We consider a generalization of the Thirring model in 2+1 dimensions at finite density. We employ stochastic quantization and check for the applicability in the finite density case to circumvent the sign problem. To this end we derive analytical results in the heavy dense limit and compare with numerical ones obtained from a complex Langevin evolution. Furthermore we make use of indirect indicators to check for incorrect convergence of the underlying complex Langevin evolution. The method allows the numerical evaluation of observables at arbitrary values of the chemical potential. We evaluate the results and compare to the (0 + 1)-dimensional case.

In this paper we discuss one-dimensional models reproducing some features of quantum electrodynamics and quantum chromodynamics at nonzero density and temperature. Since a severe sign problem makes a numerical treatment of QED and QCD at high density difficult, such models help to explore various effects peculiar to the full theory. Studying them gives insights into the large density behavior of the Polyakov loop by taking both bosonic and fermionic degrees of freedom into account, although in one dimension only the implementation of a global gauge symmetry is possible. For these models we evaluate the respective partition functions and discuss several observables as well as the Silver Blaze phenomenon.

We consider a generalized Thirring model in 0 + 1 dimensions at finite density. In order to deal with the resulting sign problem we employ stochastic quantization, i.e., a complex Langevin evolution. We investigate the convergence properties of this approach and check in which parameter regions complex Langevin evolutions are applicable in this setting. To this end we derive numerous analytical results and compare directly with numerical results. In addition we employ indirect indicators to check for correctness. Finally we interpret and discuss our findings.

We follow up on a suggestion by Adams and construct explicit domain wall fermion operators with staggered kernels. We compare different domain wall formulations, namely the standard construction as well as Boriçi's modified and Chiu's optimal construction, utilizing both Wilson and staggered kernels. In the process, we generalize the staggered kernels to arbitrary even dimensions and introduce both truncated and optimal staggered domain wall fermions. Some numerical investigations are carried out in the (1 + 1)-dimensional setting of the Schwinger model, where we explore spectral properties of the bulk, effective and overlap Dirac operators in the free-field case, on quenched thermalized gauge configurations and on smooth topological configurations. We compare different formulations using the effective mass, deviations from normality and violations of the Ginsparg-Wilson relation as measures of chirality.