Vanishing and Nonvanishing Persistent Currents of Various Conserved Quantities

Area of Science:

• Condensed Matter Physics
• Quantum Many-Body Systems
• Statistical Mechanics

Background:

• Conserved quantities in physical systems are associated with current operators satisfying continuity equations.
• Persistent currents at equilibrium characterize spontaneous flows in quantum many-body systems.
• Understanding the system-size dependence of these currents is crucial for characterizing equilibrium properties.

Purpose of the Study:

• To investigate the scaling of persistent currents with system size in finite one-dimensional quantum many-body systems.
• To differentiate the behavior of persistent currents arising from Noether charges versus accidentally conserved quantities.
• To analyze the role of symmetries, such as time-reversal symmetry, in the persistence of currents.

Main Methods:

• Analysis of current operators derived from conserved quantities (Noether charges and Hamiltonian).
• Bounding persistent currents using correlation functions of operators separated by system-size-dependent distances.
• Investigating the S=1/2 XXZ spin chain as a specific model to derive analytic expressions for persistent currents.

Main Results:

• Persistent currents associated with Noether charges decay algebraically with increasing system size.
• Accidentally conserved quantities can lead to non-zero persistent currents even in the thermodynamic limit.
• An analytic expression for the persistent current of energy current in the S=1/2 XXZ spin chain was obtained.

Conclusions:

• The nature of conserved quantities dictates the system-size dependence of persistent currents.
• Accidental conservation laws offer a mechanism for sustained equilibrium flows, even with time-reversal symmetry.
• The study provides insights into the fundamental properties of quantum many-body systems and their equilibrium dynamics.