Phases of 2D massless QCD with qubit regularization

We investigate the possibility of reproducing the continuum physics of 2D <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>S</a:mi><a:mi>U</a:mi></a:mrow><a:mo stretchy="false">(</a:mo><a:mi>N</a:mi><a:mo stretchy="false">)</a:mo></a:math> gauge theory coupled to a single flavor of massless Dirac fermion using qubit regularization. The continuum theory is described by <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>N</e:mi></e:math> free fermions in the ultraviolet (UV) and a coset Wess-Zumino-Witten (WZW) model in the infrared (IR). In this work, we first explore how well these features can be reproduced using the Kogut-Susskind (KS) Hamiltonian with a finite-dimensional link Hilbert space and a generalized Hubbard coupling. We do this by analyzing the renormalization group (RG) flow diagram of the continuum theory and identifying important phases of the theory. Using strong coupling expansions, we show that our lattice model exhibits a gapped dimer phase and a spin-chain phase. Furthermore, for <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>N</g:mi><g:mo>=</g:mo><g:mn>2</g:mn></g:math>, using tensor network methods, we show that there is a second-order phase transition between these two phases, which we identify as the critical surface of the continuum theory that connects the IR and UV fixed points. In the IR, we identify the critical theory at the transition as the expected <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mrow><i:mi>S</i:mi><i:mi>U</i:mi></i:mrow><i:mo stretchy="false">(</i:mo><i:mn>2</i:mn><i:msub><i:mo stretchy="false">)</i:mo><i:mn>1</i:mn></i:msub></i:math> WZW model. Lastly, we argue that modifications of our model may allow the study of the UV physics of free fermions.