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Rate function modeling of quantum many-body adiabaticity

Vibhu Mishra*, Salvatore R. Manmana†, and Stefan Kehrein‡

  • *Contact author: vibhu.mishra@uni-goettingen.de
  • †Contact author: salvatore.manmana@theorie.physik.uni-goetting en.de
  • ‡Contact author: stefan.kehrein@theorie.physik.uni-goettingen.de
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Phys. Rev. B 112, 014306 – Published 7 July, 2025

DOI: https://doi.org/10.1103/xtkk-5xhw

Abstract

The quantum adiabatic theorem is a fundamental result in quantum mechanics, with a multitude of applications, both theoretical and practical. Here, we investigate the dynamics of adiabatic processes for quantum many-body systems by analyzing the properties of observable-free intensive quantities. In particular, we study the adiabatic rate function f(T,Δλ) in dependence of the ramp time T, which gives us a complete characterization of the many-body adiabatic fidelity as a function of T and the strength of the parameter displacement Δλ. f(T,Δλ) quantifies the deviation from adiabaticity for a given process and therefore allows us to control and define the notion of adiabaticity in many-body systems. First we study f(T,Δλ) for the one-dimensional transverse field Ising model and the Luttinger liquid, both of which are quadratic systems and therefore allow us to look at the thermodynamic limit. For ramps across gapped phases, we relate f(T,Δλ) to the transition probability of the system and for ramps across a gapless point, or gapless phase we relate it to the excitation density of the relevant quasiparticles. Then we investigate the XXZ model, which allows us to see the qualitative features that survive when interactions are turned on. Several key results in the literature regarding the interplay of the thermodynamic and the adiabatic limit are obtained as inferences from the properties of f(T,Δλ) in the large-T limit.

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Outline

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Phys. Rev. B 112, 014306– Published 7 July, 2025
  • Received 21 March 2024
  • Revised 1 June 2025
  • Accepted 13 June 2025
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