Duality study of the chiral Heisenberg-Gross-Neveu model in 1+1 dimensions - Thies, Michael (Physical Review D, 2020)
We consider a version of the Gross-Neveu model in 1+1 dimensions with discrete chiral and continuous flavor symmetry (isospin). In 2+1 dimensions, this model is known as the chiral Heisenberg-Gross-Neveu model. Spontaneous symmetry breaking and the emergence of two massless and one massive scalar bosons are shown. A duality to the Nambu-Jona-Lasinio model with isospin is exhibited, provided that the isovector pseudoscalar mean field is constrained to a plane in isospin space. This enables us to find the phase diagram as a function of temperature, chemical potential, and isospin chemical potential as well as twisted kinks. A bare mass term acts quite differently when added to this model as compared to other chiral variants of the Gross-Neveu model.
CRIS-Team Scopus Importer:2020-11-27

Exact tricritical point from next-to-leading-order stability analysis - Thies, Michael (Physical Review D, 2022)
In the massive chiral Gross-Neveu model, a phase boundary separates a homogeneous from an inhomogeneous phase. It consists of two parts, a second order line and a first order line, joined at a tricritical point. Whereas the first order phase boundary requires a full, numerical Hartree-Fock calculation, the second order phase boundary can be determined exactly and with less effort by a perturbative stability analysis. We extend this stability analysis to higher order perturbation theory. This enables us to locate the tricritical point exactly, without need to perform a Hartree-Fock calculation. Divergencies due to the emergence of spectral gaps in a spatially periodic perturbation are handled using well established tools from many body theory.
CRIS-Team WoS Importer:2022-12-30

First-order phase boundaries of the massive (1+1)-dimensional Nambu-Jona-Lasinio model with isospin - Thies, Michael (Physical Review D, 2020)
The massive two-dimensional Nambu-Jona-Lasinio model with isospin (isoNJL) is reconsidered in the large N-c limit. We continue the exploration of its phase diagram by constructing missing first-order phase boundaries. At zero temperature, a phase boundary in the plane of baryon and isospin chemical potentials separates the vacuum from a crystal phase. We derive it from the baryon spectrum of the isoNJL model which, in turn, is obtained via a numerical Hartree-Fock (HF) calculation. At finite temperature, a first-order phase boundary sheet is found using a thermal HF calculation. It interpolates smoothly between the zero temperature phase boundary and the perturbative sheet. The calculations remain tractable owing to the assumption that the charged pion condensate vanishes. In that case, most of the calculations can be done with methods developed in the past for solving the massive one-flavor NJL model.
CRIS-Team WoS Importer:2020-04-28

Gross-Neveu model with O (2)L× O (2)R chiral symmetry: Duality with Zakharov-Mikhailov model and large N solution - Thies, Michael (Physical Review D, 2023)
The two-flavor Gross-Neveu model with U(2)L×U(2)R chiral symmetry in 1+1 dimensions is used to construct a novel variant of four-fermion theories with O(2)L×O(2)R chiral symmetry. The spontaneous breaking of the group O(2), a continuous group with two connected components (rotations and reflections), gives rise to new phenomena. It is ideally suited to describe a situation where two distinct kinds of condensation compete, in particular chiral symmetry breaking (particle-hole condensation) and Cooper pairing (particle-particle condensation). After solving the O(2) chiral Gross-Neveu model in detail, we demonstrate that it is dual to another classically integrable model due to Zakharov and Mikhailov. The duality enables us to solve the quantum version of this model in the large N limit with semiclassical methods, supporting its integrability at the quantum level. The resulting model is the unique four-fermion theory sharing the full Pauli-Gürsey symmetry with free, massless fermions ("perfect Gross-Neveu model") and provides us with a solvable model for competing chiral and Cooper pair condensates, including explicit soliton dynamics and the phase diagram.
CRIS-Team Scopus Importer:2023-05-26

Nonperturbative phase boundaries in the Gross-Neveu model from a stability analysis - Thies, Michael (Physical Review D, 2024)
Two out of three phase boundaries of the 1+1-dimensional Gross-Neveu model in the chiral limit can be obtained from a standard, perturbative stability analysis of the homogeneous phases. The third one separating the massive homogeneous phase from the kink crystal is nonperturbative and could so far only be inferred from the full solution of the model. We show that this phase boundary can also be obtained via a modified stability analysis, based on the thermodynamic potential of a single kink or baryon. The same method works for the massive Gross-Neveu model, so that all phase boundaries of the Gross-Neveu model could have been predicted quantitatively without prior knowledge of the full crystal solution.
CRIS-Team Scopus Importer:2024-11-29

Phase structure of the (1+1)-dimensional Nambu-Jona-Lasinio model with isospin - Thies, Michael (Physical Review D, 2020)
The phase diagram of the two-dimensional Nambu-Jona-Lasinio model with isospin is explored in the large N-c limit with semiclassical methods. We consider finite temperature and include chemical potentials for all conserved charges. In the chiral limit, a full analytical solution is presented, expressed in terms of known results for the single-flavor Gross-Neveu and Nambu-Jona-Lasinio models. A novel crystalline structure appears and is shown explicitly to be thermodynamically more stable than the homogeneous phase at zero temperature. If we include a bare fermion mass, the problem reduces again to solved problems in one-flavor models provided that either the fermionic or the isospin chemical potentials vanish. In the general case, a stability analysis is used to construct the perturbative phase boundary between homogeneous and inhomogeneous phases. This is sufficient to get a good overview of the complete phase diagram. Missing nonperturbative phase boundaries requiring a full numerical Hartree-Fock calculation will be presented in future work.
CRIS-Team WoS Importer:2020-01-31

Tricritical curve of massive chiral Gross-Neveu model with isospin - Thies, Michael (Physical Review D, 2022)
We reconsider the two-flavor version of the massive chiral Gross-Neveu model in 1+1 dimensions. Its phase diagram as a function of baryon chemical potential, isospin chemical potential, and temperature has previously been explored. We recapitulate the results, adding the missing tricritical curves. They can be determined exactly by extending the standard stability analysis, using fourth-order almost degenerate perturbation theory. Results for three different bare masses are presented and discussed.
CRIS-Team Scopus Importer:2022-10-21

Twisted kink dynamics in multiflavor chiral Gross-Neveu model - Thies, Michael (Journal of Physics A: Mathematical and Theoretical, 2022)
The Gross-Neveu model with U-L(N (f)) x U-R(N (f)) chiral symmetry is reconsidered in the large N (c) limit. The known analytical solution for the time dependent interaction of any number of twisted kinks and breathers is cast into a more revealing form. The (x, t)-dependent factors are isolated from constant coefficients and twist matrices. These latter generalize the twist phases of the single flavor model. The crucial tool is an identity for the inverse of a sum of two square matrices, derived from the known formula for the determinant of such a sum.
CRIS-Team WoS Importer:2021-12-24