Quantum Monte Carlo simulations in the restricted Hilbert space of Rydberg atom arrays, by Pranay Patil

SciPost Physics Home Authoring Refereeing Submit a manuscript About Quantum Monte Carlo simulations in the restricted Hilbert space of Rydberg atom arrays Pranay Patil SciPost Phys. 20, 022 (2026) · published 27 January 2026 doi: 10.21468/SciPostPhys.20.1.022 pdf BiBTeX RIS Submissions/Reports 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 kagomé link lattice. This is of broad interest as the presence of a $Z_2$ spin liquid has been hypothesized recently. × TY - JOURPB - SciPost FoundationDO - 10.21468/SciPostPhys.20.1.022TI - Quantum Monte Carlo simulations in the restricted Hilbert space of Rydberg atom arraysPY - 2026/01/27UR - https://scipost.org/SciPostPhys.20.1.022JF - SciPost PhysicsJA - SciPost Phys.VL - 20IS - 1SP - 022A1 - Patil, PranayAB - 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 kagomé link lattice. This is of broad interest as the presence of a $Z_2$ spin liquid has been hypothesized recently.ER - × @Article{10.21468/SciPostPhys.20.1.022, title={{Quantum Monte Carlo simulations in the restricted Hilbert space of Rydberg atom arrays}}, author={Pranay Patil}, journal={SciPost Phys.}, volume={20}, pages={022}, year={2026}, publisher={SciPost}, doi={10.21468/SciPostPhys.20.1.022}, url={https://scipost.org/10.21468/SciPostPhys.20.1.022},} Supplementary Information External links to supplemental resources; opens in a new tab. Data repository Author / Affiliation: mappings to Contributors and Organizations See all Organizations. 1 Pranay Patil 1 Max-Planck-Institut für Physik komplexer Systeme / Max Planck Institute for the Physics of Complex Systems Funder for the research work leading to this publication Max-Planck-Institut für Physik Komplexer Systeme