Nonequilibrium Probes of Quantum Geometry in Gapless Systems

TL;DR

This paper explores how finite-time, driven conformal systems reveal quantum geometric properties, such as the quantum metric and Berry phase, through measurable responses, providing universal insights into gapless quantum matter.

Contribution

It introduces a universal framework linking measurable responses to quantum geometry in gapless systems driven by conformal transformations, supported by simulations and exact results.

Findings

Perturbation theory predicts absorption rates probing quantum geometry.

Periodic drives reveal nontrivial return amplitudes involving the quantum metric.

Responses are robust and experimentally accessible, connecting theory with measurable quantities.

Abstract

Much of our understanding of gapless quantum matter stems from low-energy descriptions using conformal field theory. This is especially true in 1+1 dimensions, where such theories have an infinite-dimensional parameter space induced by their conformal symmetry. We reveal the underlying quantum geometry by considering finite many-body systems driven by time-dependent conformal transformations. For small deformations, perturbation theory predicts absorption rates and linear responses that probe the quantum geometric tensor. For arbitrarily large but adiabatic deformations, we show that periodic drives give rise to nontrivial return amplitudes involving the quantum metric, beyond the familiar leading order that only features a Berry phase. The former is less sensitive to decoherence than the latter, so it can provide robust experimental signatures of our predictions. Our field-theoretic findings are universal, comprising general relations between measurable quantities and quantum geometry that only depend on the emergent effective description. This is supported both by numerical simulations of gapless lattice models, and by exact results for quantum dynamics under certain Floquet drives, probing the full dynamical parameter space.