Quantum Monte Carlo simulations in the restricted Hilbert space of Rydberg atom arrays

TL;DR

This paper introduces a quantum Monte Carlo method tailored for Rydberg atom arrays, enabling efficient simulation of their quantum phases and phase transitions within the constrained Hilbert space.

Contribution

The authors develop a novel Monte Carlo sampling technique in the restricted Hilbert space of Rydberg blockade, with new cluster algorithms based on a hard rod gas mapping.

Findings

Efficient phase diagram generation at low temperatures

Identification of a $Z_2$ spin liquid phase

Enhanced simulation efficiency in constrained Hilbert spaces

Abstract

Rydberg atom arrays have emerged as a powerful platform to simulate a number of exotic quantum ground states and phase transitions. To verify these capabilities numerically, we develop a versatile quantum Monte Carlo sampling technique which operates in the reduced Hilbert space generated by enforcing the constraint of a Rydberg blockade. We use the framework of stochastic series expansion and show that in the restricted space, the configuration space of operator strings can be understood as a hard rod gas in $d+1$ dimensions. We use this mapping to develop cluster algorithms which can be visualized as various non-local movements of rods. We study the efficiency of each of our updates individually and collectively. To elucidate the utility of the algorithm, we show that it can efficiently generate the phase diagram of a Rydberg atom array, to temperatures much smaller than all energy scales involved, on a Kagom\'e link lattice. This is of broad interest as the presence of a $Z_2$ spin liquid has been hypothesized recently.