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Quantum Monte Carlo simulations in the restricted Hilbert space of Rydberg atom arrays
by Pranay Patil
Submission summary
| Authors (as registered SciPost users): | Pranay Patil |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2309.00482v4 (pdf) |
| Date submitted: | 2024-09-06 02:59 |
| Submitted by: | Patil, Pranay |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Computational |
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.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
I have taken into consideration all the comments made by the referees and revised the manuscript based on their recommendations. Thanks to these changes, the manuscript is now more accessible to relevant readers. New numerical results are presented as additional evidence for the phase diagram discussed in Sec.4 and detailed pseudo-codes are provided in the appendices for readers who would like to write their own code. Additionally, detailed benchmarks for the efficiency of individual updates is included to clarify their capabilities. In conclusion, in my opinion this makes the manuscript suitable for publication in this journal.
Thank you,
Pranay Patil
List of changes
1. For each of Sec. 3.2, 3.3, 3.4, the details of the algorithm have been moved to the new appendices A,B,C (respectively), and discussion of autocorrelation functions is included for each update specifically along with data from simulations to support the claims in the discussions.
2. Pseudo-code for each update is now provided in the appendices. It is expected that following the pseudo-code will allow interested readers to easily develop their own version of the algorithm.
3. Data for entropy, dimer density and string order parameters is now presented in Sec.4 . This allows for a more comprehensive understanding of the phase diagram.
4. Minor typos and grammatical errors have been fixed after a re-reading.
Current status:
Reports on this Submission
Report
For the revised version of the manuscript, the author has essentially taken the suggestions and criticism with regards to the previous version into account. To me the manuscript is now much clearer and accessible. I would still suggest a few minor changes, as specified below prior to acceptance.
Requested changes
1-Currently, Fig. 2 is cited prior to Fig. 1, please relabel the figures.
2-The discussion of Fig. 6(a) is now in the appendix, consider to also move that panel to the appendix
3-Refer to QMC system sizes explicitly as "L=4" in order to avoid confusion.
4-In discussing the results for the Kagome lattice, the author should more carefully separate between the notion of quantum spin liquid vs. classical spin liquid vs. paramagnetic state. Thus far, some statements in the discussion of the new material in Sec. 4 appear confusing.
Recommendation
Ask for minor revision