scholarly journals Many-body localization enables iterative quantum optimization

2021 ◽  
Author(s):  
Hanteng Wang ◽  
Hsiu-Chung Yeh ◽  
Alex Kamenev
Keyword(s):  
Optimization Problems ◽  
Tricritical Point ◽  
Many Body ◽  
Small Probability ◽  
Absolute Minimum ◽  
Localization Transition ◽  
Local Energy Minimum ◽  
The Many ◽  
Quantum Protocol ◽  
Quantum Optimization

Abstract We suggest an iterative quantum protocol, allowing to solve optimization problems with a glassy energy landscape. It is based on a periodic cycling around the tricritical point of the many-body localization transition. This ensures that each iteration leads to a non-exponentially small probability to find a lower local energy minimum. The other key ingredient is to tailor the cycle parameters to a currently achieved optimal state (the "reference" state) and to reset them once a deeper minimum is found. We show that, if the position of the tricritical point is known, the algorithm allows to approach the absolute minimum with any given precision in a polynomial time.

scholarly journals Exact solution of a percolation analog for the many-body localization transition

2019 ◽  
Vol 99 (22) ◽  
Author(s):  
Sthitadhi Roy ◽  
David E. Logan ◽  
J. T. Chalker
Keyword(s):  
Exact Solution ◽  
Many Body ◽  
Localization Transition ◽  
The Many

scholarly journals The ergodic side of the many-body localization transition

2017 ◽  
Vol 529 (7) ◽  
pp. 1600350 ◽  
Author(s):  
David J. Luitz ◽  
Yevgeny Bar Lev
Keyword(s):  
Many Body ◽  
Localization Transition ◽  
The Many

scholarly journals Finite-size scaling analysis of the many-body localization transition in quasiperiodic spin chains

2021 ◽  
Vol 104 (21) ◽  
Author(s):  
Adith Sai Aramthottil ◽  
Titas Chanda ◽  
Piotr Sierant ◽  
Jakub Zakrzewski
Keyword(s):  
Finite Size ◽  
Spin Chains ◽  
Scaling Analysis ◽  
Finite Size Scaling ◽  
Many Body ◽  
Localization Transition ◽  
Size Scaling ◽  
The Many

scholarly journals Signatures of a critical point in the many-body localization transition

2021 ◽  
Vol 10 (5) ◽  
Author(s):  
Ángel L. Corps ◽  
Rafael Molina ◽  
Armando Relaño
Keyword(s):  
Singular Point ◽  
Critical Point ◽  
Chaotic Behavior ◽  
Finite Size ◽  
System Size ◽  
Disorder Strength ◽  
Many Body ◽  
Localization Transition ◽  
Spectral Statistics ◽  
The Many

Disordered interacting spin chains that undergo a many-body localization transition are characterized by two limiting behaviors where the dynamics are chaotic and integrable. However, the transition region between them is not fully understood yet. We propose here a possible finite-size precursor of a critical point that shows a typical finite-size scaling and distinguishes between two different dynamical phases. The kurtosis excess of the diagonal fluctuations of the full one-dimensional momentum distribution from its microcanonical average is maximum at this singular point in the paradigmatic disordered J_1J1-J_2J2 model. For system sizes accessible to exact diagonalization, both the position and the size of this maximum scale linearly with the system size. Furthermore, we show that this singular point is found at the same disorder strength at which the Thouless and the Heisenberg energies coincide. Below this point, the spectral statistics follow the universal random matrix behavior up to the Thouless energy. Above it, no traces of chaotic behavior remain, and the spectral statistics are well described by a generalized semi-Poissonian model, eventually leading to the integrable Poissonian behavior. We provide, thus, an integrated scenario for the many-body localization transition, conjecturing that the critical point in the thermodynamic limit, if it exists, should be given by this value of disorder strength.

scholarly journals Multifractal Scalings Across the Many-Body Localization Transition

2019 ◽  
Vol 123 (18) ◽  
Author(s):  
Nicolas Macé ◽  
Fabien Alet ◽  
Nicolas Laflorencie
Keyword(s):  
Many Body ◽  
Localization Transition ◽  
The Many
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