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We consider asymptotically free nonlinear sigma models in two dimensions which, due to their internal symmetries, allow for a conserved charge. Introducing nonzero chemical potential for the SO(2) subgroup of the symmetry group, we discuss two expected phase transitions, which are related to charge condensation and percolation of merons, respectively. The latter are topological objects with half integer charge similar to vortices in the Abelianized O(2) theory that emerge for large chemical potentials due to the suppression of the complementary field components. We conjecture a particular ordering of these transitions supported by large N calculations, and discuss dualities helpful for the understanding of these systems in the continuum and on the lattice. We suggest that a similar behavior is to be expected in QCD at nonzero density. [ABSTRACT FROM AUTHOR]

We analyze the Euclidean version of supersymmetric quantum mechanics on the lattice by means of a numerical path integral. We consider two different lattice derivatives and improve the actions containing them with respect to supersymmetry by systematically adding interaction terms with nonzero extent. To quantize this improvement, we measure boson and fermion masses and Ward identities for the naive as well as the improved models. The masses are degenerate in all models, but the magnitude of the Ward identities decreases significantly for both derivative operators using the improved actions. This is a clear sign that the breaking of supersymmetry due to lattice artifacts is reduced. [ABSTRACT FROM AUTHOR]

We give analytical and numerical solutions for the zero modes of the Dirac operator in topological SU(2) gauge backgrounds at nonzero chemical potential. Continuation from imaginary to real chemical potential is used to systematically derive analytical zero modes for calorons at arbitrary holonomy and, in particular limits, for instantons and dyons (magnetic monopoles). For the latter a spherical ansatz is explored as well. All the zero modes exhibit stronger peaks at the core and negative regions in their densities. We discuss the structure of the corresponding overlap matrix elements. For discretized calorons on the lattice we consider the staggered operator and show that it does possess (quartet quasi)zero modes, whose eigenmodes agree very well with the continuum profiles, for zero as well as nonzero chemical potential. [ABSTRACT FROM AUTHOR]

We provide a status report on the advances in blocking-inspired supersymmetric actions. This is done with the example of interacting supersymmetric quantum mechanics as well as the Wess-Zumino model. We investigate in particular the implications of a nontrivial realization of translational symmetry on the lattice in this approach. We also discuss the locality of symmetry generators. [ABSTRACT FROM AUTHOR]

We explain the physical nature of the subset solution to the sign problem in chiral random matrix theory: the subset sum over configurations is shown to project out the canonical determinant with zero quark charge from a given configuration. As the grand canonical chiral random matrix partition function is independent of the chemical potential, the zero-quark-charge sector provides the full result. [ABSTRACT FROM AUTHOR]

As an approach to describe the long-range properties of non-Abelian gauge theories at nonzero temperature T < Tc, we consider a noninteracting ensemble of dyons (magnetic monopoles) with nontrivial holonomy. We show analytically that the quark-antiquark free energy from the Polyakov loop correlator grows linearly with the distance, and how the string tension scales with the dyon density. In numerical treatments, the long-range tails of the dyon fields cause severe finite-volume effects. Therefore, we demonstrate the application of Ewald's summation method to this system. Finite-volume effects are shown to be under control, which is a crucial requirement for numerical studies of interacting dyon ensembles. [ABSTRACT FROM AUTHOR]

We introduce dressed Wilson loops as a novel confinement observable. It consists of closed planar loops of arbitrary geometry but fixed area, and its expectation values decay with the latter. The construction of dressed Wilson loops is based on chiral condensates in response to magnetic and electric fields, thus linking different physical concepts. We present results for generalized condensates and dressed Wilson loops on dynamical lattice configurations and confirm the agreement with conventional Wilson loops in the limit of large probe mass. We comment on the renormalization of dressed Wilson loops. [ABSTRACT FROM AUTHOR]

We investigate low-lying fermion modes in SU(2) gauge theory at temperatures above the phase transition. Both staggered and overlap spectra reveal transitions from chaotic (random matrix) to integrable (Poissonian) behavior accompanied by an increasing localization of the eigenmodes. We show that the latter are trapped by local Polyakov loop fluctuations. Islands of such "wrong" Polyakov loops can therefore be viewed as defects leading to Anderson localization in gauge theories. We find strong similarities in the spatial profile of these localized staggered and overlap eigenmodes. We discuss possible interpretations of this finding and present a sparse random matrix model that reproduces these features. [ABSTRACT FROM AUTHOR]

Perturbative expansions in many physical systems yield "only" asymptotic series which are not even Borel resummable. Interestingly, the corresponding ambiguities point to nonperturbative physics. We numerically verify this renormalon mechanism for the first time in two-dimensional sigma models, that, like four-dimensional gauge theories, are asymptotically free and generate a strong scale through dimensional transmutation. We perturbatively expand the energy through a numerical version of stochastic quantization. In contrast to the first energy coefficients, the high-order coefficients are independent on the rank of the model. Technically, they require a sophisticated analysis of finite volume effects and the continuum limit of the discretized model. Although the individual coefficients do not grow factorially (yet), but rather decrease strongly, the ratios of consecutive coefficients clearly obey the renormalon asymptotics. [ABSTRACT FROM AUTHOR]

We numerically study the spectral properties, the entanglement and the zero-temperature phase structure at nonvanishing chemical potential of the O(3) nonlinear sigma model. Using matrix product states, a particular kind of one-dimensional tensor network state, we show that we are able to reach the asymptotic scaling regime and to reproduce the analytical predictions for the mass gap at vanishing chemical potential. In addition, we study the scaling of the entanglement entropy towards the continuum limit obtaining a central charge consistent with 2. Moreover, our approach does not suffer from the sign problem and we also explore the phase structure of the model for nonzero chemical potential and map out the location of the transitions between different charge sectors with high precision. [ABSTRACT FROM AUTHOR]

We analyze two-dimensional nonlinear sigma models at nonzero chemical potentials, which are governed by a complex action. In the spirit of contour deformations (thimbles), we extend the fields into the complex plane, which allows us to incorporate the chemical potentials μ as twisted boundary conditions. We write down the equations of motion and find exact BPS-like solutions in terms of pairs of (anti)holomorphic functions, in particular generalizations of unit charge and fractional instantons to generic μ. The decay of these solutions is controlled by the imaginary part of μ and a vanishing imaginary part causes jumps in the action. We analyze how the total charge is distributed into localized objects and to what extent these are characterized by topology. [ABSTRACT FROM AUTHOR]

We consider QCD at strong coupling with scalar quarks coupled to a chemical potential. Performing the link integrals we present a diagrammatic representation of the path integral weight. It is based on mesonic and baryonic building blocks, in close analogy to fermionic QCD. Likewise, the baryon loops are subject to a manifest conservation of the baryon number. The sign problem is expected to disappear in this representation and we do confirm this for three flavors, where a scalar baryon can be built and, thus, a dependence on the chemical potential occurs. For higher flavor number, we analyze examples for a potential sign problem in the baryon sector and conjecture that all weights are positive upon exploring the current conservation of each flavor. [ABSTRACT FROM AUTHOR]

We discuss the thermodynamics of the O(3) nonlinear sigma model in 1 + 1 dimensions at nonzero chemical potential (equivalent to a magnetic field). In its conventional field theory representation the model suffers from a sign problem. By dualizing the model, we are able to fully access the nonzero density regime of an asymptotically free theory with dynamical mass gap at arbitrary chemical potential values. We find a quantum phase transition at zero temperature where as a function of the chemical potential the density assumes a nonzero value. Measuring the spin stiffness we present evidence for a corresponding dynamical critical exponent z close to 2. The low energy O(3) model is conjectured to be described by a massive boson triplet with repulsive interactions. We confirm the universal square-root behavior expected for such a system at low density (and temperature) and compare our data to the results of Bethe Ansatz solutions of the relativistic and nonrelativistic one-dimensional Bose gas. We also comment on a potential Berezinskii-Kosterlitz-Thouless transition at nonzero density. [ABSTRACT FROM AUTHOR]