Papers
Topics
Authors
Recent
Assistant
AI Research Assistant
Well-researched responses based on relevant abstracts and paper content.
Custom Instructions Pro
Preferences or requirements that you'd like Emergent Mind to consider when generating responses.
Gemini 2.5 Flash
Gemini 2.5 Flash 54 tok/s
Gemini 2.5 Pro 54 tok/s Pro
GPT-5 Medium 22 tok/s Pro
GPT-5 High 25 tok/s Pro
GPT-4o 99 tok/s Pro
Kimi K2 196 tok/s Pro
GPT OSS 120B 333 tok/s Pro
Claude Sonnet 4.5 34 tok/s Pro
2000 character limit reached

Metal-insulator transition and quantum magnetism in the SU(3) Fermi-Hubbard Model: Disentangling Nesting and the Mott Transition (2306.16464v1)

Published 28 Jun 2023 in cond-mat.str-el and cond-mat.quant-gas

Abstract: We use state-of-the-art numerical techniques to compute ground state correlations in the two-dimensional SU(3) Fermi Hubbard model at $1/3$-filling, modeling fermions with three possible spin flavors moving on a square lattice with an average of one particle per site. We find clear evidence of a quantum critical point separating a non-magnetic uniform metallic phase from a regime where long-range `spin' order is present. In particular, there are multiple successive transitions to states with regular, long-range alternation of the different flavors, whose symmetry changes as the interaction strength increases. In addition to the rich quantum magnetism, this important physical system allows one to study integer filling and the associated Mott transition disentangled from nesting, in contrast to the usual SU(2) model. Our results also provide a significant step towards the interpretation of present and future experiments on fermionic alkaline-earth atoms, and other realizations of SU($N$) physics.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (49)
  1. H. J., Electron correlations in narrow energy bands, Proc. R. Soc. Lond. A 276, 238–257 (1963).
  2. M. C. Gutzwiller, Correlation of electrons in a narrow s band, Physical Review 137, A1726 (1965).
  3. M. Rasetti, The Hubbard model: recent results, Vol. 7 (World Scientific, 1991).
  4. D. Scalapino, Distinguishing high-Tc𝑐{}_{c}start_FLOATSUBSCRIPT italic_c end_FLOATSUBSCRIPT theories, Journal of Physics and Chemistry of Solids 56, 1669 (1995).
  5. F. Gebhard, Metal—insulator transitions (Springer, 1997).
  6. J. E. Hirsch, Two-dimensional Hubbard model: Numerical simulation study, Physical Review B 31, 4403 (1985).
  7. P. Fazekas, Lecture notes on electron correlation and magnetism, Vol. 5 (World scientific, 1999).
  8. H. Tasaki, The Hubbard model - an introduction and selected rigorous results, J. Phys.: Condens. Matter 10, 4353 (1998).
  9. C. Honerkamp and W. Hofstetter, Ultracold fermions and the SU⁢(N)SU𝑁\mathrm{SU}(N)roman_SU ( italic_N ) Hubbard model, Phys Rev Lett 92, 170403 (2004).
  10. A. Sotnikov and W. Hofstetter, Magnetic ordering of three-component ultracold fermionic mixtures in optical lattices, Phys. Rev. A 89, 063601 (2014).
  11. A. Sotnikov, Critical entropies and magnetic-phase-diagram analysis of ultracold three-component fermionic mixtures in optical lattices, Phys. Rev. A 92, 023633 (2015).
  12. M. Hafez-Torbati and W. Hofstetter, Artificial SU(3) spin-orbit coupling and exotic Mott insulators, Phys. Rev. B 98, 245131 (2018).
  13. M. Hafez-Torbati and W. Hofstetter, Competing charge and magnetic order in fermionic multicomponent systems, Phys. Rev. B 100, 035133 (2019).
  14. W. Nie, D. Zhang, and W. Zhang, Ferromagnetic ground state of the SU(3) Hubbard model on the Lieb lattice, Phys. Rev. A 96, 053616 (2017).
  15. E. V. Gorelik and N. Blümer, Mott transitions in ternary flavor mixtures of ultracold fermions on optical lattices, Phys Rev A 80, 051602 (2009).
  16. A. Pérez-Romero, R. Franco, and J. Silva-Valencia, Phase diagram of the SU(3) Fermi Hubbard model with next-neighbor interactions, The European Physical Journal B 94, 10.1140/epjb/s10051-021-00242-4 (2021).
  17. M. Hermele, V. Gurarie, and A. M. Rey, Mott insulators of ultracold fermionic alkaline earth atoms: Underconstrained magnetism and chiral spin liquid, Phys Rev Lett 103, 135301 (2009).
  18. M. Hermele and V. Gurarie, Topological liquids and valence cluster states in two-dimensional SU(N)𝑁(N)( italic_N ) magnets, Phys Rev B 84, 174441 (2011).
  19. P. Nataf and F. Mila, Exact diagonalization of Heisenberg SU(N𝑁Nitalic_N) models, Phys Rev Lett 113, 127204 (2014).
  20. C. Romen and A. M. Läuchli, Structure of spin correlations in high-temperature SU(N𝑁Nitalic_N) quantum magnets, Phys. Rev. Research 2, 043009 (2020).
  21. H. Song and M. Hermele, Mott insulators of ultracold fermionic alkaline earth atoms in three dimensions, Phys Rev B 87, 144423 (2013).
  22. A. Cichy and A. Sotnikov, Orbital magnetism of ultracold fermionic gases in a lattice: Dynamical mean-field approach, Phys. Rev. A 93, 053624 (2016).
  23. V. Unukovych and A. Sotnikov, Su(4)-symmetric hubbard model at quarter filling: Insights from the dynamical mean-field approach, Phys. Rev. B 104, 245106 (2021).
  24. N. Blümer and E. V. Gorelik, Mott transitions in the half-filled SU(2M𝑀{M}italic_M) symmetric Hubbard model, Phys. Rev. B 87, 085115 (2013).
  25. D. Wang, L. Wang, and C. Wu, Slater and Mott insulating states in the SU(6) Hubbard model, Phys. Rev. B 100, 115155 (2019).
  26. F. F. Assaad, Phase diagram of the half-filled two-dimensional SU⁢(N)SU𝑁\mathrm{SU}({N})roman_SU ( italic_N ) Hubbard-Heisenberg model: A quantum monte carlo study, Phys. Rev. B 71, 075103 (2005).
  27. M. A. Cazalilla and A. M. Rey, Ultracold Fermi gases with emergent SU(N𝑁Nitalic_N) symmetry, Rep. Prog. Phys. 77, 124401 (2014).
  28. C. Wu, J.-P. Hu, and S.-C. Zhang, Exact SO(5) symmetry in the spin-3/2323/23 / 2 fermionic system, Phys. Rev. Lett. 91, 186402 (2003).
  29. M. A. Cazalilla, A. F. Ho, and M. Ueda, Ultracold gases of ytterbium: ferromagnetism and Mott states in an SU(6) Fermi system, New Journal of Physics 11, 103033 (2009).
  30. Y. Takahashi, Quantum simulation of quantum many-body systems with ultracold two-electron atoms in an optical lattice, Proceedings of the Japan Academy, Series B 98, 141 (2022).
  31. C. Gross and I. Bloch, Quantum simulations with ultracold atoms in optical lattices, Science 357, 995 (2017).
  32. I. Bloch, J. Dalibard, and S. Nascimbène, Quantum simulations with ultracold quantum gases, Nat. Phys. 8, 267 (2012).
  33. C. Gross and W. S. Bakr, Quantum gas microscopy for single atom and spin detection, Nat Phys 17, 1316 (2021).
  34. S. Zhang, J. Carlson, and J. E. Gubernatis, Constrained path Monte Carlo method for fermion ground states, Phys. Rev. B 55, 7464 (1997).
  35. M. Qin, H. Shi, and S. Zhang, Coupling quantum Monte Carlo and independent-particle calculations: Self-consistent constraint for the sign problem based on the density or the density matrix, Phys. Rev. B 94, 235119 (2016a).
  36. H. Shi and S. Zhang, Symmetry in auxiliary-field quantum Monte Carlo calculations, Phys. Rev. B 88, 125132 (2013).
  37. W. Purwanto and S. Zhang, Quantum Monte Carlo method for the ground state of many-boson systems, Phys. Rev. E 70, 056702 (2004).
  38. M. Hohenadler and G. G. Batrouni, Dominant charge density wave correlations in the Holstein model on the half-filled square lattice, Phys. Rev. B 100, 165114 (2019).
  39. C. Feng and R. T. Scalettar, Interplay of flat electronic bands with Holstein phonons, Phys. Rev. B 102, 235152 (2020).
  40. C. Feng, H. Guo, and R. T. Scalettar, Charge density waves on a half-filled decorated honeycomb lattice, Phys. Rev. B 101, 205103 (2020).
  41. X. Cai, Z.-X. Li, and H. Yao, Antiferromagnetism induced by bond Su-Schrieffer-Heeger electron-phonon coupling: A quantum Monte Carlo study, Phys. Rev. Lett. 127, 247203 (2021).
  42. M. Troyer and U.-J. Wiese, Computational complexity and fundamental limitations to fermionic quantum monte carlo simulations, Phys. Rev. Lett. 94, 170201 (2005).
  43. R. Mondaini, S. Tarat, and R. T. Scalettar, Quantum critical points and the sign problem, Science 375, 418 (2022).
  44. C.-C. Chang and S. Zhang, Spatially inhomogeneous phase in the two-dimensional repulsive Hubbard model, Phys. Rev. B 78, 165101 (2008).
  45. M. Qin, H. Shi, and S. Zhang, Benchmark study of the two-dimensional Hubbard model with auxiliary-field quantum Monte Carlo method, Phys. Rev. B 94, 085103 (2016b).
  46. E. Vitali, P. Rosenberg, and S. Zhang, Exotic superfluid phases in spin-polarized Fermi gases in optical lattices, Phys. Rev. Lett. 128, 203201 (2022).
  47. S. Sorella, Finite-size scaling with modified boundary conditions, Phys. Rev. B 91, 241116 (2015).
  48. C. Gros, Control of the finite-size corrections in exact diagonalization studies, Phys. Rev. B 53, 6865 (1996).
  49. C. Lin, F. H. Zong, and D. M. Ceperley, Twist-averaged boundary conditions in continuum quantum monte carlo algorithms, Phys. Rev. E 64, 016702 (2001).
Citations (4)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
Lightbulb Streamline Icon: https://streamlinehq.com

Continue Learning

We haven't generated follow-up questions for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now
List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up

Don't miss out on important new AI/ML research

See which papers are being discussed right now on X, Reddit, and more:

Explore Trending Papers

“Emergent Mind helps me see which AI papers have caught fire online.”

Philip

Philip

Creator, AI Explained on YouTube