Variational method for $\mathbb{Z}_K$ wavefunctions in spin-$J$ PXP model

TL;DR

This paper applies the time-dependent variational principle to the spin-$J$ PXP model using $ abla_K$ matrix-product-states, providing exact solutions in certain limits and demonstrating efficient variational dynamics.

Contribution

It introduces a variational approach using $ abla_K$ MPS for the spin-$J$ PXP model, with exact results in specific limits and rapid convergence in the thermodynamic limit.

Findings

Variational dynamics can be expressed as rapidly convergent series.

Exact results obtained for $J=1/2$ and $J ightarrow abla$, simplifying analysis.

The method is relevant for programmable Rydberg atom arrays.

Abstract

We investigate the approach of time-dependent variational principle (TDVP) for the one-dimensional spin-$J$ PXP model with detuning, which is relevant for programmable Rydberg atom arrays. The variational manifold is chosen as the minimally entangled $\mathbb{Z}_K$ matrix-product-states (MPS). We demonstrate that variational dynamics and variational error can be expressed as rapidly convergent series in the thermodynamic limit. In particular, for $J=1/2$ and the limiting case $J\rightarrow \infty$, the TDVP results become exact and significantly simplified.