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Many-body localization: stability and instability
Wojciech De Roeck1, John Z Imbrie2
1Instituut voor Theoretische Fysica, KU Leuven, 3000 Leuven, Belgium.
Summary
Weakly disordered regions can disrupt localization in quantum systems. This study constructs local integrals of motion (LIOMs) for 1D spin chains, showing ergodicity is restored in higher dimensions, albeit with slow equilibration.
Area of Science:
- Quantum physics
- Condensed matter physics
- Statistical mechanics
Background:
- Rare regions with weak disorder, known as Griffiths regions, can impede localization phenomena in quantum systems.
- Understanding the behavior of these regions is crucial for comprehending ergodicity and equilibration in many-body quantum systems.
Purpose of the Study:
- To develop a non-perturbative construction of local integrals of motion (LIOMs) for weakly interacting spin chains in one dimension.
- To explore the implications of Griffiths regions in higher dimensions and their effect on ergodicity and equilibration.
Main Methods:
- Construction of local integrals of motion (LIOMs) using a non-perturbative approach.
- Analysis of eigenvalue statistics in weakly disordered spin chains.
- Theoretical investigation of quantum systems in dimensions greater than one.
Main Results:
- A method for constructing LIOMs in 1D spin chains was successfully developed under specific eigenvalue statistics.
- It was demonstrated that interactions within Griffiths regions may not be negligible compared to energy-level spacing in higher dimensions.
- Ergodicity is predicted to be restored in dimensions d > 1.
Conclusions:
- The construction of LIOMs provides a framework for understanding localization breakdown in disordered quantum systems.
- Higher-dimensional systems with Griffiths regions are expected to exhibit slow equilibration, analogous to the dynamics observed in glasses.
- The findings contribute to the understanding of the breakdown of ergodicity in quantum systems across various physical platforms.
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