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Michael Thies

Publications and source records attributed to Michael Thies.

53 records · Page 3Linked to original sources
arXiv2007

Tricritical behavior of the massive chiral Gross-Neveu model

The phase diagram of the massive chiral Gross-Neveu model (the 1+1-dimensional Nambu-Jona-Lasinio model at large N) is investigated in the vicinity of the tricritical point. Using the derivative expansion, the grand canonical potential is cast into the form of a Ginzburg-Landau effective action. Minimization of this action by variational and numerical methods reveals both 1st and 2nd order phase transitions to a chiral crystal phase, separated by a tricritical line. These findings are contrasted to the massive Gross-Neveu model with discrete chiral symmetry where only 2nd order transitions have been observed.

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arXiv2006

How to get from imaginary to real chemical potential

Using the exactly solvable Gross-Neveu model as theoretical laboratory, we analyse in detail the relationship between a relativistic quantum field theory at real and imaginary chemical potential. We find that one can retrieve the full information about the phase diagram of the theory from an imaginary chemical potential calculation. The prerequisite is to evaluate and analytically continue the effective potential for the chiral order parameter, rather than thermodynamic observables or phase boundaries. In the case of an inhomogeneous phase, one needs to compute the full effective action, a functional of the space-dependent order parameter, at imaginary chemical potential.

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arXiv2006

From relativistic quantum fields to condensed matter and back again: Updating the Gross-Neveu phase diagram

During the last few years, the phase diagram of the large N Gross-Neveu model in 1+1 dimensions at finite temperature and chemical potential has undergone a major revision. Here we present a streamlined account of this development, collecting the most important results. Quasi-one-dimensional condensed matter systems like conducting polymers provide real physical systems which can be approximately described by the Gross-Neveu model and have played some role in establishing its phase structure. The kink-antikink phase found at low temperatures is closely related to inhomogeneous superconductors in the Larkin-Ovchinnikov-Fulde-Ferrell phase. With the complete phase diagram at hand, the Gross-Neveu model can now serve as a firm testing ground for new algorithms and theoretical ideas.

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arXiv2005

Full Phase Diagram of the Massive Gross-Neveu Model

The massive Gross-Neveu model is solved in the large N limit at finite temperature and chemical potential. The scalar potential is given in terms of Jacobi elliptic functions. It contains three parameters which are determined by transcendental equations. Self-consistency of the scalar potential is proved. The phase diagram for non-zero bare quark mass is found to contain a kink-antikink crystal phase as well as a massive fermion gas phase featuring a cross-over from light to heavy effective fermion mass. For zero bare quark mass we recover the three known phases kink-antikink crystal, massless fermion gas, and massive fermion gas. All phase transitions are shown to be of second order. Equations for the phase boundaries are given and solved numerically. Implications on condensed matter physics are indicated where our results generalize the bipolaron lattice in non-degenerate conducting polymers to finite temperature.

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arXiv2005

The phase diagram of the massive Gross-Neveu model, revisited

The massive Gross-Neveu model is solved in the large N limit at finite temperature and chemical potential. The phase diagram features a kink-antikink crystal phase which was missed in previous works. Translated into the framework of condensed matter physics our results generalize the bipolaron lattice in non-degenerate conducting polymers to finite temperature.

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arXiv2005

Phase Diagram of the Gross-Neveu Model: Exact Results and Condensed Matter Precursors

Recently the revised phase diagram of the (large N) Gross-Neveu model in 1+1 dimensions with discrete chiral symmetry has been determined numerically. It features three phases, a massless and a massive Fermi gas and a kink-antikink crystal. Here we investigate the phase diagram by analytical means, mapping the Dirac-Hartree-Fock equation onto the non-relativistic Schroedinger equation with the (single gap) Lame potential. It is pointed out that mathematically identical phase diagrams appeared in the condensed matter literature some time ago in the context of the Peierls-Froehlich model and ferromagnetic superconductors.

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arXiv2005

From non-degenerate conducting polymers to dense matter in the massive Gross-Neveu model

Using results from the theory of non-degenerate conducting polymers like cis-polyacetylene, we generalize our previous work on dense baryonic matter and the soliton crystal in the massless Gross-Neveu model to finite bare fermion mass. In the large N limit, the exact crystal ground state can be constructed analytically, in close analogy to the bipolaron lattice in polymers. These findings are contrasted to the standard scenario with homogeneous phases only and a first order phase transition at a critical chemical potential.

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arXiv2005

Baryons in Massive Gross-Neveu Models

Baryons in the large N limit of (1+1)-dimensional Gross-Neveu models with either discrete or continuous chiral symmetry have long been known. We generalize their construction to the case where the symmetry is explicitly broken by a bare mass term in the Lagrangian. In the discrete symmetry case, the exact solution is found for arbitrary bare fermion mass, using the Hartree-Fock approach. It is mathematically closely related to polarons and bipolarons in conducting polymers. In the continuous symmetry case, a derivative expansion allows us to rederive a formerly proposed Skyrme-type model and to compute systematically corrections to the leading order description based on an effective sine-Gordon theory.

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arXiv2003

Analytical solution of the Gross-Neveu model at finite density

Recent numerical calculations have shown that the ground state of the Gross-Neveu model at finite density is a crystal. Guided by these results, we can now present the analytical solution to this problem in terms of elliptic functions. The scalar potential is the superpotential of the non-relativistic Lame Hamiltonian. This model can also serve as analytically solvable toy model for a relativistic superconductor in the Larkin-Ovchinnikov-Fulde-Ferrell phase.

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arXiv2003

Revised Phase Diagram of the Gross-Neveu Model

We confirm earlier hints that the conventional phase diagram of the discrete chiral Gross-Neveu model in the large N limit is deficient at non-zero chemical potential. We present the corrected phase diagram constructed in mean field theory. It has three different phases, including a kink-antikink crystal phase. All transitions are second order. The driving mechanism for the new structure of baryonic matter in the Gross-Neveu model is an Overhauser type instability with gap formation at the Fermi surface.

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arXiv2002

Chiral Condensate and Short-Time Evolution of QCD(1+1) on the Light-Cone

Chiral condensates in the trivial light-cone vacuum emerge if defined as short-time limits of fermion propagators. In gauge theories, the necessary inclusion of a gauge string in combination with the characteristic light-cone infrared singularities contain the relevant non-perturbative ingredients responsible for formation of the condensate, as demonstrated for the 't Hooft model.

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arXiv2001

No First-Order Phase Transition in the Gross-Neveu Model?

Within a variational calculation we investigate the role of baryons for the structure of dense matter in the Gross-Neveu model. We construct a trial ground state at finite baryon density which breaks translational invariance. Its scalar potential interpolates between widely spaced kinks and antikinks at low density and the value zero at infinite density. Its energy is lower than the one of the standard Fermi gas at all densities considered. This suggests that the discrete gamma_5 symmetry of the Gross-Neveu model does not get restored in a first order phase transition at finite density, at variance with common wisdom.

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arXiv2000

2d Model Field Theories at Finite Temperature and Density

In certain 1+1 dimensional field theoretic toy models, one can go all the way from microscopic quarks via the hadron spectrum to the properties of hot and dense baryonic matter in an essentially analytic way. This "miracle" is illustrated through case studies of two popular large N models, the Gross-Neveu and the 't Hooft model - caricatures of the Nambu-Jona-Lasinio model and real QCD, respectively. The main emphasis will be on aspects related to spontaneous symmetry breaking (discrete or continuous chiral symmetry, translational invariance) and confinement.

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arXiv2000

Phases and Residual Gauge Symmetries of Higgs Models

After elimination of the redundant variables, gauge theories may still exhibit symmetries associated with the gauge fields. The role of these residual gauge symmetries is discussed within the Abelian Higgs model and the Georgi-Glashow model. In the different phases of these models, these symmetries are realized differently. The characteristics of emergence and disappearance of the symmetries are studied in detail and the implications for the dynamics in Coulomb, Higgs, and confining phases are discussed.

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arXiv2000

Emergence of Skyrme crystal in Gross-Neveu and 't Hooft models at finite density

We study two-dimensional, large $N$ field theoretic models (Gross-Neveu model, 't Hooft model) at finite baryon density near the chiral limit. The same mechanism which leads to massless baryons in these models induces a breakdown of translational invariance at any finite density. In the chiral limit baryonic matter is characterized by a spatially varying chiral angle with a wave number depending only on the density. For small bare quark masses a sine-Gordon kink chain is obtained which may be regarded as simplest realization of the Skyrme crystal for nuclear matter. Characteristic differences between confining and non-confining models are pointed out.

hep-th↗
arXiv2000

Decompactification of space or time in large N QCD_2

QCD_2 with fundamental quarks on a cylinder is solved to leading order in the 1/N expansion, including the zero mode gluons. As a result of the non-perturbative dynamics of these gauge degrees of freedom, the compact space-time direction gets effectively decompactified. In a thermodynamic interpretation, this implies that there is no pressure of order N and that the chiral condensate of order N is temperature independent. These findings are consistent with confinement of quarks, rule out both chiral and deconfining phase transitions in the finite temperature 't Hooft model, and help to resolve some controversial issues in the literature

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