# Ground-state phase diagram of quantum link electrodynamics in $(2+1)$-d

### Submission summary

 As Contributors: Debasish Banerjee · Tomohiro Hashizume Arxiv Link: https://arxiv.org/abs/2112.00756v2 (pdf) Data repository: https://doi.org/10.15129/cd4b3d5d-a8c2-4549-a1a5-0fef178ed097 Date submitted: 2022-05-20 09:52 Submitted by: Hashizume, Tomohiro Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Theory Condensed Matter Physics - Computational High-Energy Physics - Experiment Quantum Physics Approaches: Theoretical, Computational

### Abstract

The exploration of phase diagrams of strongly interacting gauge theories coupled to matter in lower dimensions promises the identification of exotic phases and possible new universality classes, and it facilitates a better understanding of salient phenomena in Nature, such as confinement or high-temperature superconductivity. The emerging new techniques of quantum synthetic matter experiments as well as efficient classical computational methods with matrix product states have been extremely successful in one spatial dimension, and are now motivating such studies in two spatial dimensions. In this work, we consider a $\mathrm{U}(1)$ quantum link lattice gauge theory where the gauge fields, represented by spin-$\frac{1}{2}$ operators are coupled to a single flavor of staggered fermions. Using matrix product states on infinite cylinders with increasing diameter, we conjecture its phase diagram in $(2+1)$-d. This model allows us to smoothly tune between the $\mathrm{U}(1)$ quantum link and the quantum dimer models by adjusting the strength of the fermion mass term, enabling us to connect to the well-studied phases of those models. Our study reveals a rich phase diagram with exotic phases and interesting phase transitions to a potential liquid-like phase. It thus furthers the collection of gauge theory models that may guide future quantum-simulation experiments.

###### Current status:
Editor-in-charge assigned

Dear editors,
We would like to thank you for reconsidering our manuscript "Ground-state phase diagram of quantum link electrodynamics in $(2+1)$-d." We would also like to use this opportunity to thank reviewers for the helpful comments for further improving our manuscript.

Revisions are made to the figures and the text to address the reviewer comments. We believe that the revision has led to an improved clarity of the manuscript.

We very much hope that the revised manuscript is accepted for publication in SciPost.

Best regards,

on behalf of the authors, Tomohiro Hashizume

### List of changes

List of revised or added figures :
1. Fig. 2. : Sketch of the phases are added for the quantum dimer and quantum link phase.
2. Fig. 3 a. : Removed an erroneously placed label "J/t".
3. Fig. 5, Fig. 11, and Fig. 12. : Tick label "0.5" is added on the y-axis on all the subfigures to clarify that the smallest value of J/t is 0.5 NOT J/t=0.
4. Fig. 4, Fig. 6, and Fig. 12 c. : Labels "PBC", labels "OBC", and coordinates are added to clarify the imposed boundary conditions and the coordinates of the lattice.
5. Fig. 4, Fig. 6, and Fig. 12 c. : The last sentence in the caption is added for explaining the changes made in the point 4.
6. Fig. 13 : This figure is added with an accompanied caption as a support to Appendix E.

List of revisions in the text :
1. Page 1 , Column 1, Index : Index element "Appendix E: E. Order Parameters and Structure factors at vanishing bare mass" is added (automatically generated).
2. Page 3 , Column 1, Line 5-31 : A paragraph is added.
3. Page 4 , Column 2, Line 9-15 : Two sentences starting from "We note that..." are added.
4. Page 5 , Column 1, Line 17-26 : Three sentences starting from "The symmetry is the..." are added.
5. Page 7 , Column 2, Line 40-42 : One sentence starting from "The expression within..." is added.
6. Page 11, Column 1, Line 6-12 : One sentence starting from "We substantiate this claim..." is added.
7. Page 15, Column 1, Line 7-Page 16, column 2, Line 7 (end) : The entirety of Appendix E "Order Parameters and Structure factors at vanishing bare mass" is added.

### Submission & Refereeing History

Resubmission 2112.00756v2 on 20 May 2022
Submission 2112.00756v1 on 17 December 2021

## Reports on this Submission

[see the report]

[see the report]

### Report

I have reviewed the new version of the manuscript and the reply from the authors to my comments. Since the authors addressed all my questions on-point and made appropriate changes to the document, I can give my positive recommendation of the manuscript for publication on Scipost.

• validity: good
• significance: good
• originality: good
• clarity: high
• formatting: good
• grammar: good