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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 longrange 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 AndersonMott
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 nonergodic
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.
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Week 1 Brainstorming: Questions in MBL
Dynamics are essentially involved. Cannot easily speak about transitions
Markus Mueller
 Numerical hardness of various measures (ranging from trying to resolve exponentially small MB level spacings to
coarser measures like spectral functions, local observables etc.).Bela Bauer's notes on numerical approaches to MBL. He lead a Friday discussion.