Driven Spin-Boson Luttinger Liquids

TL;DR

This paper presents a lattice model of interacting spins and bosons that exhibits Luttinger-liquid behavior, enabling experimental tests of bosonization theory and exploring the potential of quantum simulations to outperform classical methods.

Contribution

It introduces a new spin-boson lattice model that demonstrates Luttinger-liquid physics and provides a variational bosonization approach validated by numerical methods.

Findings

Correlation functions show power-law decay dependent on bosonic driving.

Small driving regimes are efficiently simulated by MPS methods.

Large-driving regimes challenge classical numerics, highlighting quantum simulation advantages.

Abstract

We introduce a lattice model of interacting spins and bosons that leads to Luttinger-liquid physics, and allows for quantitative tests of the theory of bosonization by means of trapped-ion or superconducting-circuit experiments. By using a variational bosonization ansatz, we calculate the power-law decay of spin and boson correlation functions, and study their dependence on a single tunable parameter, namely a bosonic driving. For small drivings, Matrix-Product-States (MPS) numerical methods are shown to be efficient and validate our ansatz. Conversely, even static MPS become inefficient for large-driving regimes, such that the experiment can potentially outperform classical numerics, achieving one of the goals of quantum simulations.