[Paper Review] Superdiffusive Energy Transport in Kinetically Constrained Models

Marko Ljubotina, Jean-Yves Desaules+2 more|arXiv (Cornell University)|Oct 3, 2022

Quantum, superfluid, helium dynamics4 citations

TL;DR

This study reveals superdiffusive energy transport in the kinetically constrained PXP model at infinite temperature, driven by multiple approximate su(2) algebra representations hidden in its spectrum. Using exact diagonalization and time-evolving block decimation, the authors identify oscillatory dynamics at short times due to these representations and a long-lived superdiffusive regime with dynamical exponent $ z \approx 3/2 $, stabilized by a strong chemical potential deformation, suggesting constrained models as hosts of novel non-equilibrium transport phases.

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. Here, we study infinite-temperature energy transport in the kinetically-constrained PXP model describing Rydberg atom quantum simulators. Our state-of-the-art numerical simulations, including exact diagonalization and time-evolving block decimation methods, 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 su(2) representations hidden within the spectrum. These families of eigenstates generalize 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 $z\approx3/2$. Our results suggest constrained models to be potential hosts of novel transport regimes and call for developing an analytic understanding of their energy transport.

Motivation & Objective

• To investigate infinite-temperature energy transport in the kinetically constrained PXP model, a paradigmatic system for Rydberg quantum simulators.
• To identify the origin of oscillatory dynamics in energy transport at short times, linking them to hidden approximate su(2) algebra representations in the spectrum.
• To explore how integrability-breaking deformations affect energy transport, particularly whether superdiffusion persists beyond the integrable limit.
• To determine whether strong chemical potential deformations can stabilize a robust superdiffusive regime with $ z \approx 3/2 $.
• To assess the role of kinetic constraints and long-range blockade in enabling or suppressing superdiffusive transport.

Proposed method

• Numerical simulations using exact diagonalization and time-evolving block decimation (TEBD) to compute the energy-energy correlation function at infinite temperature.
• Analysis of the energy-density spreading dynamics to extract the instantaneous dynamical exponent $ z(t) $, identifying superdiffusive scaling.
• Identification of multiple approximate su(2) representations via the projection of spin operators $ S^x, S^y, S^z $ onto the PXP Hilbert space, yielding effective operators $ J^y, J^z $.
• Study of time evolution of projected operators $ J^y(t)J^y(0) $ and $ J^z(t)J^z(0) $, showing cosine-like oscillations consistent with su(2) algebraic structure.
• Systematic deformation of the PXP Hamiltonian with chemical potential and other terms (e.g., PNP, PPP, PXXP, PPXPP) to probe the stability of superdiffusion.
• Use of bond dimensions up to $ \chi = 256 $ to ensure convergence of TEBD simulations across various deformation strengths.

Experimental results

Research questions

• RQ1 What causes the oscillatory behavior in energy transport at short times in the PXP model?
• RQ2 How do multiple approximate su(2) representations in the spectrum influence infinite-temperature energy transport?
• RQ3 Does superdiffusive energy transport persist when the PXP model is deformed away from integrability?
• RQ4 Can a strong chemical potential deformation stabilize a superdiffusive regime with $ z \approx 3/2 $?
• RQ5 How does increasing the range of kinetic constraints (e.g., PPXPP model) affect the transport regime?

Key findings

• The short-time energy transport in the PXP model exhibits periodic oscillations due to the presence of multiple approximate su(2) representations in the spectrum, generalizing known quantum many-body scar states.
• The oscillations are confirmed by time evolution of projected operators $ J^y $ and $ J^z $, which show cosine-like decay consistent with su(2) algebraic dynamics.
• At later times, the system enters a long-lived superdiffusive regime with a dynamical exponent $ z \approx 3/2 $, indicating non-diffusive, non-ballistic transport.
• Deformation of the PXP model with a strong chemical potential stabilizes the superdiffusive regime, with $ z \approx 3/2 $ observed across accessible time scales, despite breaking integrability.
• Other deformations such as PNPNP, PPP, and PXXP also show superdiffusion at weak coupling, but transition to diffusive behavior as deformation strength increases.
• Increasing the blockade range to PPXPP leads to diffusive transport, indicating that long-range constraints suppress superdiffusion, highlighting the sensitivity of transport to constraint structure.