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Finite-Temperature Topological Invariant for Interacting Systems.

Razmik Unanyan1, Maximilian Kiefer-Emmanouilidis1,2, Michael Fleischhauer1,3

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We generalized the ensemble geometric phase to finite temperatures in 1D interacting systems. This topological invariant remains stable below a critical temperature, even for fractional fillings.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Statistical Mechanics

Background:

  • The ensemble geometric phase classifies topological properties of quantum states.
  • Generalizing this to finite temperatures in interacting systems is crucial for understanding real-world materials.

Purpose of the Study:

  • To extend the ensemble geometric phase to finite-temperature states in one-dimensional (1D) interacting systems.
  • To investigate its behavior in gapped, fractionally filled, and degenerate ground states.

Main Methods:

  • Generalization of the ensemble geometric phase formalism.
  • Numerical simulations using the 1D extended superlattice Bose-Hubbard model.
  • Analysis of topological invariants at zero and finite temperatures.

Main Results:

  • The generalized ensemble geometric phase at finite temperatures matches the ground state value below a critical temperature (T_c).
  • A topological charge pump with fractional winding (ν=1/2) was observed in simulations.
  • Particle transport loses quantization near the many-body gap, but the topological winding persists.

Conclusions:

  • The ensemble geometric phase provides a robust topological invariant for finite-temperature states in 1D interacting systems.
  • This framework is applicable even when particle transport is not quantized.
  • The study offers insights into topological phase transitions in realistic condensed matter systems.