Breakdown of ergodicity in quantum systems: from solids to synthetic matter

In considering the phenomenon of localization in isolated many-body quantum systems, it is important to get past perturbative analysis, as rare regions with weak disorder (Griffiths regions) have the potential to spoil localization. In his talk, John describes a non-perturbative construction of local integrals of motion (LIOMs) for a weakly interacting spin chain in one dimension. This leads to a proof that many-body localization follows from a physically reasonable assumption that limits the extent of level attraction in the statistics of eigenvalues. In a Kolmogorov-Arnold-Moser-style construction, a sequence of local unitary transformations is used to diagonalize the Hamiltonian by deforming the initial tensor-product basis into a complete set of exact many-body eigenfunctions. John discusses prospects for the level-statistics problem by reviewing recent work elucidating the way randomness localizes eigenfunctions, smooths out eigenvalue distributions, and produces eigenvalue separation.

The construction breaks down in higher dimensions, as one can no longer ensure that interactions involving the Griffiths regions are much smaller than the typical energy-level spacing for such regions. Is this an artefact of the method or is there a real barrier to exact many-body localization in dimensions 2 or more? 

A fundamental assumption in statistical physics is that generic closed quantum many-body systems thermalise under their own dynamics. Recently, the emergence of many-body localised (MBL) systems has questioned this concept, challenging our understanding of the connection between statistical physics and quantum mechanics. In his talk, Immanuel reports on several recent experiments carried out in his group on the observation of Many-Body Localisation in different scenarios, ranging from 1D fermionic quantum gas mixtures in driven and undriven Aubry-André type disorder potentials and 2D systems of interacting bosons in 2D random potentials. It is shown that the memory of the system on its initial non-equilibrium state can serve as a useful indicator for a non-ergodic, MBL phase. Furthermore, he will present new results on the slow relaxation dynamics in the ergodic phase below the MBL transition, where he finds evidence for Griffith’s type slow dynamics.

His group’s experiments represent a demonstration and in-depth characterisation of many-body localisation, often in regimes not accessible with state-of-the-art simulations on classical computers.

Antonello discusses the interplay of two phenomena arising in disordered quantum spin systems: the appearance of a glassy phase, and the complete suppression of transport due to many-body localization. He will review work done (analytical and numerical) on some models, under various approximations, and try to sketch a universal physical picture for how the two dynamical phases interplay. Antonello will also comment on the implications of this picture for the performance of quantum computers and in particular those implementing the quantum adiabatic algorithm.

Quantum phase slips, i.e., the primary excitations in one-dimensional superfluids at low temperature, have been well characterized in most condensed-matter systems, with the notable exception of ultracold quantum gases. Chiara presents the experimental investigation of the dissipation in one-dimensional Bose superfluids flowing along a periodic potential, which show signatures of the presence of quantum phase slips. In particular, by controlling the velocity of the superfluid and the interaction between the bosons, the D’Errico group are able to drive a crossover from a regime of thermal phase slips into a regime of quantum phase slips. Achieving a good control of quantum phase slips in ultracold quantum gases requires to keep under control other phenomena such as the breaking of superfluidity at the critical velocity or the appearance of a Mott insulator in the strongly correlated regime. Chiara presents the group’s current results in these directions.

Many-body localization (MBL) provides the only known robust mechanism to break ergodicity and avoid thermalization in quantum many-body systems. Many-body localized systems are characterized by emergent local integrability and low, area-law entanglement of excited eigenstates. It is well-known that symmetries of the system modify single-particle, Anderson localization in non-trivial ways. Do symmetries have a significant effect on MBL and thermalization in many-body systems? In this talk, Abanin will focus on disordered systems with continuous, non-Abelian symmetries, one example being the random Heisenberg model, which has SU(2) symmetry. The symmetry dictates that the system cannot have a complete set of local integrals of motion, and therefore cannot be MBL in the conventional sense. Abanin will describe a potential non-ergodic phase, which is consistent with the symmetry. In this phase, the eigenstates have sub-thermal, logarithmic scaling of entanglement with the system size. Abanin will introduce a method for probing the stability of non-ergodic many-body phases, and apply it to the SU(2)-symmetric case, finding that the non-ergodic phase becomes unstable due to proliferation of multi-spin resonances. Such processes are missed by other approaches, such as strong-disorder renormalization group, but are crucial for thermalization in these systems. He will discuss the case of discrete non-Abelian groups, and will speculate about the possibility of ergodicity-breaking phases beyond conventional many-body localization.

An important point in characterizing a given phase, for instance a many-body localized one, is to understand how it arises from neighbouring phases and how it breaks down under external influence. Znidaric will discuss three different ways of failing to be localized: an insufficient disorder strength, disorder with symmetries, and coupling to Markovian environment. If disorder is too small transport properties can be very rich, ranging from subdiffusion to superdiffusion. If disorder is strong but has symmetries, an example being the Hubbard model with charge disorder realized in experiments, the system also fails to be fully localized. Finally Znidaric will briefly mention classical-like break down of localization due to coupling to environment.