arXiv:2311.11643

Dense $\textrm{QCD}_2$ with matrix product states

Tomoya Hayata, Yoshimasa Hidaka, Kentaro Nishimura

Published Nov 20, 2023• 1 citation

Abstract

We study one-flavor $\mathrm{SU}(2)$ and $\mathrm{SU}(3)$ lattice QCD in ($1+1$) dimensions at zero temperature and finite density using matrix product states and the density matrix renormalization group. We compute physical observables such as the equation of state, chiral condensate, and quark distribution function as functions of the baryon number density. As a physical implication, we discuss the inhomogeneous phase at nonzero baryon density, where the chiral condensate is inhomogeneous, and baryons form a crystal. We also discuss how the dynamical degrees of freedom change from hadrons to quarks through the formation of quark Fermi seas.

DOI: 10.48550/arxiv.2311.11643

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arXiv:2311.11643

Dense $\textrm{QCD}_2$ with matrix product statesDense $\textrm{QCD}_2$ with matrix product states

Tomoya Hayata, Yoshimasa Hidaka, Kentaro Nishimura

Published Nov 20, 2023• 1 citation

arXiv HTML PDF

Abstract

We study one-flavor

\mathrm{SU}(2)

and

\mathrm{SU}(3)

lattice QCD in (

1+1

) dimensions at zero temperature and finite density using matrix product states and the density matrix renormalization group. We compute physical observables such as the equation of state, chiral condensate, and quark distribution function as functions of the baryon number density. As a physical implication, we discuss the inhomogeneous phase at nonzero baryon density, where the chiral condensate is inhomogeneous, and baryons form a crystal. We also discuss how the dynamical degrees of freedom change from hadrons to quarks through the formation of quark Fermi seas.

DOI: 10.48550/arxiv.2311.11643

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Dense

\textrm{QCD}_2

with matrix product states

We study one-flavor

\mathrm{SU}(2)

and

\mathrm{SU}(3)

lattice QCD in (

1+1

Dense

\mathrm{QC_2D_2}

with uniform matrix product states

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.

We perform a zero temperature analysis of a non-Abelian lattice gauge model corresponding to an SU(3) Yang-Mills theory in

1+1\mathrm{D}

at low energies. Specifically, we characterize the model ground states via gauge-invariant matrix product states, identifying its phase diagram at finite density as a function of the matter-gauge interaction coupling, the quark filling, and their bare mass. Overall, we observe an extreme robustness of baryons: For positive free-field energy couplings, all detected phases exhibit colorless quasiparticles, a strong numerical hint that QCD does not deconfine in 1D. Additionally, we show that, having access to finite-density properties, it is possible to study the stability of composite particles, including multibaryon bound states such as the deuteron.