scholarly journals Local integrals of motion in many-body localized systems

2017 ◽  
Vol 529 (7) ◽  
pp. 1600278 ◽  
Author(s):  
John Z. Imbrie ◽  
Valentina Ros ◽  
Antonello Scardicchio
Keyword(s):  
Many Body ◽  
Integrals Of Motion

scholarly journals Integrals of motion in the many-body localized phase

2015 ◽  
Vol 891 ◽  
pp. 420-465 ◽  
Author(s):  
V. Ros ◽  
M. Müller ◽  
A. Scardicchio
Keyword(s):  
Many Body ◽  
Integrals Of Motion ◽  
The Many

scholarly journals Comparing many-body localization lengths via nonperturbative construction of local integrals of motion

2019 ◽  
Vol 100 (21) ◽  
Author(s):  
Pai Peng ◽  
Zeyang Li ◽  
Haoxiong Yan ◽  
Ken Xuan Wei ◽  
Paola Cappellaro
Keyword(s):  
Many Body ◽  
Integrals Of Motion

scholarly journals Constructing local integrals of motion in the many-body localized phase

2015 ◽  
Vol 91 (8) ◽  
Author(s):  
Anushya Chandran ◽  
Isaac H. Kim ◽  
Guifre Vidal ◽  
Dmitry A. Abanin
Keyword(s):  
Many Body ◽  
Integrals Of Motion ◽  
The Many

scholarly journals Many-body localization: stability and instability

2017 ◽  
Vol 375 (2108) ◽  
pp. 20160422 ◽  
Author(s):  
Wojciech De Roeck ◽  
John Z. Imbrie
Keyword(s):  
Higher Dimensions ◽  
Quantum Systems ◽  
One Dimension ◽  
Reasonable Assumption ◽  
Level Spacing ◽  
Weak Disorder ◽  
Many Body ◽  
Integrals Of Motion ◽  
Stability And Instability ◽  
Rare Regions

Rare regions with weak disorder (Griffiths regions) have the potential to spoil localization. We describe a non-perturbative construction of local integrals of motion (LIOMs) for a weakly interacting spin chain in one dimension, under a physically reasonable assumption on the statistics of eigenvalues. We discuss ideas about the situation in higher dimensions, where one can no longer ensure that interactions involving the Griffiths regions are much smaller than the typical energy-level spacing for such regions. We argue that ergodicity is restored in dimension d >1, although equilibration should be extremely slow, similar to the dynamics of glasses. This article is part of the themed issue ‘Breakdown of ergodicity in quantum systems: from solids to synthetic matter’.

scholarly journals Flow equations for disordered Floquet systems

2021 ◽  
Vol 11 (2) ◽  
Author(s):  
Steven Thomson ◽  
Duarte Magano ◽  
Marco Schiro'
Keyword(s):  
Flow Equation ◽  
Two Dimensional ◽  
Many Body ◽  
Integrals Of Motion ◽  
Exact Methods ◽  
New Approach ◽  
Flow Equations ◽  
Periodically Driven ◽  
Floquet Modes ◽  
Many Body Systems

In this work, we present a new approach to disordered, periodically driven (Floquet) quantum many-body systems based on flow equations. Specifically, we introduce a continuous unitary flow of Floquet operators in an extended Hilbert space, whose fixed point is both diagonal and time-independent, allowing us to directly obtain the Floquet modes. We first apply this method to a periodically driven Anderson insulator, for which it is exact, and then extend it to driven many-body localized systems within a truncated flow equation ansatz. In particular we compute the emergent Floquet local integrals of motion that characterise a periodically driven many-body localized phase. We demonstrate that the method remains well-controlled in the weakly-interacting regime, and allows us to access larger system sizes than accessible by numerically exact methods, paving the way for studies of two-dimensional driven many-body systems.

scholarly journals Local integrals of motion and the quasiperiodic many-body localization transition

2021 ◽  
Vol 103 (22) ◽  
Author(s):  
Hansveer Singh ◽  
Brayden Ware ◽  
Romain Vasseur ◽  
Sarang Gopalakrishnan
Keyword(s):  
Many Body ◽  
Integrals Of Motion ◽  
Localization Transition
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