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Published on: April 19, 2018
Braid group and topological phase transitions in nonequilibrium stochastic dynamics
1Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA. renjie@lanl.gov
Summary
Topological phases in non-Hermitian Hamiltonians are classified using braid group elements. These distinct topological phases exhibit detectable properties in nonequilibrium stochastic currents.
Area of Science:
- Condensed matter physics
- Quantum mechanics
- Statistical mechanics
Background:
- Non-Hermitian Hamiltonians describe open quantum systems and have unique topological properties.
- Classifying topological phases is crucial for understanding exotic quantum phenomena.
- Braid group theory provides a mathematical framework for classifying topological structures.
Purpose of the Study:
- To classify distinct topological phases of non-Hermitian Hamiltonians using braid group elements.
- To demonstrate a proof of principle by analyzing nonequilibrium stochastic currents.
- To identify detectable properties associated with topologically nontrivial phases.
Main Methods:
- Utilizing elements of the braid group for topological phase classification.
- Investigating the non-Hermitian evolution of stochastic current statistics.
- Analyzing parity and state probabilities for decaying oscillations.
- Examining steady-state current statistics for discontinuities.
Main Results:
- Distinct topological phases of non-Hermitian Hamiltonians can be classified by braid group elements.
- Topologically nontrivial phases exhibit unique, detectable properties.
- Decaying oscillations in parity and state probabilities are observed.
- Discontinuities in steady-state current statistics are identified.
Conclusions:
- The braid group offers a robust framework for classifying topological phases in non-Hermitian systems.
- The identified detectable properties provide experimental signatures for topological phases.
- This work bridges topological physics, non-Hermitian systems, and statistical mechanics.
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