Probing the Topology of Density Matrices

Bardyn CE, Wawer L, Altland A, Fleischhauer M, Diehl S (2018)

Publication Type: Journal article

Publication year: 2018

Journal

Physical Review X American Physical Society

Book Volume: 8

Article Number: 011035

Journal Issue: 1

DOI: 10.1103/PhysRevX.8.011035

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.

Involved external institutions

University of Geneva / Université de Genève (UNIGE) CH Switzerland (CH) Technische Universität Kaiserslautern DE Germany (DE) University of California US United States (USA) (US) Universität zu Köln DE Germany (DE)

How to cite

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://dx.doi.org/10.1103/PhysRevX.8.011035

MLA:

Bardyn, Charles-Edouard, et al. "Probing the Topology of Density Matrices." Physical Review X 8.1 (2018).

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