- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Crystalline phases at finite winding densities in a quantum link ladder

Paolo Stornati1,*, Philipp Krah2, Karl Jansen3, and Debasish Banerjee4,5

  • 1ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss 3, 08860 Castelldefels (Barcelona), Spain
  • 2TU Berlin, Institute of Mathematics, Straße des 17. Juni 136, 10623 Berlin, Germany
  • 3Deutsches Elektronen-Synchrotron DESY, Platanenallee 6, 15738 Zeuthen, Germany
  • 4Theory Division, Saha Institute of Nuclear Physics, 1/AF Bidhan Nagar, Kolkata 700064, India
  • 5Homi Bhabha National Institute, Training School Complex, Anushaktinagar, Mumbai 400094, India

  • *paolo.stornati@icfo.eu
PDF

Phys. Rev. D 107, L031504 – Published 23 February, 2023

DOI: https://doi.org/10.1103/PhysRevD.107.L031504

Abstract

Condensed matter physics of gauge theories coupled to fermions can exhibit a rich phase structure, but are nevertheless very difficult to study in Monte Carlo simulations when they are afflicted by a sign problem. As an alternate approach, we use tensor network methods to explore the finite density physics of Abelian gauge theories without dynamical matter. As a concrete example, we consider the U(1) gauge invariant quantum link ladder with spin-12 gauge fields in an external electric field, which causes the winding electric fluxes to condense in the ground state. We demonstrate how the electric flux tubes arrange themselves in the bulk, giving rise to crystalline patterns, whose period can be controlled by tuning the external field. We propose observables to detect the transitions in ground state properties not only in numerical experiments, but also in future cold-atom realizations. A systematic procedure for reaching the thermodynamic limit, as well as extending the studies from ladders to extended geometries is outlined.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (39)

  1. D. Banerjee and S. Chandrasekharan, Finite size effects in the presence of a chemical potential: A study in the classical nonlinear o(2) sigma model, Phys. Rev. D 81, 125007 (2010).
  2. G. Aarts and F. A. James, On the convergence of complex langevin dynamics: The three-dimensional XY model at finite chemical potential, J. High Energy Phys. 08 (2010) 020.
  3. S. Katz, F. Niedermayer, D. Nogradi, and C. Torok, Comparison of algorithms for solving the sign problem in the O(3) model in 1+1 dimensions at finite chemical potential, Phys. Rev. D 95, 054506 (2017).
  4. J. Bloch, R. G. Jha, R. Lohmayer, and M. Meister, Tensor renormalization group study of the three-dimensional o(2) model, Phys. Rev. D 104, 094517 (2021).
  5. S. Gupta, QCD at finite density, Proc. Sci. LATTICE2010 (2010) 007 [arXiv:1101.0109].
  6. V. Ayyar, S. Chandrasekharan, and J. Rantaharju, Benchmark results in the 2D lattice Thirring model with a chemical potential, Phys. Rev. D 97, 054501 (2018).
  7. M. C. Bañuls, K. Cichy, J. I. Cirac, K. Jansen, and S. Kühn, Density Induced Phase Transitions in the Schwinger Model: A Study with Matrix Product States, Phys. Rev. Lett. 118, 071601 (2017).
  8. H. Nielsen and P. Olesen, Vortex-line models for dual strings, Nucl. Phys. B61, 45 (1973).
  9. T. Banks, R. Myerson, and J. Kogut, Phase transitions in Abelian lattice gauge theories, Nucl. Phys. B129, 493 (1977).
  10. A. M. Polyakov, Quark confinement and topology of gauge groups, Nucl. Phys. B120, 429 (1977).
  11. G. ’t Hooft, On the phase transition towards permanent quark confinement, Nucl. Phys. B138, 1 (1978).
  12. H. D. Trottier and R. M. Woloshyn, Flux tubes in three-dimensional lattice gauge theories, Phys. Rev. D 48, 2290 (1993).
  13. M. Zach, M. Faber, and P. Skala, Flux tubes and their interaction in U(1) lattice gauge theory, Nucl. Phys. B529, 505 (1998).
  14. Y. Koma, M. Koma, and P. Majumdar, Static potential, force, and flux-tube profile in 4D compact U(1) lattice gauge theory with the multi-level algorithm, Nucl. Phys. B692, 209 (2004).
  15. A. Athenodorou and M. Teper, On the spectrum and string tension of u(1) lattice gauge theory in 2+1 dimensions, J. High Energy Phys. 01 (2019) 063.
  16. S. Chandrasekharan and U. J. Wiese, Quantum link models: A discrete approach to gauge theories, Nucl. Phys. B492, 455 (1997).
  17. D. Banerjee, F.-J. Jiang, P. Widmer, and U.-J. Wiese, The (2+1)-d u(1) quantum link model masquerading as deconfined criticality, J. Stat. Mech. (2013) P12010.
  18. D. Banerjee and A. Sen, Quantum Scars from Zero Modes in an Abelian Lattice Gauge Theory on Ladders, Phys. Rev. Lett. 126, 220601 (2021).
  19. N. Shannon, G. Misguich, and K. Penc, Cyclic exchange, isolated states, and spinon deconfinement in an xxz heisenberg model on the checkerboard lattice, Phys. Rev. B 69, 220403 (2004).
  20. O. Benton, O. Sikora, and N. Shannon, Seeing the light: Experimental signatures of emergent electromagnetism in a quantum spin ice, Phys. Rev. B 86, 075154 (2012).
  21. D. Banerjee, Recent progress on cluster and meron algorithms for strongly correlated systems, Ind. J. Phys. 95, 1669 (2021).
  22. U. Schollwöck, The density-matrix renormalization group in the age of matrix product states, Ann. Phys (N. Y.) 326, 96 (2011).
  23. A. Celi, B. Vermersch, O. Viyuela, H. Pichler, M. D. Lukin, and P. Zoller, Emerging Two-Dimensional Gauge Theories in Rydberg Configurable Arrays, Phys. Rev. X 10, 021057 (2020).
  24. D. Paulson, L. Dellantonio, J. F. Haase, A. Celi, A. Kan, A. Jena, C. Kokail, R. van Bijnen, K. Jansen, P. Zoller, and C. A. Muschik, Simulating 2D effects in lattice gauge theories on a quantum computer, PRX Quantum 2, 030334 (2021).
  25. E. Huffman, M. G. Vera, and D. Banerjee, Real-time dynamics of plaquette models using NISQ hardware (2021).
  26. Z.-Y. Zhou, G.-X. Su, J. C. Halimeh, R. Ott, H. Sun, P. Hauke, B. Yang, Z.-S. Yuan, J. Berges, and J.-W. Pan, Thermalization dynamics of a gauge theory on a quantum simulator, Science 377, 311 (2022).
  27. J. Mildenberger, W. Mruczkiewicz, J. C. Halimeh, Z. Jiang, and P. Hauke, Probing confinement in a Z2 lattice gauge theory on a quantum computer (2022).
  28. J. C. Halimeh, I. P. McCulloch, B. Yang, and P. Hauke, Tuning the topological θ-angle in cold-atom quantum simulators of gauge theories (2022).
  29. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevD.107.L031504, for more details.
  30. T. D. Cohen, Functional Integrals for QCD at Nonzero Chemical Potential and Zero Density, Phys. Rev. Lett. 91, 222001 (2003).
  31. M. Luscher, Volume dependence of the energy spectrum in massive quantum field theories. 1. Stable particle states, Commun. Math. Phys. 104, 177 (1986).
  32. A. Honecker, J. Schulenburg, and J. Richter, Magnetization plateaus in frustrated antiferromagnetic quantum spin models, J. Phys. Condens. Matter 16, S749 (2004).
  33. M. Sarkar, M. Pal, A. Sen, and K. Sengupta, Quantum order-by-disorder induced phase transition in Rydberg ladders with staggered detuning, arXiv:2204.12515.
  34. M. Aidelsburger et al., Cold atoms meet lattice gauge theory, Phil. Trans. R. Soc. A 380, 20210064 (2022).
  35. E. A. Martinez et al., Real-time dynamics of lattice gauge theories with a few-qubit quantum computer, Nature (London) 534, 516 (2016).
  36. H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner et al., Probing many-body dynamics on a 51-atom quantum simulator, Nature (London) 551, 579 (2017).
  37. C. Schweizer, F. Grusdt, M. Berngruber, L. Barbiero, E. Demler, N. Goldman, I. Bloch, and M. Aidelsburger, Floquet approach to Z2 lattice gauge theories with ultracold atoms in optical lattices, Nat. Phys. 15, 1168 (2019).
  38. A. Mil, T. V. Zache, A. Hegde, A. Xia, R. P. Bhatt, M. K. Oberthaler, P. Hauke, J. Berges, and F. Jendrzejewski, A scalable realization of local U(1) gauge invariance in cold atomic mixtures, Science 367, 1128 (2020).
  39. B. Yang, H. Sun, R. Ott, H.-Y. Wang, T. V. Zache, J. C. Halimeh, Z.-S. Yuan, P. Hauke, and J.-W. Pan, Observation of gauge invariance in a 71-site Bose–Hubbard quantum simulator, Nature (London) 587, 392 (2020).

Outline

Information

Phys. Rev. D 107, L031504– Published 23 February, 2023
  • Received 28 September 2022
  • Accepted 5 January 2023
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation