Correlated Fermions with Spin-Orbit Coupling and Competing Orders in Solids
Final Report Abstract
We have investigated the quantum phase transition of U (1)-charged Dirac fermions towards Kekulé order with Z3 symmetry. The presence of a symmetry-allowed cubic order parameter term in the Landau-Ginzburg free energy is conventionally expected to render the considered phase transition discontinuous. Here, we studied the corresponding Gross-Neveu-Yukawa theory for the transition employing a perturbative renormalization group approach in 4 − ε spacetime dimensions. In different scenarios – with and without the coupling to a fluctuating U (1)-gauge field – we showed that quantum fluctuations of the massless fermions can turn the putative first order phase transition into a continuous one. This illuminates an unconventional aspect of quantum phase transitions beyond the Landau-Ginzburg paradigm. In a second project, we investigated the bosonized version of the standard Gross-Neveu model with a real scalar order parameter field at three-loop order, and provided analytical estimates for the critical exponents in 4 − ε dimensions for arbitrary number of fermion flavors. This was motivated by the recent interest in various possible quantum transitions of Dirac and Weyl fermions belonging to the universality class of different versions of the Gross-Neveu model. We discussed applications of the computed series for the critical exponents and evaluated Padé approximants for the metal-insulator transitions of honeycomb fermions, emergent supersymmetry in topological phases and the replica limit N → 0 which was suggested to describe the disorder-induced quantum transition in Weyl semimetals. Finally, we provided comparisons to the results of other perturbative and non-perturbative renormalization approaches, the conformal bootstrap and and numerical methods.
Publications
- Gauge-field-assisted Kekulé quantum criticality, Phys. Rev. B 94, 205136 (2016)
M. M. Scherer, and I. F. Herbut
(See online at https://doi.org/10.1103/PhysRevB.94.205136) - Gross-Neveu-Yukawa model at three loops and Ising critical behavior of Dirac systems
L. N. Mihaila, N. Zerf, B. Ihrig, I. F. Herbut, M. M. Scherer
