Simulating <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo><mml:mi mathvariant="normal">D</mml:mi></mml:math> SU(2) Yang-Mills lattice gauge theory at finite density with tensor networks

Abstract

We numerically simulate a non-Abelian lattice gauge theory in two spatial dimensions, with tensor networks (TN), up to intermediate sizes (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mo>&gt;</a:mo><a:mn>30</a:mn></a:mrow></a:math> matter sites) well beyond exact diagonalization. We focus on the SU(2) Yang-Mills model in Hamiltonian formulation, with dynamical matter and minimally truncated gauge field (hardcore gluon). Thanks to the TN sign-problem-free approach, we characterize the phase diagram of the model at zero and finite baryon number as a function of the quark bare mass and color charge. At intermediate system sizes, we detect a liquid phase of quark-pair bound-state quasiparticles (baryons), whose mass is finite towards the continuum limit. Interesting phenomena arise at the transition boundary where color-electric and color-magnetic terms are maximally frustrated: For low quark masses, we see traces of potential deconfinement, while for high masses, signatures of a possible topological order. Published by the American Physical Society 2024

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