On Many-Body Localization for Quantum Spin Chains - INSPIRE

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On Many-Body Localization for Quantum Spin Chains

John Z. Imbrie

Jun 1, 2016

51 pages

Published in:

J.Statist.Phys. 163 (2016) 5, 998-1048

Published: Jun 1, 2016

DOI:

10.1007/s10955-016-1508-x

reference search310 citations

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Abstract: (Springer)

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.

Many-body Localization (MBL)
Step Jumps
Resonant Graphs
Inductive Bounds
Resonator Block

References(51)

Figures(0)

Absence of Diffusion in Certain Random Lattices

P.W. Anderson
(
- Bell Labs
)

- Phys.Rev. 109 (1958) 1492-1505
•
DOI:
- 10.1103/PhysRev.109.1492

Metal–insulator transition in a weakly interacting many-electron system with localized single-particle states

- Annals Phys. 321 (2006) 5, 1126-1205
•
DOI:
- 10.1016/j.aop.2005.11.014

: Interactions and the Anderson transition

L. Fleishman
,
P. Anderson

- Phys.Rev.B 21 (1980) 2366-2377
•
DOI:
- 10.1103/PhysRevB.21.2366

: Localization and interaction in one-dimensional quantum fluids

T. Giamarchi
,
H.J. Schulz

- EPL 3 (1987) 1287-1293
•
DOI:
- 10.1209/0295-5075/3/12/007

Interacting Electrons in Disordered Wires: Anderson Localization and Low- $T$ Transport

- Phys.Rev.Lett. 95 (2005) 20, 206603
•
DOI:
- 10.1103/PhysRevLett.95.206603

Many-body localization phase transition

- Phys.Rev.B 82 (2010) 17, 174411
•
DOI:
- 10.1103/PhysRevB.82.174411

Entanglement versus chaos in disordered spin chains

- Phys.Rev.A 69 (2004) 042304
•
e-Print:
- quant-ph/0310177
•
DOI:
- 10.1103/PhysRevA.69.042304

Many-body localization in the Heisenberg $X X Z$ magnet in a random field

- Phys.Rev.B 77 (2008) 6, 064426
•
DOI:
- 10.1103/PhysRevB.77.064426

: Absence of diffusion in the Anderson tight binding model for large disorder or low energy

J. Fröhlich
,
T. Spencer

- Commun.Math.Phys. 88 (1983) 151-184
•
DOI:
- 10.1007/BF01209475

Localization at large disorder and at extreme energies: An Elementary derivation

Michael Aizenman
(
- Princeton U. and
- Princeton U., Math. Dept.
)
,
Stanislaw Molchanov
(
- Moscow State U.
)

- Commun.Math.Phys. 157 (1993) 245-278
•
DOI:
- 10.1007/BF02099760

Localization transition in the Anderson model on the Bethe lattice: Spontaneous symmetry breaking and correlation functions

- Nucl.Phys.B 366 (1991) 507-532
•
DOI:
- 10.1016/0550-3213(91)90028-V

: Localization bounds for multiparticle systems

M. Aizenman
,
S. Warzel

- Commun.Math.Phys. 290 (2009) 903-934
•
DOI:
- 10.1007/s00220-009-0792-6

: Direct scaling analysis of localization in disordered systems. II. Multi-particle lattice systems

V. Chulaevsky

e-Print:
- 1106.2234

: Dynamical localization for a multi-particle model with an alloy-type external random potential

V. Chulaevsky
,
A.B. de Monvel
,
Y. Suhov

- Nonlinearity 24 (2011) 1451-1472
•
DOI:
- 10.1088/0951-7715/24/5/004

: Eigenfunctions in a two-particle Anderson tight binding model

V. Chulaevsky
,
Y. Suhov

- Commun.Math.Phys. 289 (2009) 701-723
•
DOI:
- 10.1007/s00220-008-0721-0

: Multi-particle Anderson localisation: induction on the number of particles

V. Chulaevsky
,
Y. Suhov

- Math.Phys.Anal.Geom. 12 (2009) 117-139
•
DOI:
- 10.1007/s11040-008-9055-6

: Multiparticle localization for disordered systems on continuous space via the fractional moment method

M. Fauser
,
S. Warzel

- Rev.Math.Phys. 27 (2015) 1550010
•
DOI:
- 10.1142/S0129055X15500105

: The bootstrap multiscale analysis for the multi-particle Anderson model

A. Klein
,
S.T. Nguyen

- J.Statist.Phys. 151 (2013) 938-973
•
DOI:
- 10.1007/s10955-013-0734-8

: Dynamical localization in disordered quantum spin systems

E. Hamza
,
R. Sims
,
G. Stolz

- Commun.Math.Phys. 315 (2012) 215-239
•
DOI:
- 10.1007/s00220-012-1544-6

: Asymptotic quantum many-body localization from thermal disorder

W. De Roeck
,
F. Huveneers

- Commun.Math.Phys. 332 (2014) 1017-1082
•
DOI:
- 10.1007/s00220-014-2116-8

: An explicit bound for dynamical localisation in an interacting many-body system

P.L. Giscard
,
Z. Choo
,
M.T. Mitchison
,
J.J. Mendoza-Arenas
,
D. Jaksch

e-Print:
- 1402.1421

: Level-spacing for non-monotone Anderson models

J.Z. Imbrie
,
R. Mavi

- J.Statist.Phys. 162 (2016) 1451-1484
•
DOI:
- 10.1007/s10955-016-1461-8

Localization of interacting fermions at high temperature

- Phys.Rev.B 75 (2007) 15, 155111
•
DOI:
- 10.1103/PhysRevB.75.155111

Quantum statistical mechanics in a closed system

J.M. Deutsch

- Phys.Rev.A 43 (1991) 4, 2046
•
DOI:
- 10.1103/PhysRevA.43.2046

Thermalization and its mechanism for generic isolated quantum systems

- Nature 452 (2008) 7189, 854-858
•
e-Print:
- 0708.1324
•
DOI:
- 10.1038/nature06838

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