Dense $\mathrm{QC_2D_2}$ with uniform matrix product states

TL;DR

This paper uses a gauge-invariant matrix product state approach to study dense SU(2) gauge theory in 1+1 dimensions, revealing a quarkyonic phase with Luttinger liquid behavior and a smooth crossover at high density.

Contribution

It introduces a sign-problem-free variational method to analyze dense QCD in low dimensions, providing first-principles evidence for quarkyonic matter and Luttinger liquid characteristics.

Findings

Infrared behavior matches Tomonaga--Luttinger liquid with central charge c=1.

Baryon-number density shows spatial modulation consistent with Luttinger theory.

Quark distribution indicates coexistence of Fermi sea and baryonic infrared description.

Abstract

We study cold dense single-flavor $\mathrm{SU}(2)$ gauge theory in $(1+1)$ dimensions in the thermodynamic limit using a gauge-invariant variational uniform matrix product state ansatz. This formulation provides a sign-problem-free, first-principles approach to dense QCD. We show that, at finite baryon density, the infrared behavior is consistent with a Tomonaga--Luttinger liquid: the central charge is determined to be $c=1$, and the two-point function of the baryon-number density exhibits spatial modulation with the wavenumber predicted by Tomonaga--Luttinger liquid theory. The Luttinger parameter varies smoothly from $K\simeq 1$ in the dilute-baryon regime to $K\simeq 1/2$ at higher densities, suggesting a quarkyonic crossover. Furthermore, the quark distribution reveals the coexistence of a quark Fermi sea with a baryonic infrared description, thereby realizing the quarkyonic picture from first principles.