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Uhlmann phase as a topological measure for one-dimensional fermion systems
O Viyuela1, A Rivas1, M A Martin-Delgado1
1Departamento de Física Teórica I, Universidad Complutense, 28040 Madrid, Spain.
Physical Review Letters
|April 22, 2014
Summary
We introduce the Uhlmann geometric phase to characterize topological phases in 1D fermion systems, extending properties to finite temperatures. A critical temperature marks a sharp transition between distinct topological phases.
Area of Science:
- Condensed Matter Physics
- Quantum Mechanics
Background:
- Symmetry-protected topological phases are crucial in condensed matter.
- Characterizing these phases at finite temperatures remains challenging.
Purpose of the Study:
- To introduce the Uhlmann geometric phase as a novel tool for characterizing topological phases.
- To extend the concept of topological properties to finite temperature regimes.
Main Methods:
- Utilizing the Uhlmann geometric phase for general mixed quantum states.
- Applying the method to paradigmatic one-dimensional fermion models, including topological insulators and superconductors.
Main Results:
- The Uhlmann geometric phase successfully characterizes symmetry-protected topological phases.
- A critical temperature (Tc) was identified where the Uhlmann phase drops abruptly to zero.
- This critical temperature signifies a phase transition boundary concerning temperature.
Conclusions:
- The Uhlmann geometric phase provides a robust method for analyzing topological phases in 1D fermion systems.
- It effectively bridges the gap between quantum topology and finite-temperature physics.
- The identified critical temperature offers a new perspective on topological phase transitions driven by temperature.
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