Lattice QCD at finite isospin density at zero and finite temperature

TL;DR

This study uses lattice QCD with two degenerate light quarks at finite isospin density μ_I to circumvent the sign problem and map the phase structure at zero and finite temperature. Leveraging a small explicit I_3-breaking term, it demonstrates a zero-temperature second-order transition at μ_I^c ≈ m_π where a charged pion condensate forms and parity is broken, with scaling consistent with mean-field predictions from effective chiral Lagrangians. At finite temperature, the I_3-restoration transition is first order for large μ_I and becomes second order as μ_I approaches μ_I^c, connecting to the zero-temperature transition; the finite-temperature phase boundary shows nuanced behavior, including observed coincidences with deconfinement and parallels to 2-color QCD. The results advance understanding of QCD at finite density, provide benchmarks for effective theories, and motivate larger-scale simulations to refine the phase diagram and possible astrophysical relevance.

Abstract

We simulate lattice QCD with dynamical $u$ and $d$ quarks at finite chemical potential, $μ_I$, for the third component of isospin ($I_3$), at both zero and at finite temperature. At zero temperature there is some $μ_I$, $μ_c$ say, above which $I_3$ and parity are spontaneously broken by a charged pion condensate. This is in qualitative agreement with the prediction of effective (chiral) Lagrangians which also predict $μ_c=m_π$. This transition appears to be second order, with scaling properties consistent with the mean-field predictions of such effective Lagrangian models. We have also studied the restoration of $I_3$ symmetry at high temperature for $μ_I > μ_c$. For $μ_I$ sufficiently large, this finite temperature phase transition appears to be first order. As $μ_I$ is decreased it becomes second order connecting continuously with the zero temperature transition.

Figures (9)

• Figure 1: Charged pion condensate as a function of $\mu_I$ for $\lambda=0.0025$, $\lambda=0.005$ and $\lambda \longrightarrow 0$. The curves are fits of the finite $\lambda$ measurements to the scaling forms defined in the text.
• Figure 2: Chiral condensate as a function of $\mu_I$ for $\lambda=0.0025$ and $\lambda=0.005$.
• Figure 3: Isospin($I_3$) density as a function of $\mu_I$ for $\lambda=0.0025$ and $\lambda=0.005$.
• Figure 4: Pion condensates as functions of $\mu_I$ for $\lambda=0.005$, $\lambda=0.01$ and a linear extrapolation to $\lambda=0.0$. The lines are the tricritical fit described in the text.
• Figure 5: Pion condensate as a function of $\beta$ for $m=0.05$, $\lambda=0.005$, and $\mu_I=0.8$ on an $8^3 \times 4$ lattice.