Razmik Unanyan, Maximilian Kiefer-Emmanouilidis, and Michael Fleischhauer:
Phys. Rev. Lett., 125, 215701 (2020)
🔓 arXiv:1906.11553 (2019)
We generalize the ensemble geometric phase, recently introduced to classify the topology of density matrices, to finite-temperature states of interacting systems in one spatial dimension (1D). This includes cases where the gapped ground state has a fractional filling and is degenerate. At zero temperature the corresponding topological invariant agrees with the well-known invariant of Niu, Thouless, and Wu. We show that its value at finite temperatures is identical to that of the ground state below some critical temperature Tc larger than the many-body gap. We illustrate our result with numerical simulations of the 1D extended superlattice Bose-Hubbard model at quarter filling. Here, a cyclic change of parameters in the ground state leads to a topological charge pump with fractional winding ν=1/2. The particle transport is no longer quantized when the temperature becomes comparable to the many-body gap, yet the winding of the generalized ensemble geometric phase is.