Future directions in non-ergodic dynamics in quantum systems

Robust edge zero modes guaranteeing ground-state degeneracy are common in a topological phase of matter. A more dramatic effect occurs in the Ising/Majorana/Kitaev chain: “strong” edge zero modes result in identical spectra in the entire even and odd fermion-number sectors, up to exponentially small finite-size corrections. A strong zero mode in a clean system is not a free-fermionic fluke. In the XYZ chain/coupled Majorana wires, its presence guarantees infinite coherence time for the edge spin, even with an infinite-temperature initial state. In non-integrable systems like the Ising chain with four-fermion interactions, an “almost” strong zero mode results in a very long coherence time, falling off very slowly with system size.

The long time dynamics of generic strongly interacting quantum systems presents a fundamental challenge for theory and computation. Matrix product states, useful for describing quantum ground states, are commonly thought to be inadequate for description of dynamics. The main obstruction is the linear growth of the entanglement entropy in time, which implies exponential growth of the required matrix sizes. In his talk Altman will discuss a new approach to overcome this obstruction and accurately describe the chaotic dynamics and emergent hydrodynamic behaviour at long times using matrix product states. The key idea is that local observables thermalize quickly when subject to generic evolution and consequently follow effective classical hydrodynamics. This suggests that the entanglement growth can be truncated after the local equilibration time without sacrificing information about local observables. Our scheme for implementing this truncation is based on the time dependent variational principle, which ensures that the approximate dynamics respects all conservation laws and can be systematically improved by increasing the bond dimension. Altman will present results for thus obtained transport coefficients and chaos characteristics in the Ising model subject to both transverse and longitudinal fields.

Atomic gases cooled to Nanokelvin temperatures are a new exciting tool to study a broad range of quantum phenomena. In particular, an outstanding and rapid control over the fundamental parameters, such as interaction strength, spin composition, and dimensionality allows to realize and observe many different situations far from equilibrium. Long-standing questions such as the coupling to an environment can be investigated. In her talk, Kollath will address the question of the influence of a coupling to an environment on the system dynamics in bosonic optical lattice gases. The interplay between the interaction, the kinetic energy and the coupling to the environment causes a critical dynamics with algebraic decaying observable or a glass-like dynamics. Also the propagation of correlations will be discussed.

A novel feature of cold gases is the possibility to couple the motional dynamics of a quantum many body system to (one or more) quantized bosonic modes, describing the light fields in optical cavities. Such matter-light coupled systems show interesting forms of collective dynamics. They are subject to dissipation through fluctuations/damping of the cavity mode.  Cooper will present theoretical results that demonstrate examples of these novel collective dynamics, both in uniform and disordered settings, focusing on the question of whether or not the dissipative dynamics drive the system to a unique steady state.

Recent experiments [1,2] indicate that selective optical driving of phonons may generate or enhance ordered phases in strongly correlated quantum materials. In his talk Jaksch will discuss quantum optically inspired models that may help explain and engineer such phenomena. Specifically, Jaksch will consider a driven fermionic Hubbard model in the strongly correlated limit where the onsite interaction dominates over the kinetic energy [3]. The driving is modelled as an alternating periodic modulation of the lattice site energy offsets. He will demonstrate how this modulation suppresses tunnelling and induces exchange interactions. The combination of these effects changes the nature of the system into an attractive Luttinger liquid and leads to enhanced fermion pairing in one spatial dimension. Jaksch will present results at zero and finite temperatures and discuss the prospect of observing driven out-of-equilibrium superconductivity in this model system.

1. D. Fausti, R.I. Tobey, N. Dean, S. Kaiser, A. Dienst, M.C. Hoffmann, S. Pyon, T. Takayama, H. Takagi, and A. Cavalleri, Light-Induced Superconductivity in a Stripe-Ordered Cuprate. Science 331, 189 (2011).
2. M. Mitrano, A. Cantaluppi, D. Nicoletti, S. Kaiser, A. Perucchi, S. Lupi, P. Di Pietro, D. Pontiroli, M. Ricco, S.R. Clark, D. Jaksch and A. Cavalleri, Possible light-induced superconductivity in K3C60 at high temperature. Nature 530, 461-464 (2016). 
3. J. Coulthard, S.R. Clark, S. Al-Assam, A. Cavalleri and D. Jaksch, Enhancement of super-exchange pairing in the periodically-driven Hubbard model, arXiv:1608.03964 (2016).

The statistical properties of the entanglement spectrum of a disordered many-particle system are studied, in order to identify the localized to extended transition as function of interaction strength and excitation energy expected from the many-body localization transition. In his talk, Berkovits shows that an indication of such a transition is indeed observed, and some of the features may be interpreted as a signature of non-ergodic behaviour.

The time-dependent microscopic control available in experiments with systems of ultracold atoms has opened new opportunities to explore many-body dynamics, addressing fundamental questions both in and out of equilibrium. This control can also be extended beyond the coherent dynamics of the system, as in typical experimental regimes the dominant mechanisms for dissipation can both be described microscopically from first principles, and can be controlled with external fields. Such control originates in the separation of timescales for coupling to a reservoir and for the relaxation of the reservoir, which is typical in quantum optics. This allows us to calculate and explore the effect of dissipation on the many-body dynamics, including on the ergodicity of dynamics after a parameter quench. We can also go further, especially in engineering dissipative processes that will drive the system into specific interacting many-body states. Daley will discuss his group’s recent work in this direction, especially looking at the microscopic description of dissipation for cold atoms in optical lattices in the presence of light scattering or with the addition of a second species that acts as a reservoir, and describe applications towards the generation of strongly correlated many-body states, and the investigation of out-of-equilibrium dynamics (including in systems exhibiting many-body-localisation).