Many-Body Delocalization as Symmetry Breaking.

Area of Science:

• Quantum physics
• Condensed matter physics
• Statistical mechanics

Background:

• Many-body localization (MBL) describes a phase of matter where quantum systems fail to thermalize.
• Ergodic phases, in contrast, exhibit thermalization and are characterized by delocalized wavefunctions.
• Understanding the transitions between these phases is crucial for comprehending quantum dynamics.

Purpose of the Study:

• To present a theoretical framework for the transition between many-body localized (MBL) and ergodic phases.
• To investigate the role of symmetry breaking in this transition.
• To analyze the spectral properties of random Floquet spin chains.

Main Methods:

• The study employs a transfer matrix formalism acting in the space direction to analyze the spectral form factor (SFF).
• The SFF is calculated as a function of time for random Floquet spin chains.
• Leading eigenvalues of the transfer matrix are used to characterize the phases.

Main Results:

• A unique leading eigenvalue of the transfer matrix characterizes the MBL phase (symmetry-unbroken).
• Asymptotically degenerate leading eigenvalues characterize the ergodic phase and late-time dynamics (symmetry-breaking).
• A local order parameter for the transition is identified, with long-ranged correlations only in the ergodic phase.

Conclusions:

• The transition between MBL and ergodic phases in random Floquet spin chains is a symmetry-breaking phenomenon.
• The spectral form factor and its leading eigenvalues serve as indicators of the underlying symmetry.
• The developed framework provides insights into quantum thermalization and localization transitions.