Many-body localization: answers and questions
Professor John Imbrie, University of Virginia, USA
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?
Probing many-body localisation from an ultracold atom perspective
Professor Immanuel Bloch, Ludwig-Maximilians-Universität & Max Planck Institute of Quantum Optics, Munich, Germany
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.
Many body localization and glassiness in disordered quantum systems
Professor Antonello Scardicchio, International Centre for Theoretical Physics, Italy
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.
Exploring quantum phase slips in 1D bosonic systems
Dr Chiara D'Errico, Istituto Nazionale di Ottica - CNR and LENS, Italy
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.