Equation of State and Thermometry of the 2D SU⁡(𝑁) Fermi-Hubbard Model

Creators: Pasqualetti, G.; Bettermann, O.; Darkwah Oppong, N.¹; Ibarra-García-Padilla, E.; Dasgupta, S.; Scalettar, R. T.; Hazzard, K. R. A.; Bloch, I.; Fölling, S.

1. California Institute of Technology

Abstract

We characterize the equation of state (EoS) of the SU⁡(𝑁 > 2) Fermi-Hubbard Model (FHM) in a two-dimensional single-layer square optical lattice. We probe the density and the site occupation probabilities as functions of interaction strength and temperature for 𝑁 = 3, 4, and 6. Our measurements are used as a benchmark for state-of-the-art numerical methods including determinantal quantum Monte Carlo and numerical linked cluster expansion. By probing the density fluctuations, we compare temperatures determined in a model-independent way by fitting measurements to numerically calculated EoS results, making this a particularly interesting new step in the exploration and characterization of the SU⁡(𝑁) FHM.

Copyright and License

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. Open access publication funded by the Max Planck Society.

Acknowledgement

We thank Alexander Impertro for his contributions in the early phase of the experiment. We thank Hao-Tian Wei for useful conversations and the exact diagonalization code used in the NLCE. N. D. O. acknowledges funding from the International Max Planck Research School for Quantum Science and Technology. E. I. G. P. is supported by Grant No. DE-SC-0022311, funded by the U.S. Department of Energy, Office of Science, and acknowledges support from the Robert A. Welch Foundation (C-1872) and the National Science Foundation (PHY-1848304). K. H. acknowledges support from the Robert A. Welch Foundation (C-1872) and the National Science Foundation (PHY-1848304), and the W. F. Keck Foundation (Grant No. 995764). Computing resources were supported in part by the Big-Data Private-Cloud Research Cyberinfrastructure MRI award funded by NSF under Grant No. CNS-1338099 and by Rice University’s Center for Research Computing (CRC). K. H.’s contribution benefited from discussions at the Aspen Center for Physics, supported by the National Science Foundation Grant No. PHY1066293, and the KITP, which was supported in part by the National Science Foundation under Grant No. NSF PHY1748958. R. T. S. is supported by Grant No. DE-SC0014671 funded by the U.S. Department of Energy, Office of Science.

Data Availability

supplemental material contains additional details about the measurement process and about the measured data, additional calibration methods as well as supplemental information about the numerics implementations

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PhysRevLett.132.083401.pdf

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