Quantum sine-Gordon dynamics in coupled spin chains

TL;DR

This paper demonstrates the emergence of sine-Gordon dynamics in a quantum spin ladder system, providing quantitative validation of the field theory through numerical simulations and spectral analysis.

Contribution

It offers the first quantitative boundary for the sine-Gordon model's validity in a quantum spin ladder, bridging microscopic dynamics and effective field theory.

Findings

Quantitative boundaries for sine-Gordon validity in quantum regimes

Observation of integrable dynamics signatures in scattering events

Numerical characterization aligning with exact field theory predictions

Abstract

The sine-Gordon field theory emerges as the low-energy description in a wealth of quantum many-body systems. Recent efforts have been directed towards realizing quantum simulators of the model, by interfering two weakly coupled one-dimensional cold atomic gases. The weak interactions within the atomic clouds provide a sine-Gordon realization in the semiclassical regime. Furthermore, the complex microscopic dynamics prevents a quantitative understanding of the effective sine-Gordon validity realm. In this work, we focus on a spin ladder realization and observe the emergent sine-Gordon dynamics deep in the quantum regime. We use matrix-product state techniques to numerically characterize the low-energy sector of the system and compare it with the exact field theory predictions. From this comparison, we obtain quantitative boundaries for the validity of the sine-Gordon description. We provide encompassing evidence for the emergent field theory by probing its rich spectrum and by observing the signatures of integrable dynamics in scattering events.