The Schrödinger functional for Gross-Neveu models

We compute a variational approximation to the entanglement entropy for states of the Gross-Neveu model. Further, we examine the functional dependence of the entanglement entropy on the coupling and number of colors in the theory. Our results display non-peturbative behavior. It is shown that the entanglement entropy is monotonically decreasing and convex with respect to the coupling. We also show how the behavior of the entanglement entropy under renormalization group transformations is related to the beta function of the Gross-Neveu model, and compare these renormalization group results to our previous work on interacting scalar field theories.We compute a variational approximation to the entanglement entropy for states of the Gross-Neveu model. Further, we examine the functional dependence of the entanglement entropy on the coupling and number of colors in the theory. Our results display non-peturbative behavior. It is shown that the entanglement entropy is monotonically decreasing and convex with respect to the coupling. We also show how the behavior of the entanglement entropy under renormalization group transformations is related to the beta function of the Gross-Neveu model, and compare these renormalization group results to our previous work on interacting scalar field theories.

arXiv:1512.00023Nov 30, 20154 citations

Generalized Schrödinger representations. II

Annals of PhysicsSep 1, 19690 citations

Ising and Gross-Neveu model in next-to-leading order

Benjamin Knorr

We study scalar and chiral fermionic models in next-to-leading order with the help of the functional renormalization group. Their critical behavior is of special interest in condensed-matter systems, in particular graphene. To derive the $\ensuremath{\beta}$ functions, we make extensive use of computer algebra. The resulting flow equations were solved with pseudospectral methods to guarantee high accuracy. New estimates of critical quantities for both the Ising and the Gross-Neveu model are provided. For the Ising model, the estimates agree with earlier renormalization-group studies of the same level of approximation. By contrast, the approximation for the Gross-Neveu model retains many more operators than all earlier studies. For two Dirac fermions, the results agree with both lattice and large- ${N}_{f}$ calculations, but for a single flavor, different methods disagree quantitatively, and further studies are necessary.We study scalar and chiral fermionic models in next-to-leading order with the help of the functional renormalization group. Their critical behavior is of special interest in condensed-matter systems, in particular graphene. To derive the $\ensuremath{\beta}$ functions, we make extensive use of computer algebra. The resulting flow equations were solved with pseudospectral methods to guarantee high accuracy. New estimates of critical quantities for both the Ising and the Gross-Neveu model are provided. For the Ising model, the estimates agree with earlier renormalization-group studies of the same level of approximation. By contrast, the approximation for the Gross-Neveu model retains many more operators than all earlier studies. For two Dirac fermions, the results agree with both lattice and large-${N}_{f}$ calculations, but for a single flavor, different methods disagree quantitatively, and further studies are necessary.

arXiv:1609.03824Physical review. B./Physical review. BDec 1, 201660 citations

Generalized schrödinger representations. II

John S. Nodvik

Annals of PhysicsOct 1, 19692 citations

Form factors of the O(6) Gross Neveu-model

Hrachya M. Babujian, Angela Foerster, Michael Karowski

The isomorphism $SU(4) \simeq O(6)$ is used to construct the form factors of the O(6) Gross-Neveu model as bound state form factors of the SU(4) chiral Gross-Neveu model. This technique is generalized and is then applied to use the O(6) as the starting point of the nesting procedure to obtain the O(N) form factors for general even N.The isomorphism $SU(4) \simeq O(6)$ is used to construct the form factors of the O(6) Gross-Neveu model as bound state form factors of the SU(4) chiral Gross-Neveu model. This technique is generalized and is then applied to use the O(6) as the starting point of the nesting procedure to obtain the O(N) form factors for general even N.

arXiv:1703.05973Mar 17, 20171 citation

{N}_{f}

calculations, but for a single flavor, different methods disagree quantitatively, and further studies are necessary.

The isomorphism

SU(4) \simeq O(6)

is used to construct the form factors of the O(6) Gross-Neveu model as bound state form factors of the SU(4) chiral Gross-Neveu model. This technique is generalized and is then applied to use the O(6) as the starting point of the nesting procedure to obtain the O(N) form factors for general even N.