Matrix model of two-color one-flavor QCD: The ultrastrong coupling regime

Using variational methods, we numerically investigate the matrix model for the two-color QCD coupled to a single quark (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mtext>matrix-QCD</a:mtext><a:mrow><a:mn>2</a:mn><a:mo>,</a:mo><a:mn>1</a:mn></a:mrow></a:msub></a:math>) in the limit of ultrastrong Yang-Mills coupling (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>g</c:mi><c:mo>=</c:mo><c:mi>∞</c:mi></c:math>). The spectrum of the model has superselection sectors labeled by baryon number <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>B</e:mi></e:math> and spin <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>J</g:mi></g:math>. We study sectors with <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>B</i:mi><i:mo>=</i:mo><i:mn>0</i:mn></i:math>, 1, 2 and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>J</k:mi><k:mo>=</k:mo><k:mn>0</k:mn></k:math>, 1, which may be organized as mesons, (anti-)diquarks and (anti-)tetraquarks. For each of these sectors, we study the properties of the respective ground states in both chiral and heavy quark limits, and uncover a rich quantum phase transition (QPT) structure. We also investigate the division of the total spin between the glue and the quark and show that glue contribution is significant for several of these sectors. For the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mo stretchy="false">(</m:mo><m:mi>B</m:mi><m:mo>,</m:mo><m:mi>J</m:mi><m:mo stretchy="false">)</m:mo><m:mo>=</m:mo><m:mo stretchy="false">(</m:mo><m:mn>0</m:mn><m:mo>,</m:mo><m:mn>0</m:mn><m:mo stretchy="false">)</m:mo></m:math> sector, we find that the dominant glue contribution to the ground state comes from reducible connections. Finally, in the presence of nontrivial baryon chemical potential <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>μ</s:mi></s:math>, we construct the phase diagram of the model. For sufficiently large <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>μ</u:mi></u:math>, we find that the ground state of the theory may have nonzero spin. Published by the American Physical Society 2024