Probing sine-Gordon dynamics in coupled spin chains

The recent progress in the control and manipulation of synthetic quantum matter has sparked a large interest in the realization of effective theories that form a low-energy description of a wide class of systems. A very prominent example of such an effective theory is the quantum sine-Gordon field theory, which naturally describes many one-dimensional quantum systems at low temperatures.

With the uprising interest in non-equilibrium dynamics of many-body quantum systems, testing the validity of these realizations far from the ground state is of utmost importance.

We investigate the emergence of the sine-Gordon theory as the low-energy description of a one-dimensional spin ladder. We use matrix-product state techniques to numerically characterize its low-energy sector and probe the validity of the effective dynamics deeply in the quantum regime.

Then, we probe the integrability of the sine-Gordon dynamics by realizing wave-packet scattering events. We introduce experimentally relevant probes of the sine-Gordon field theory in the described setup. Our results can be readily verified with currently available ultracold atom quantum simulators.