Weak ergodicity breaking, many-body scars and superdiffusive energy transport in the PXP model
Abstract: Universal nonequilibrium properties of isolated quantum systems are typically probed by studying transport of conserved quantities, such as charge or spin, while transport of energy has received considerably less attention. I will present results of our recent study [arXiv:2210.01146] of infinite-temperature energy transport in the kinetically-constrained PXP model describing Rydberg atom quantum simulators. The numerics in large systems reveal the existence of two distinct transport regimes. At moderate times, the energy-energy correlation function displays periodic oscillations due to families of eigenstates forming different representations of su(2) algebra, hidden within the spectrum. These families of eigenstates generalise the quantum many-body scarred states found in previous works and leave an imprint on the infinite-temperature energy transport. At later times, we observe a broad superdiffusive transport regime that we attribute to the proximity of a nearby integrable point. Intriguingly, strong deformations of the PXP model by the chemical potential do not restore diffusion, but instead lead to a stable superdiffusive exponent close to the Kardar-Parisi-Zhang value.