Non-Adiabatic Effect in Topological and Interacting Charge Pumping

TL;DR

This paper investigates how non-adiabatic effects influence topological charge pumping, linking deviations from quantization to entanglement, and introduces a solvable model to analyze these effects with interactions and finite temperature.

Contribution

It proposes a theoretical relation between pumping efficiency and entanglement, and introduces a solvable Rice--Mele--Hubbard model for numerical analysis of non-adiabatic effects.

Findings

Pumping efficiency bounds entanglement generation.

Numerical results support the conjecture $ ext{P}< ext{R}$ with interactions and temperature.

Two regimes identified where ramping velocity affects pumping efficiency.

Abstract

Topological charge pumping occurs in the adiabatic limit, and the non-adiabatic effect due to finite ramping velocity reduces the pumping efficiency and leads to deviation from quantized charge pumping. In this work, we discuss the relation between this deviation from quantized charge pumping and the entanglement generation after a pumping circle. In the simplest setting, we show that purity $\mathcal{P}$ of the half system reduced density matrix equals to $\mathcal{R}$ defined as $(1-\kappa)^2+\kappa^2$, where $\kappa$ denotes the pumping efficiency. In generic situations, we argue $\mathcal{P}<\mathcal{R}$ and the pumping efficiency can provide an upper bound for purity and, therefore, a lower bound for generated entanglement. To support this conjecture, we propose a solvable pumping scheme in the Rice--Mele--Hubbard model, which can be represented as brick-wall type quantum circuit model. With this pumping scheme, numerical calculation of charge pumping only needs to include at most six sites, and therefore, the interaction and the finite temperature effects can be both included reliably in the exact diagonalization calculation. The numerical results using the solvable pumping circle identify two regimes where the pumping efficiency is sensitive to ramping velocity and support the conjecture $\mathcal{P}<\mathcal{R}$ when both interaction and finite temperature effects are present.