Supersymmetric fixed points of the hubbard model

Kareljan Schoutens

P. Coleman, C. Pépin

Fabian H. L. Eßler, V. E. Korepin

Piers Coleman, C. Pépin

We present a preliminary discussion on the use of supersymmetric representation of the Hubbard operator which unifies the slave boson and slave fermion representations into a single U(1) × SU(1|1) gauge theory to treat the physics of the infinite U Hubbard model. By looking for solutions to the Hamiltonian in which the spins can exist as both condensed ordered moments and as mobile charged carriers, we examine the possibility of a Nagaoka ferromagnetic phase at finite doping with a quantum critical point into the paramagnetic phase. Key words: Hubbard model, Supersymmetry, Ferromagnetism The infinite U Hubbard model[1] is a prototype model for strongly correlated electron systems. Interest in this venerable model has grown in recent times because of its link with one of the basic models of high temperature superconductivity, the t − J model.[2] The infinite U Hubbard model corresponds to the t − J model without antiferromagnetic interactions (J → 0). Despite the absence of antiferromagnetic interactions, evidence from finite temperature Lanzcos studies[3] suggests that many of high temperature properties associated with the cuprate metals are already present in the infinite U Hubbard model. The U = ∞ Hubbard hamiltonian is written HK = − t

Yu Nakayama, Ken Kikuchi

Abstract We investigate the fate of the non-supersymmetric Gross-Neveu-Yukawa fixed point found by Fei et al. in 4 − ϵ dimensions with a two-component Majorana fermion continued to two dimensions. Assuming that it is a fermionic minimal model which possesses a chiral ℤ2 symmetry (in addition to fermion number parity) and just two relevant singlet operators, we can zero in on four candidates. Assuming further that the least relevant deformation leads to the supersymmetric Gross-Neveu-Yukawa fixed point (i.e. fermionic tricritical Ising model), we can rule out two of them by matching the spin contents of the preserved topological defect lines. The final candidates are the fermionic (11, 4) minimal model if it is non-unitary, and the fermionic (E6, A10) minimal model if it is unitary. If we further use a constraint from the double braiding relation proposed by one of the authors, the former scenario is preferable.

J. M. Drummond, Giovanni Feverati, L. Frappat +1 more