Phase structure of (3+1)-dimensional dense two-color QCD at $T=0$ in the strong coupling limit with the tensor renormalization group

TL;DR

This work investigates the phase structure of (3+1)-dimensional dense two-color QCD at zero temperature in the strong coupling limit using Grassmann tensor renormalization group methods. By computing the chiral condensate, diquark condensate, and quark number density as functions of the chemical potential, and by extracting critical exponents near the diquark onset, the study reveals mean-field-like behavior and provides a sign-problem-free benchmark on a large 1024^4 lattice. The results show qualitative agreement with mean-field predictions and support the feasibility of TRG approaches for finite-density QCD-like systems, offering a pathway toward more realistic gauge dynamics. Future work could incorporate finite-coupling gauge fields and Wilson fermions to extend these insights toward true QCD.

Abstract

We investigate the phase structure of the (3+1)-dimensional strong coupling two-color QCD at zero temperature ($T=0$) with finite chemical potential using the tensor renormalization group method. The chiral and diquark condensates and the quark number density are evaluated as a function of the chemical potential. We further determine the critical exponents associated with the diquark condensate, which suggest consistency with the predictions of mean-field theory.

Figures (6)

• Figure 1: Convergence behaviors of thermodynamic potential as a function of $D$ at $(m,\lambda)=(1.0,0)$ on a $1024^4$.$\mu=1.08$ and 1.12 cases are plotted.
• Figure 2: $\mu$ dependence of $\langle {\bar{\chi}} \chi\rangle$, $\langle \chi \chi\rangle$ and $\langle n\rangle/2$ at $(m,\lambda)=(1.0,0)$ on a $1024^4$ lattice with $D=55$.
• Figure 3: Volume dependence of $\langle {\bar{\chi}} \chi\rangle$ and $\langle n\rangle/2$ at $(m,\lambda)=(1.0,0)$ with $D=55$.
• Figure 4: Volume dependence of $\langle \chi \chi\rangle$ at $(m,\lambda)=(1.0,0)$ with $D=55$.
• Figure 5: $\mu$ dependence of $\langle \chi \chi\rangle$ around $\mu_c^{\rm low}$ at $(m,\lambda)=(1.0,0)$ on a $1024^4$ lattice with $D=55$.