Lattice QCD at finite isospin density at zero and finite temperature

TL;DR

This study uses lattice QCD simulations to explore how isospin chemical potential affects phase transitions, revealing a second-order pion condensation transition at zero temperature and a temperature-dependent transition order at finite temperature.

Contribution

First lattice QCD simulation of finite isospin density at both zero and finite temperature, confirming effective theory predictions and analyzing phase transition orders.

Findings

Pion condensate forms above critical isospin chemical potential, $ eq m_$

Transition at zero temperature is second order with mean-field scaling

Finite temperature transition varies from first to second order as $ eq$ decreases

Abstract

We simulate lattice QCD with dynamical $u$ and $d$ quarks at finite chemical potential, $\mu_I$, for the third component of isospin ($I_3$), at both zero and at finite temperature. At zero temperature there is some $\mu_I$, $\mu_c$ 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 $\mu_c=m_\pi$. 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 $\mu_I > \mu_c$. For $\mu_I$ sufficiently large, this finite temperature phase transition appears to be first order. As $\mu_I$ is decreased it becomes second order connecting continuously with the zero temperature transition.