Fidelity susceptibility and quantum adiabatic condition in thermodynamic limits

TL;DR

This paper investigates the quantum adiabatic theorem in thermodynamic systems, revealing that the required adiabatic process duration depends on the fidelity susceptibility's scaling dimension, which can lead to violations of the theorem.

Contribution

It establishes a quantitative relationship between the adiabatic process duration and the fidelity susceptibility's scaling dimension in many-body systems.

Findings

The adiabatic process duration is independent of microscopic details.

Violation of the quantum adiabatic theorem occurs when the fidelity susceptibility's scaling dimension exceeds the system's dimension.

Provides a new criterion for the validity of the quantum adiabatic theorem in large systems.

Abstract

In this work, we examine the validity of quantum adiabatic theorem in thermodynamic systems. For a $d$-dimensional quantum many-body system, we show that the duration time $\tau_0$ required by its ground-state adiabatic process does not depend on the microscopic details, but the scaling dimension of the fidelity susceptibility $d_a$. Our result, therefore, provides a quantitative time scale of the quantum adiabatic theorem in thermodynamic systems. The quantum adiabatic theorem might be violated in case that the scaling dimension of the fidelity susceptibility is larger than the system's real dimension ($d_a>d$).