Unanyan Razmik, Kiefer-Emmanouilidis Maximilian, Fleischhauer Michael
Department of Physics and Research Center OPTIMAS, University of Kaiserslautern, 67663 Kaiserslautern, Germany.
Department of Physics, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2.
Phys Rev Lett. 2020 Nov 20;125(21):215701. doi: 10.1103/PhysRevLett.125.215701.
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 T_{c} 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.
我们将最近引入用于对密度矩阵拓扑进行分类的系综几何相位推广到一维（1D）相互作用系统的有限温度态。这包括能隙基态具有分数填充且简并的情况。在零温度下，相应的拓扑不变量与牛、 Thouless 和吴的著名不变量一致。我们表明，在有限温度下其值与低于某个高于多体能隙的临界温度(T_{c})的基态值相同。我们用四分之一填充时的一维扩展超晶格玻色 - 哈伯德模型的数值模拟来说明我们的结果。在这里，基态参数的循环变化导致具有分数缠绕数(\nu = 1/2)的拓扑电荷泵。当温度变得与多体能隙相当时，粒子输运不再是量子化的，但广义系综几何相位的缠绕数仍然是量子化的。
