The fine structure of heating in a quasiperiodically driven critical quantum system

TL;DR

This paper investigates how a critical quantum system driven quasiperiodically exhibits complex heating behavior, revealing fractal structures in the Lyapunov exponent that influence energy absorption and localization.

Contribution

It introduces a detailed analysis of heating dynamics in a quasiperiodically driven critical quantum system, highlighting fractal Lyapunov structures and their effects on energy localization and delocalization.

Findings

Lyapunov exponent has a fractal structure with Cantor lines where it is zero.

System heats rapidly to infinite energy away from Cantor lines.

Near Cantor lines, heating slows down and quasiparticles delocalize.

Abstract

We study the heating dynamics of a generic one dimensional critical system when driven quasiperiodically. Specifically, we consider a Fibonacci drive sequence comprising the Hamiltonian of uniform conformal field theory (CFT) describing such critical systems and its sine-square deformed counterpart. The asymptotic dynamics is dictated by the Lyapunov exponent which has a fractal structure embedding Cantor lines where the exponent is exactly zero. Away from these Cantor lines, the system typically heats up fast to infinite energy in a non-ergodic manner where the quasiparticle excitations congregate at a small number of select spatial locations resulting in a build up of energy at these points. Periodic dynamics with no heating for physically relevant timescales is seen in the high frequency regime. As we traverse the fractal region and approach the Cantor lines, the heating slows enormously and the quasiparticles completely delocalise at stroboscopic times. Our setup allows us to tune between fast and ultra-slow heating regimes in integrable systems.