Functional RG investigation of the antiferromagnetic phase diagram of the three dimensional Hubbard model

Paul R. C. Kent, M. Jarrell, Thomas Maier +1 more

The dynamical cluster approximation (DCA) with Betts clusters is used to calculate the antiferromagnetic phase diagram of the three-dimensional Hubbard model at half-filling. Betts clusters are a set of periodic clusters which best reflect the properties of the lattice in the thermodynamic limit and provide an optimal finite-size scaling as a function of cluster size. Using a systematic finite-size scaling as a function of cluster space-time dimensions, we calculate the antiferromagnetic phase diagram. Our results are qualitatively consistent with the results of Staudt et al. [Eur. Phys. J. B 17, 411 (2000)], but require the use of much smaller clusters: 48 compared to 1000.

Michael Plischke

Sebastian J. Wetzel

This thesis is dedicated to provide physicists with new and improved techniques to \nexamine phase diagrams and phase transitions. \nOne the one hand, an analysis of the effects of different regularization schemes in \nfunctional renormalization group calculations is provided. Building on this knowledge, \nan investigation of the phase diagram of the Hubbard-Model on the square \nlattice is performed using the functional renormalization group. The calculation \nreveals leading instabilities in the d-wave superconducting and different antiferromagnetic \nchannels. In the symmetry broken phases there are a changing Fermi \nsurface geometry, coexistence phases of d-wave superconductivity and antiferromagnetism \nas well as a mutual tendency of superconductivity and antiferromagnetism \nto repel each other. \nOn the other hand, a scheme to discover phase transitions using unsupervised \nartifcial neural networks is developed. Further, a method to interpret artifcial \nneural networks is introduced. These methods are applied to systems ranging from \nthe two dimensional Ising Model to four dimensional SU(2) lattice gauge theory. \nThey find the existence of different phases, calculate phase boundaries and derive \nthe explicit formulas of the quantities by which the neural network distinguishes \nbetween phases. It turns out that these quantities are order parameters and other \nthermodynamic quantities.

Hou-Ji Shao, Yu‐Xuan Wang, De-Zhi Zhu +9 more

A. Nihat Berker

Hui‐Quan Nie, Bao-Hua Zhao, Kaiyi Zhang +2 more

We have used the fourth order perturbation expansion to construct the magnetic phase diagram of the two-dimensional Hubbard model. To the contrary of the three-dimensional case, a stable antiferromagnetic phase is found at the limit of (t/U)≃0 if the electron density n lies in the region 0.95<n<1.05. Our results for n=0.9 are compared to the recent indecisive Monte-Carlo investigation on the magnetic structure factor regarding the antiferromagnetic ordering.