quantum simulation with cold ions.

Localization in space and time in disordered-lattice open quantum dynamics.

We study a two-dimensional tight-binding lattice for excitons with on-site disorder, coupled to a thermal environment at infinite temperature. The disorder acts to localize an exciton spatially, while the environment generates dynamics which enable exploration of the lattice. Although the steady state of the system is trivially uniform, we observe a rich dynamics and uncover a dynamical phase transition in the space of temporal trajectories. This transition is identified as a localization in the dynamics generated by the bath. We explore spatial features in the dynamics and employ a generalization of the inverse participation ratio to deduce an ergodic timescale for the lattice.

Fluctuation theorems and the generalized Gibbs ensemble in integrable systems.

We derive fluctuation relations for a many-body quantum system prepared in a generalized Gibbs ensemble subject to a general nonequilibrium protocol. By considering isolated integrable systems, we find generalizations to the Tasaki-Crooks and Jarzynski relations. Our approach is illustrated by studying the one-dimensional quantum Ising model subject to a sudden change in the transverse field, where we find that the statistics of the work done and irreversible entropy show signatures of quantum criticality. We discuss these fluctuation relations in the context of thermalization.

Trajectory phases of a quantum dot model

We present a thermodynamic formalism to study the trajectories of charge transport through a quantum dot coupled to two leads in the resonant-level model. We show that a close analogue of equilibrium phase transitions exists for the statistics of transferred charge; by tuning an appropriate ‘counting field’, crossovers to different trajectory phases are possible. Our description reveals a mapping between the statistics of a given device and current measurements over a range of devices with different dot–lead coupling strengths. Furthermore insight into features of the trajectory phases are found by studying the occupation of the dot conditioned on the transported charge between the leads; this is calculated from first principles using a trajectory biased two-point projective measurement scheme.