By investigating the SU(2) Yang-Mills matrix model coupled to fundamental fermions in the adiabatic limit, we demonstrate quantum critical behaviour at special corners of the gauge field configuration space. The quantum scalar potential for the gauge field induced by the fermions diverges at the corners and is intimately related to points of enhanced degeneracy of the fermionic Hamiltonian. This in turn leads to superselection sectors in the Hilbert space of the gauge field, the ground states in different sectors being orthogonal to each other. As a consequence of our analysis, we show that 2-color quantum chromodynamics coupled to two Weyl fermions has three quantum phases. When coupled to a massless Dirac fermion, the number of quantum phases is four. One of these phases is the color-spin locked phase.
We numerically simulate a non-Abelian lattice gauge theory in two spatial dimensions, with tensor networks (TN), up to intermediate sizes ( > 30 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
In this paper we study a (
1+1)-dimensional version of the famous Nambu--Jona-Lasinio model of quantum chromodynamics (QCD2) both at zero and at finite baryon density. We use nonperturbative techniques (non-Abelian bosonization and the truncated conformal spectrum approach). When the baryon chemical potential, $\ensuremath{\mu}$, is zero, we describe the formation of fermion three-quark (nucleons and $\mathrm{\ensuremath{\Delta}}$ baryons) and boson (two-quark mesons, six-quark deuterons) bound states. We also study at $\ensuremath{\mu}=0$ the formation of a topologically nontrivial phase. When the chemical potential exceeds the critical value and a finite baryon density appears, the model has a rich phase diagram which includes phases with a density wave and superfluid quasi-long-range (QLR) order, as well as a phase of a baryon Tomonaga-Luttinger liquid (strange metal). The QLR order results in either a condensation of scalar mesons (the density wave) or six-quark bound states (deuterons).
The phase diagram of QCD is a central research topic in modern particle physics. Its calculation, however, is notoriously difficult especially when not only nonzero temperatures
T but also non-vanishing baryon densities are considered – as is relevant for heavy‑ion collisions or inside large neutron stars. At the theoretical level, nonzero baryon densities are achieved by introducing a nonzero chemical potential
μ, which creates a particle-antiparticle asymmetry. It turns out that for nonzero chemical potential, the fermion determinant is no longer real but complex, and therefore standard approaches based on importance sampling break down. In the literature, this is commonly referred to as the sign problem. In order to circumvent this sign problem, a variety of methods has been proposed. Examples include a Taylor expansion in
μ, reweighting, complex Langevin, thimbles or path optimization. Nevertheless, none of the proposed remedies can successfully reach regimes in which
μ/T>1, and therefore even today the full QCD phase diagram in the
μ−T plane cannot be calculated. There is a promising further approach, called tensor-network approach, that differs crucially from all of the aforementioned approaches. In this approach, the partition function is written as a contraction of a large number of local tensors. Of special relevance is the higher order tensor renormalization group (HOTRG) approach, which can be applied for arbitrary number of dimensions, and in particular its generalization, the Grassmann HOTRG (GHOTRG) approach, which is applicable to theories including fermions. Recently, GHOTRG was tailored to strong-coupling QCD using one flavor of staggered quarks in two dimensions. It was observed that, for a non‑zero chemical potential, no numerical instabilities arise. In this thesis, we go beyond both the strong-coupling limit and the single-flavor case. We express the partition function of lattice QCD with staggered fermions in the strong-coupling expansion in terms of a tensor network. This is done for an arbitrary number of dimensions, flavors, and orders of the strong-coupling expansion. Further, the GHOTRG approach is extended such that every coefficient
Zn of the partition function
Z=∑nZnβn can be calculated separately. Finally, numerical results in two dimensions are studied.