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Quantum Monte Carlo simulations in the restricted Hilbert space of Rydberg atom arrays
by Pranay Patil
|Authors (as registered SciPost users):||Pranay Patil|
|Preprint Link:||https://arxiv.org/abs/2309.00482v2 (pdf)|
|Date submitted:||2023-09-14 11:06|
|Submitted by:||Patil, Pranay|
|Submitted to:||SciPost Physics|
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.
Submission & Refereeing History
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Reports on this Submission
1-An unbiased numerical method is presented for constrained quantum many-body Rydberg atom systems that are of current interest in different fields.
2-Several complementary update schemes are presented.
3-Benchmarking and efficiency tests has been performed.
4-Some physical results on the kagome link lattice model are presented.
1-In the application to the kagome link lattice model, only a single observable (the specific heat) is discussed.
2-For some update schemes, more technical details could be provided (see below).
3-Minor issues in the presentation (see below).
This manuscript presents a quantum Monte Carlo approach to study Rydberg atom arrays by treating them directly within the reduced Hilbert space enforced by the Rydberg blockade. Using this restriction explicitly in the construction of the stochastic series expansion algorithm, the author introduces various local and non-local update schemes. He also provides benchmarking and an efficiency analysis. As an explicit application, the case of the kagome link lattice is discussed, based on specific heat data down to the relevant low temperatures. No indication for a previously proposed quantum spin liquid phase is obtained from these simulations.
The algorithm introduced here is well explained on a non-technical level and the relevant update schemes are motivated and a performance analysis is provided. For most of the updates, a more technical treatment, or a code base, would certainly be useful for readers who actually want to implement these algorithms themselves. In the application to the kagome link lattice model, only a single observable is considered, the specific heat. This analysis could be extended, e.g., by examining also correlation functions.
Overall, this manuscript certainly is valuable in introducing an unbiased QMC algorithm to provide unbiased numerical data on a very timely topic in quantum many-body systems. Indeed, Rydberg atom arrays are realized in recent experiments, and are met with a broad interest in different communities, including frustrated magnetism and quantum computation. I recommend to publish this paper, after a few changes, requested below, have been considered by the author.
1-In Sec. 4 it would be useful to expand beyond the discussion of the specific heat, e.g., by considering relevant correlation functions.
2-I find the sentence "In the time direction, these operators are neighbors..." in Sec. 3.2 confusing. If these operators are not meant to be neighbors to each other, please rephrase this sentence, e.g., by replacing the "are" by "have" or alike. Otherwise, please explain better how these operators are specified.
3-The whole text should be given a careful reading , as it still contains several typos, e.g., "An Extension", "the the", "rydberg" in various references.
4-For the updates in Sec. 3.2-3.4, the author should provide more technical details regarding the actual implementation of the algorithms, e.g., by providing a code base or appropriate pseudo-code.