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Anatomy of localisation protected quantum order on Hilbert space
1International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India.
Summary
Many-body localized (MBL) phases exhibit quantum order. Analyzing eigenstate correlations reveals these correlations characterize MBL order and entanglement structures, aiding transition studies.
Area of Science:
- Quantum physics
- Condensed matter theory
- Statistical mechanics
Background:
- Many-body localized (MBL) phases in disordered quantum systems exhibit unique properties.
- These phases allow for exotic, localization-protected quantum order at high energy densities.
- Understanding the structure of eigenstates is crucial for characterizing these phases.
Purpose of the Study:
- To analyze how quantum order manifests in the Hilbert-space structure of eigenstates.
- To establish a connection between eigenstate correlations and the presence of MBL order.
- To explore the use of higher-point correlations for characterizing entanglement in different quantum phases.
Main Methods:
- Quantification of non-local Hilbert-spatial correlations of eigenstate amplitudes.
- Analysis of the spread of eigenstates on the Hilbert-space graph.
- Investigation of higher-point eigenstate correlations.
Main Results:
- The spread of eigenstates on the Hilbert-space graph directly correlates with order parameters.
- These Hilbert-spatial correlations serve as indicators of localization-protected order.
- Higher-point correlations distinguish entanglement structures across MBL and ergodic phases.
Conclusions:
- Eigenstate correlations in Hilbert space provide a robust method for characterizing MBL order.
- The developed correlation measures can differentiate between ordered MBL, disordered MBL, and ergodic phases.
- This work lays the foundation for studying phase transitions using correlation length scales on the Hilbert-space graph.
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