Probing the Topology of Density Matrices

19Citations
Citations of this article
85Readers
Mendeley users who have this article in their library.

Abstract

The mixedness of a quantum state is usually seen as an adversary to topological quantization of observables. For example, exact quantization of the charge transported in a so-called Thouless adiabatic pump is lifted at any finite temperature in symmetry-protected topological insulators. Here, we show that certain directly observable many-body correlators preserve the integrity of topological invariants for mixed Gaussian quantum states in one dimension. Our approach relies on the expectation value of the many-body momentum-translation operator and leads to a physical observable - the "ensemble geometric phase" (EGP) - which represents a bona fide geometric phase for mixed quantum states, in the thermodynamic limit. In cyclic protocols, the EGP provides a topologically quantized observable that detects encircled spectral singularities ("purity-gap" closing points) of density matrices. While we identify the many-body nature of the EGP as a key ingredient, we propose a conceptually simple, interferometric setup to directly measure the latter in experiments with mesoscopic ensembles of ultracold atoms.

Cite

CITATION STYLE

APA

Bardyn, C. E., Wawer, L., Altland, A., Fleischhauer, M., & Diehl, S. (2018). Probing the Topology of Density Matrices. Physical Review X, 8(1). https://doi.org/10.1103/PhysRevX.8.011035

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free