Tomonaga-Luttinger Liquid Behavior in a Rydberg-encoded Spin Chain

TL;DR

This study uses a Rydberg quantum simulator to observe Tomonaga-Luttinger liquid behavior in a spin chain, revealing power-law correlations, impurity effects, and correlation propagation influenced by long-range interactions.

Contribution

First experimental observation of TLL behavior in a Rydberg-encoded spin chain, including correlation decay, impurity effects, and dynamics under long-range dipolar interactions.

Findings

Power-law decay of spin-spin correlations observed

Tunable Friedel oscillations in the presence of impurities

Correlation propagation exhibits a light-cone structure

Abstract

Quantum fluctuations can disrupt long-range order in one-dimensional systems, and replace it with the universal paradigm of the Tomonaga-Luttinger liquid (TLL), a critical phase of matter characterized by power-law decaying correlations and linearly dispersing excitations. Using a Rydberg quantum simulator, we study how TLL physics manifests in the low-energy properties of a spin chain, interacting under either the ferromagnetic or the antiferromagnetic dipolar XY Hamiltonian. Following quasi-adiabatic preparation, we directly observe the power-law decay of spin-spin correlations in real-space, allowing us to extract the Luttinger parameter. In the presence of an impurity, the chain exhibits tunable Friedel oscillations of the local magnetization. Moreover, by utilizing a quantum quench, we directly probe the propagation of correlations, which exhibit a light-cone structure related to the linear sound mode of the underlying TLL. Our measurements demonstrate the influence of the long-range dipolar interactions, renormalizing the parameters of TLL with respect to the case of nearest-neighbor interactions. Finally, comparison to numerical simulations exposes the high sensitivity of TLLs to doping and finite-size effects.