Level Spacing for Non-Monotone Anderson Models

Mavi, Rajinder

doi:10.1007/s10955-016-1461-8

Cited by 8 publications

(11 citation statements)

References 33 publications

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“…However, at this point we lack the tools to adequately deal with such questions of level statistics. (For a step in this direction, see [36] for a proof of a level-spacing condition for a block Anderson model.) Nevertheless, LLA(ν, C) is a very mild assumption from the physical point of view, since random matrices normally have either neutral statistics (ν = 1, e.g.…”

Section: Resultsmentioning

confidence: 99%

On Many-Body Localization for Quantum Spin Chains

Imbrie¹

2016

J Stat Phys

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637

655

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For a one-dimensional spin chain with random local interactions, we prove that many-body localization follows from a physically reasonable assumption that limits the amount of level attraction in the system. The construction uses a sequence of local unitary transformations to diagonalize the Hamiltonian and connect the exact many-body eigenfunctions to the original basis vectors.Comment: 62 pages, 4 figures, additional details in section 4 and references for published version. To appear in Jour. Stat. Phy

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Section: Resultsmentioning

confidence: 99%

On Many-Body Localization for Quantum Spin Chains

Imbrie¹

2016

J Stat Phys

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637

655

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“…Physically, one expects to see satisfied with

ν = 1

in a localized phase (Poisson statistics) or with

ν > 1

in a thermalized phase (repulsive statistics). Although these bounds are expected to hold, the tools for proving them are not yet available in the many‐body context (see for a potentially useful approach in the one‐body context). We discuss in the following the main steps in the diagonalization procedure.…”

Section: Construction Of Conservation Laws: Analytic Schemesmentioning

confidence: 99%

Local integrals of motion in many‐body localized systems

2017

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We review the current (as of Fall 2016) status of the studies on the emergent integrability in many-body localized models. We start by explaining how the phenomenology of fully many-body localized systems can be recovered if one assumes the existence of a complete set of (quasi)local operators which commute with the Hamiltonian (local integrals of motions, or LIOMs). We describe the evolution of this idea from the initial conjecture, to the perturbative constructions, to the mathematical proof given for a disordered spin chain. We discuss the proposed numerical algorithms for the construction of LIOMs and the status of the debate on the existence and nature of such operators in systems with a many-body mobility edge, and in dimensions larger than one.

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“…0 < ν < 1. Mathematically, techniques to prove estimates such as (2) are not yet available for many-body systems, but a promising approach is available for singlebody Hamiltonians [16].…”

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confidence: 99%

Diagonalization and Many-Body Localization for a Disordered Quantum Spin Chain

2016

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We consider a weakly interacting quantum spin chain with random local interactions. We prove that many-body localization follows from a physically reasonable assumption that limits the extent of level attraction in the statistics of eigenvalues. In a KAM-style construction, a sequence of local unitary transformations is used to diagonalize the Hamiltonian by deforming the initial tensorproduct basis into a complete set of exact many-body eigenfunctions.

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Level Spacing for Non-Monotone Anderson Models

Cited by 8 publications

References 33 publications

On Many-Body Localization for Quantum Spin Chains

On Many-Body Localization for Quantum Spin Chains

Local integrals of motion in many‐body localized systems

Diagonalization and Many-Body Localization for a Disordered Quantum Spin Chain

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