Week 1 Brainstorming: Questions in MBL



Topic
Discussion led by
Date
Existence of the MBL phase


Does MBL exist?
  • In d = 1,2, ..
  • with unbounded local Hilbert spaces/ in the continuum
  • with long-range interactions
  • If it exists, what is it? Working definitions? Are they equivalent?


Can we get MBL without disorder?
  • Translationally invariant systems
  • Deterministic potentials (quasiperiodic etc.)


Is MBL an idealized limit of a richer phase? Examples?





Transitions MBL <-> ergodic and MBL <-> MBL


Nature and universality of the transition — 1st order vs. 2nd order


Are there mobility edges?
Markus Mueller
10/21/2015
Are phase transitions within the MBL phase thermal?
  • Evidence for intermediate level statistics between two MBL phases


Overview of numerical approaches near the transitions
  • Numerics vs. forward scattering approximations
  • Harris criterion and survey of critical exponents obtained by different methods


Griffiths effects near the transition?


Chalker scaling near the transition? Multifractality


Connections with Anderson-Mott





Applications/ Usefulness


Can MBL really serve as a quantum memory?


Why are we here? What is MBL good for?





Detection of MBL phases



Probes that are better than density imbalance, conductivity etc.


Hard signatures of MBL





MBL and glasses


Can we use insights from MBL to solve the glass problem?


What is the structural (vs. spin) glass problem?
Dynamics are essentially involved. Cannot easily speak about transitions
Leticia Cugliandolo,
Markus Mueller




Numerical Techniques


Overview of numerical approaches for solving MBL.
  • Numerical hardness of various measures (ranging from trying to resolve exponentially small MB level spacings to
coarser measures like spectral functions, local observables etc.).
  • MPS/DMRG approaches
Bela Bauer




Varia


Is entanglement the right language for describing MBL?


Zero temperature interacting localization - delocalization transitions vs. T>0 MBL


MBL in open systems — what’s interesting?


MBL in driven systems
  • quasiperiodic driving


Alternatives to ETH that are delocalized but non-ergodic


What does it mean to coarse grain an MBL systems? (RSRG approaches)


Correct analytic methods? What are good disorder averaged quantities?


MBL in materials science. Complicated systems with phonons


MBL vs. integrability


Semiclassical 1/S approaches to MBL





Week 5:

Bela Bauer's notes on numerical approaches to MBL. He lead a Friday discussion.