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  • Open Access

Monomer-dimer tensor-network basis for qubit-regularized lattice gauge theories

Shailesh Chandrasekharan1,*, Rui Xian Siew1,†, and Tanmoy Bhattacharya2,‡

  • *Contact author: sch27@duke.edu
  • †Contact author: ruixian.siew@duke.edu
  • ‡Contact author: tanmoy@lanl.gov
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Phys. Rev. D 111, 114502 – Published 6 June, 2025

DOI: https://doi.org/10.1103/gns9-l3gk

Abstract

Traditional SU(N) lattice gauge theories (LGTs) can be formulated using an orthonormal basis constructed from the irreducible representations (irreps) Vλ of the SU(N) gauge symmetry. On a lattice, the elements of this basis are tensor networks comprising dimer tensors on the links labeled by a set of irreps {λℓ} and monomer tensors on sites labeled by {λs}. These tensors naturally define a local site Hilbert space, Hsg, on which gauge transformations act. Gauss’s law introduces an additional index αs=1,2,…,D(Hsg) that labels an orthonormal basis of the gauge-invariant subspace of Hsg. This monomer-dimer tensor-network (MDTN) basis, |{λs},{λℓ},{αs}⟩, of the physical Hilbert space enables the construction of new qubit-regularized SU(N) gauge theories that are free of sign problems while preserving key features of traditional LGTs. Here, we investigate finite-temperature confinement-deconfinement transitions in a simple qubit-regularized SU(2) and SU(3) gauge theory in d=2 and d=3 spatial dimensions, formulated using the MDTN basis, and show that they reproduce the universal results of traditional LGTs at these transitions. Additionally, in d=1, we demonstrate using a plaquette chain that the string tension at zero temperature can be continuously tuned to zero by adjusting a model parameter that plays the role of the gauge coupling in traditional LGTs.

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References (67)

  1. S. Chandrasekharan, Qubit regularization of quantum field theories, Proc. Sci. LATTICE2024 (2025) 001.
  2. M. C. Bañuls et al., Simulating lattice gauge theories within quantum technologies, Eur. Phys. J. D 74, 165 (2020).
  3. C. W. Bauer, Z. Davoudi, N. Klco, and M. J. Savage, Quantum simulation of fundamental particles and forces, Nat. Rev. Phys. 5, 420 (2023).
  4. A. Di Meglio et al., Quantum computing for high-energy physics: State of the art and challenges, PRX Quantum 5, 037001 (2024).
  5. J. B. Kogut and L. Susskind, Hamiltonian formulation of Wilson’s lattice gauge theories, Phys. Rev. D 11, 395 (1975).
  6. S. Chandrasekharan and U. J. Wiese, Quantum link models: A discrete approach to gauge theories, Nucl. Phys. B492, 455 (1997).
  7. S. Chandrasekharan, Confinement, chiral symmetry breaking and continuum limits in quantum link models, Nucl. Phys. B, Proc. Suppl. 73, 739 (1999).
  8. R. Brower, S. Chandrasekharan, and U. J. Wiese, QCD as a quantum link model, Phys. Rev. D 60, 094502 (1999).
  9. R. Brower, S. Chandrasekharan, S. Riederer, and U. J. Wiese, D theory: Field quantization by dimensional reduction of discrete variables, Nucl. Phys. B693, 149 (2004).
  10. M. C. Bañuls, K. Cichy, J. I. Cirac, K. Jansen, and S. Kühn, Efficient basis formulation for 1+1 dimensional SU(2) lattice gauge theory: Spectral calculations with matrix product states, Phys. Rev. X 7, 041046 (2017).
  11. A. Alexandru, P. F. Bedaque, H. Lamm, and S. Lawrence (NuQS Collaboration), σ models on quantum computers, Phys. Rev. Lett. 123, 090501 (2019).
  12. A. Alexandru, P. F. Bedaque, S. Harmalkar, H. Lamm, S. Lawrence, and N. C. Warrington (NuQS Collaboration), Gluon field digitization for quantum computers, Phys. Rev. D 100, 114501 (2019).
  13. A. Alexandru, P. F. Bedaque, A. Carosso, M. J. Cervia, E. M. Murairi, and A. Sheng, Fuzzy gauge theory for quantum computers, Phys. Rev. D 109, 094502 (2024).
  14. T. Bhattacharya, A. J. Buser, S. Chandrasekharan, R. Gupta, and H. Singh, Qubit regularization of asymptotic freedom, Phys. Rev. Lett. 126, 172001 (2021).
  15. S. Maiti, D. Banerjee, S. Chandrasekharan, and M. K. Marinkovic, Asymptotic freedom at the Berezinskii-Kosterlitz-Thouless transition without fine-tuning using a qubit regularization, Phys. Rev. Lett. 132, 041601 (2024).
  16. H. Liu and S. Chandrasekharan, Qubit regularization and qubit embedding algebras, Symmetry 14, 305 (2022).
  17. T. Byrnes and Y. Yamamoto, Simulating lattice gauge theories on a quantum computer, Phys. Rev. A 73, 022328 (2006).
  18. A. N. Ciavarella, Quantum simulation of lattice QCD with improved Hamiltonians, Phys. Rev. D 108, 094513 (2023).
  19. R. C. Farrell, M. Illa, A. N. Ciavarella, and M. J. Savage, Quantum simulations of hadron dynamics in the Schwinger model using 112 qubits, Phys. Rev. D 109, 114510 (2024).
  20. N. A. Zemlevskiy, Scalable quantum simulations of scattering in scalar field theory on 120 qubits, arXiv:2411.02486.
  21. A. Crippa, S. Romiti, L. Funcke, K. Jansen, S. Kühn, P. Stornati, and C. Urbach, Towards determining the (2+1)-dimensional quantum electrodynamics running coupling with Monte Carlo and quantum computing methods, arXiv:2404.17545.
  22. C. Peng, M. C. Diamantini, L. Funcke, S. M. A. Hassan, K. Jansen, S. Kühn, D. Luo, and P. Naredi, Hamiltonian lattice formulation of compact Maxwell-Chern-Simons theory, arXiv:2407.20225.
  23. D. Berenstein, H. Kawai, and R. Brower, U(1) fields from qubits: An approach via D-theory algebra, Phys. Rev. D 110, 014506 (2024).
  24. T. Hashizume, J. C. Halimeh, P. Hauke, and D. Banerjee, Ground-state phase diagram of quantum link electrodynamics in (2+1)−d, SciPost Phys. 13, 017 (2022).
  25. I. Raychowdhury and J. R. Stryker, Loop, string, and hadron dynamics in SU(2) Hamiltonian lattice gauge theories, Phys. Rev. D 101, 114502 (2020).
  26. S. V. Kadam, I. Raychowdhury, and J. R. Stryker, Loop-string-hadron formulation of an SU(3) gauge theory with dynamical quarks, Phys. Rev. D 107, 094513 (2023).
  27. I. M. Burbano and C. W. Bauer, Gauge loop-string-hadron formulation on general graphs and applications to fully gauge fixed Hamiltonian lattice gauge theory, arXiv:2409.13812.
  28. A. N. Ciavarella and C. W. Bauer, Quantum simulation of SU(3) lattice Yang-Mills theory at leading order in large-Nc expansion, Phys. Rev. Lett. 133, 111901 (2024).
  29. A. Mariani, S. Pradhan, and E. Ercolessi, Hamiltonians and gauge-invariant Hilbert space for lattice Yang-Mills-like theories with finite gauge group, Phys. Rev. D 107, 114513 (2023).
  30. R. Moessner and S. L. Sondhi, Resonating valence bond phase in the triangular lattice quantum dimer model, Phys. Rev. Lett. 86, 1881 (2001).
  31. G. Chen, J. Gukelberger, S. Trebst, F. Alet, and L. Balents, Coulomb gas transitions in three-dimensional classical dimer models, Phys. Rev. B 80, 045112 (2009).
  32. R. Moessner and K. S. Raman, Quantum dimer models, in Introduction to Frustrated Magnetism: Materials, Experiments, Theory (Springer, 2010).
  33. E. Zohar, Quantum simulation of lattice gauge theories in more than one space dimension—requirements, challenges and methods, Phil. Trans. A. Math. Phys. Eng. Sci. 380, 20210069 (2021).
  34. J. C. Halimeh, M. Hanada, S. Matsuura, F. Nori, E. Rinaldi, and A. Schäfer, A universal framework for the quantum simulation of Yang-Mills theory, arXiv:2411.13161.
  35. A. Mezzacapo, E. Rico, C. Sabín, I. L. Egusquiza, L. Lamata, and E. Solano, Non-Abelian SU(2) lattice gauge theories in superconducting circuits, Phys. Rev. Lett. 115, 240502 (2015).
  36. B. Müller and X. Yao, Simple Hamiltonian for quantum simulation of strongly coupled (2+1)D SU(2) lattice gauge theory on a honeycomb lattice, Phys. Rev. D 108, 094505 (2023).
  37. W. Marshall, Antiferromagnetism, Proc. R. Soc. A 232, 48 (1955).
  38. D. H. Adams and S. Chandrasekharan, Chiral limit of strongly coupled lattice gauge theories, Nucl. Phys. B662, 220 (2003).
  39. S. Chandrasekharan and F.-J. Jiang, Phase-diagram of two-color lattice QCD in the chiral limit, Phys. Rev. D 74, 014506 (2006).
  40. 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.
  41. D. Banerjee, F. J. Jiang, T. Z. Olesen, P. Orland, and U. J. Wiese, From the SU(2) quantum link model on the honeycomb lattice to the quantum dimer model on the kagomé lattice: Phase transition and fractionalized flux strings, Phys. Rev. B 97, 205108 (2018).
  42. I. Sau, A. Sen, and D. Banerjee, Weak universality induced by Q=±2e charges at the deconfinement transition of a (2+1)-dimensional U(1) lattice gauge theory, Phys. Rev. Lett. 130, 071901 (2023).
  43. B. Svetitsky and L. G. Yaffe, Critical behavior at finite temperature confinement transitions, Nucl. Phys. B210, 423 (1982).
  44. B. Lucini, M. Teper, and U. Wenger, The high temperature phase transition in SU(N) gauge theories, J. High Energy Phys. 01 (2004) 061.
  45. A. Pelissetto and E. Vicari, Critical phenomena and renormalization group theory, Phys. Rep. 368, 549 (2002).
  46. L. D. McLerran and B. Svetitsky, Quark liberation at high temperature: A Monte Carlo study of SU(2) gauge theory, Phys. Rev. D 24, 450 (1981).
  47. L. G. Yaffe and B. Svetitsky, First order phase transition in the SU(3) gauge theory at finite temperature, Phys. Rev. D 26, 963 (1982).
  48. R. V. Gavai, The deconfinement transition in SU(2) lattice gauge theories, Nucl. Phys. B215, 458 (1983).
  49. J. B. Kogut, J. Polonyi, H. W. Wyld, J. Shigemitsu, and D. K. Sinclair, Further evidence for the first order nature of the pure gauge SU(3) deconfinement transition, Nucl. Phys. B251, 311 (1985).
  50. G. Curci and R. Tripiccione, Scaling behavior of the deconfinement temperature for SU(2) pure gauge theory at finite temperature, Phys. Lett. 151B, 145 (1985).
  51. M. Gross and J. F. Wheater, Deconfining transitions in (2+1)-dimensional SU(3) and SU(4) gauge theories, Z. Phys. C 28, 471 (1985).
  52. S. R. Das and J. B. Kogut, The deconfinement transition in SU(2) gauge theory: A finite size analysis, Nucl. Phys. B265, 303 (1986).
  53. Y. Iwasaki, K. Kanaya, T. Yoshie, T. Hoshino, T. Shirakawa, Y. Oyanagi, S. Ichii, and T. Kawai, Deconfining transition of SU(3) gauge theory on Nt=4 and 6 lattices, Phys. Rev. Lett. 67, 3343 (1991).
  54. M. Teper, The finite temperature phase transition of SU(2) gauge fields in (2+1)-dimensions, Phys. Lett. B 313, 417 (1993).
  55. S. Datta and S. Gupta, Scaling and the continuum limit of the finite temperature deconfinement transition in SU(Nc) pure gauge theory, Phys. Rev. D 80, 114504 (2009).
  56. M. Caselle, L. Castagnini, A. Feo, F. Gliozzi, and M. Panero, Thermodynamics of SU(N) Yang-Mills theories in 2+1 dimensions I—The confining phase, J. High Energy Phys. 06 (2011) 142.
  57. M. Caselle, L. Castagnini, A. Feo, F. Gliozzi, U. Gursoy, M. Panero, and A. Schafer, Thermodynamics of SU(N) Yang-Mills theories in 2+1 dimensions II. The Deconfined phase, J. High Energy Phys. 05 (2012) 135.
  58. R. V. Gavai, B. Mohanty, J. S. Rao, and S. Saha, Cumulants and ordering of their ratios in 2D Potts models: Lessons for QCD?, arXiv:2312.12130.
  59. F. Y. Wu, The Potts model, Rev. Mod. Phys. 54, 235 (1982); 55, 315(E) (1983).
  60. M. Hasenbusch, K. Pinn, and S. Vinti, Critical exponents of the three-dimensional Ising universality class from finite-size scaling with standard and improved actions, Phys. Rev. B 59, 11471 (1999).
  61. X. Yao, SU(2) gauge theory in 2+1 dimensions on a plaquette chain obeys the eigenstate thermalization hypothesis, Phys. Rev. D 108, L031504 (2023).
  62. J. Frank, E. Huffman, and S. Chandrasekharan, Emergence of Gauss’ law in a Z2 lattice gauge theory in 1+1 dimensions, Phys. Lett. B 806, 135484 (2020).
  63. J. Zhou, H. Singh, T. Bhattacharya, S. Chandrasekharan, and R. Gupta, Spacetime symmetric qubit regularization of the asymptotically free two-dimensional O(4) model, Phys. Rev. D 105, 054510 (2022).
  64. S. Chandrasekharan and U.-J. Wiese, Meron cluster solution of a fermion sign problem, Phys. Rev. Lett. 83, 3116 (1999).
  65. E. Huffman and S. Chandrasekharan, Fermion bag approach to Hamiltonian lattice field theories in continuous time, Phys. Rev. D 96, 114502 (2017).
  66. S. Chandrasekharan, S. T. Nguyen, and T. R. Richardson, Worldline Monte Carlo method for few-body nuclear physics, Phys. Rev. C 110, 024002 (2024).
  67. OpenAI, chatgpt (gpt-4) (2025), https://openai.com/chatgpt (accessed: 2025-02-14).

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Phys. Rev. D 111, 114502– Published 6 June, 2025
  • Received 6 March 2025
  • Accepted 12 May 2025
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