Quantum Many-Body Adiabaticity, Topological Thouless Pump and Driven Impurity in a One-Dimensional Quantum Fluid

TL;DR

This paper reviews the relationship between quantum adiabaticity and orthogonality catastrophe in many-body systems, applying these concepts to topological charge transport and impurity dynamics in one-dimensional quantum fluids.

Contribution

It establishes a rigorous inequality linking adiabaticity and orthogonality catastrophe, and applies it to analyze adiabatic conditions in one-dimensional quantum fluids with impurities.

Findings

Derived conditions for adiabaticity in many-body systems.

Linked adiabaticity to quantized charge transport in Thouless pump.

Analyzed impurity dynamics and Bloch oscillations in quantum fluids.

Abstract

When it comes to applying the adiabatic theorem in practice, the key question to be answered is how slow "slowly enough" is. This question can be an intricate one, especially for many-body systems, where the limits of slow driving and large system size may not commute. Recently we have shown how the quantum adiabaticity in many-body systems is related to the generalized orthogonality catastrophe [Phys. Rev. Lett. 119, 200401 (2017)]. We have proven a rigorous inequality relating these two phenomena and applied it to establish conditions for the quantized transport in the topological Thouless pump. In the present contribution we (i) review these developments and (ii) apply the inequality to establish the conditions for adiabaticity in a one-dimensional system consisting of a quantum fluid and an impurity particle pulled through the fluid by an external force. The latter analysis is vital for the correct quantitative description of the phenomenon of quasi Bloch oscillations in a one-dimensional translation invariant impurity-fluid system.