                                     number density, m = 0.1, V = 220 , K = 14
                   2.0         β   = 0, D = 84
                               β   = 0.4, D = 150
                               β   = 0.8, D = 150
                   1.5         β   = 1.2, D = 150
                               β   = 1.6, D = 150
                 hni




                   1.0




                                                                                                                JHEP03(2025)027
                   0.5



                   0.0

                         0.1        0.2         0.3      0.4       0.5           0.6
                                                         µ


Figure 15. Quark number density ⟨n⟩ as a function of chemical potential µ at m = 0.1, β =
0, 0.4, 0.8, 1.2, 1.6 in the thermodynamic limit. The bond dimension in the infinite coupling calculation
is D = 84, and the bond dimension in the finite β calculations is D = 150. At a finite β, the sample
size for the discretization of gauge group integrations is K = 14. To evaluate the numerical differences
in eq. (4.3), we set ∆µ = 0.04.


Acknowledgments
A part of the numerical calculation for the present work was carried out with ohtaka provided
by the Institute for Solid State Physics, the University of Tokyo. This work is supported by the
Endowed Project for Quantum Software Research and Education, the University of Tokyo [69],
and the Center of Innovations for Sustainable Quantum AI (JST Grant Number JPMJPF2221).
SA acknowledges the support from JSPS KAKENHI (JP23K13096, JP24H00214) and the Top
Runners in Strategy of Transborder Advanced Researches (TRiSTAR) program conducted as
the Strategic Professional Development Program for Young Researchers by the MEXT.

A     Coefficients of the Grassmann tensor F
Here, we discuss one method to derive the tensor elements of F in eq. (2.10). For simplicity, we
consider the two-color case where N = 2. We also label the spacetime direction ν by ν = x, t
not by ν = 1, 2. In this case, the integration over the original staggered fermions is written as
             Z
       F=        dχ1 dχ̄1 dχ2 dχ̄2 e−m(χ̄1 χ1 +χ̄2 χ2 ) (1 + χ̄1 A) (1 + χ1 B) (1 + χ̄2 C) (1 + χ2 D)

          = ABCD + mCD + mAB + m2 ,                                                                     (A.1)
where A, B, C, and D are sums of terms with one auxiliary Grassmann variable, and their
expressions are given by
    A = −ηx,1 − ηt,1 + (Ux† )11 ζ̄x,1 + (Ux† )12 ζ̄x,2 + (Ut† )11 ζ̄t,1 + (Ut† )12 ζ̄t,2 ,              (A.2)
        1h                                                                                       i
    B=     − (Ux )11 η̄x,1 − (Ux )21 η̄x,2 − a+ (Ut )11 η̄t,1 − a+ (Ut )21 η̄t,2 + ζx,1 + a− ζt,1 ,     (A.3)
        2



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