Superdiffusion and anomalous fluctuations in chiral integrable dynamics

TL;DR

This paper investigates how breaking time-reversal symmetry affects transport in integrable quantum systems, revealing superdiffusive behavior aligned with KPZ universality but with deviations in fluctuation properties, and introduces a quantum circuit model for further insights.

Contribution

It demonstrates that time-reversal symmetry breaking does not prevent superdiffusion in integrable systems and introduces a quantum circuit model to explore these phenomena.

Findings

Spin transport is superdiffusive with z=3/2 matching KPZ class.

Fluctuations deviate from KPZ predictions despite similar dynamical exponents.

Fluctuation symmetry persists in the probability distribution of spin current.

Abstract

Symmetries strongly influence transport properties of quantum many-body systems, and can lead to deviations from the generic case of diffusion. In this work, we study the impact of time-reversal symmetry breaking on the transport and its universal aspects in integrable chiral spin ladders. We observe that the infinite-temperature spin transport is superdiffusive with a dynamical critical exponent z = 3/2 matching the one of the Kardar-Parisi-Zhang (KPZ) universality class, which also lacks the time reversal symmetry. However, we find that fluctuations of the net magnetization transfer deviate from the KPZ predictions. Moreover, the full probability distribution of the associated spin current obeys fluctuation symmetry despite broken time-reversal and space-reflection symmetries. To further investigate the role of conserved quantities, we introduce an integrable quantum circuit that shares the essential symmetries with the chiral ladder, and which exhibits analogous dynamical behaviour in the absence of energy conservation. Our work shows that time-reversal symmetry breaking is compatible with superdiffusion, but insufficient to stabilize the KPZ universality in integrable systems. This suggests that additional fundamental features are missing in order to identify the emergence of such dynamics in quantum matter.