Constant of Motion Identifying Excited-State Quantum Phases

Area of Science:

• Quantum mechanics
• Quantum many-body physics
• Statistical mechanics

Background:

• Quantum phase transitions (QPTs) are fundamental in condensed matter physics.
• Excited-state quantum phase transitions (ESQPTs) represent a distinct class of QPTs occurring in excited states.
• Understanding the nature and classification of ESQPTs is crucial for characterizing complex quantum systems.

Purpose of the Study:

• To propose and identify a general mechanism for classifying excited-state quantum phases.
• To introduce an operator that distinguishes between different excited-state quantum phases.
• To investigate the role of this operator in systems exhibiting ESQPTs, including its relation to symmetries.

Main Methods:

• Theoretical proposal of a general classification scheme for excited-state quantum phases.
• Introduction of a conserved operator, C, to identify distinct phases.
• Numerical analysis of the Rabi and Dicke models to provide evidence for the theoretical framework.

Main Results:

• ESQPTs lead to two distinct excited-state quantum phases characterized by the conserved operator C.
• One phase exhibits dependence of observables on C, while the other depends only on energy.
• The operator C acts as a discrete symmetry in one phase, explaining spectral degeneracies.
• Numerical evidence from Rabi and Dicke models supports the exactness of these findings in the thermodynamic limit.

Conclusions:

• The proposed operator C provides a robust method for identifying and distinguishing excited-state quantum phases.
• The interplay between ESQPTs, conserved quantities, and symmetries is elucidated.
• The findings have implications for understanding the behavior of quantum systems across different energy regimes.