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Many-body localization in periodically driven systems
Pedro Ponte1,2, Z Papić1,3,4, François Huveneers5
1Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada.
Physical Review Letters
|April 25, 2015
Summary
Researchers identified two distinct phases in disordered quantum systems: a many-body localized (MBL) phase with area-law entanglement and a delocalized phase with volume-law entanglement. The MBL phase shows logarithmic entanglement growth, distinguishing it from the delocalized phase.
Area of Science:
- Quantum physics
- Condensed matter theory
- Statistical mechanics
Background:
- Disordered quantum systems with time-dependent Hamiltonians are crucial for understanding complex phenomena.
- Floquet eigenstates and entanglement entropy are key indicators of system phases.
- The eigenstate thermalization hypothesis (ETH) describes thermalization in quantum systems.
Purpose of the Study:
- To identify and characterize distinct phases in one-dimensional disordered many-body systems with periodic time-dependent Hamiltonians.
- To investigate the properties of Floquet eigenstates, including entanglement entropy and adherence to the ETH.
- To propose an effective model for the many-body localized (MBL) phase.
Main Methods:
- Analysis of Floquet eigenstates in disordered quantum systems.
- Calculation of entanglement entropy (area-law vs. volume-law).
- Numerical simulations using exact diagonalization and time-evolving block decimation (TEBD).
Main Results:
- Identification of two distinct phases: a many-body localized (MBL) phase and a delocalized phase.
- The MBL phase exhibits area-law entanglement and violates the ETH, while the delocalized phase shows volume-law entanglement and obeys the ETH.
- The MBL phase demonstrates logarithmic in time growth of entanglement entropy from a product state, unlike the delocalized phase.
Conclusions:
- A direct phase transition exists between the MBL and delocalized phases.
- An effective model based on emergent local integrals of motion explains the MBL phase's properties.
- The study provides a framework for understanding localization and thermalization in driven quantum systems.
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