Degenerated Liouvillians and steady-state reduced density matrices

Area of Science:

• Quantum Physics
• Quantum Information Theory
• Condensed Matter Physics

Background:

• Open quantum systems can exhibit symmetries, leading to degenerated Liouvillians.
• Degenerated Liouvillians imply multiple steady states, complicating the identification of true asymptotic states.
• Linear combinations of true steady states can also be valid asymptotes, posing challenges for analysis.

Purpose of the Study:

• To develop and present methods for obtaining true steady states of degenerated Liouvillians in open quantum systems.
• To provide numerical tools for analyzing complex quantum many-body open systems.
• To investigate the dynamical restoration of symmetries and eigenspacing statistics in nonequilibrium steady states.

Main Methods:

• Symmetry decomposition: Utilizing known symmetry operators to find invariant subspaces and steady states.
• Gram-Schmidt orthonormalization: A method applied to density matrices to obtain all steady states.
• Large deviations theory: Applied to identify maximum and minimum current carrying states.

Main Results:

• Demonstrated how known symmetry operators can identify steady states by revealing invariant subspaces.
• Gram-Schmidt orthonormalization successfully retrieves all steady states.
• Large deviations approach isolates non-degenerated maximum and minimum current states.
• Analysis of an open para-benzene ring showcases dynamical symmetry restoration and provides insights into eigenspacing statistics.

Conclusions:

• The presented methods offer robust approaches to determine true steady states in open quantum systems with degenerated Liouvillians.
• These techniques are valuable numerical tools for studying complex quantum many-body systems.
• The study highlights the importance of symmetry in quantum dynamics and provides a framework for analyzing nonequilibrium steady states.