Speed of sound exceeding the conformal bound in dense QCD-like theories

TL;DR

The paper uses sign-problem-free lattice Monte Carlo simulations of two-color QCD to study dense matter at low temperatures, focusing on the equation of state and the speed of sound as a function of the quark chemical potential $μ$. It reveals a rich phase structure, including a diquark superfluid phase and a continuous Bose-Einstein condensation to BCS crossover, with the onset at $μ_c \approx m_{\rm PS}/2$ and a robust, temperature-insensitive $c_s^2/c^2$ profile. In the BEC regime, the EoS matches ChPT predictions with $p_{\rm ChPT}$ and $e_{\rm ChPT}$, allowing extraction of $F$ values around $50$ MeV, while at higher density the data depart from ChPT and exhibit $c_s^2/c^2 > 1/3$, indicating a stiffer EoS toward the BCS side. This first-principles result suggests dense QCD-like theories can realize a speed of sound above the conformal bound, with potential implications for neutron-star phenomenology and guidance for effective models constrained by lattice data.

Abstract

We investigated the phase structure and the equation of state (EoS) for dense two-color QCD at low temperatures using the lattice Monte Carlo simulations. A rich phase structure below the pseudo-critical temperature $T_c$ as a function of quark chemical potential has been revealed. In a high-density regime, we can see a superfluid phase, where the diquark condensate takes a non-zero expectation value. We have newly found that the speed of sound exceeds the conformal bound, which is the value of the relativistic free theory. This talk is based on Refs.~\cite{Iida:2022hyy, Iida:2024irv, Itou:2025vcy}.

Figures (4)

• Figure 1: Two-color QCD phase diagram. The data at $160$ MeV and $80$ MeV are originally presented in Refs. Iida:2019rahIida:2022hyy, while the ones at $40$ MeV are obtained in Ref. Iida:2024irv.
• Figure 2: Our lattice data of the diquark condensate as a function of $\mu$. The data were originally obtained in Ref. Iida:2024irv.
• Figure 3: Our data for EoS as a function of $\mu$. The data were originally obtained in Ref. Iida:2024irv.
• Figure 4: Sound velocity squared as a function of $\mu$. The plot is originally shown in Ref. Iida:2024irv.