Talk by Julian Thönniß, LMU

Multiloop Functional Renormalization Group for Frustrated Spin Systems

07.11.2019 at 12:00 

Magnetically frustrated systems with strongly interacting localized magnetic moments provide valuable insights into the physics of competing ground states and strongly correlated many body systems with unusual properties where, even at T = 0, strong quantum fluctuations persist and no symmetries are broken. These states were dubbed spin liquids. However, after decades of research, there remain open questions as for the type of spin liquid that characterizes the ground state in the spin-1/2 Heisenberg model on the Kagome lattice. In this talk, I will approach this question under use of the functional Renormalization Group (fRG). Though previous fRG studies of Heisenberg models [1,2] have demonstrated the power of this technique, their quantitative reliability was severely limited by the fact that the RG flow depends on the choice of regulator. This dependence is the result of the so-called one-loop approximation – an uncontrolled approximation where the flow equations are truncated such that one neglects the 6-point and all higher-order vertices in order to render the flow equations solvable. Recently, based on the self-consistent parquet equations, a multiloop fRG framework has been developed in our group by Fabian Kugler that overcomes this issue and restores the regulator independence of the flow equations, allowing also for quantitative analyses [3]. I will present this framework, relate it to the conventional one-loop approximation, mention the particularities for the implementation in spin models and show some results for the Kagome Heisenberg model. [1] J. Reuther and P. Wölfle. J 1 −J 2 frustrated two-dimensional heisenberg model: Random phase approximation and functional renormalization group. Phys. Rev. B, 81:144410, Apr 2010. [2] F. L. Buessen and S. Trebst. Competing magnetic orders and spin liquids in two- and three- dimensional kagome systems: Pseudofermion functional renormalization group perspective. Phys. Rev. B, 94:235138, Dec 2016. [3] F. B. Kugler and J. von Delft. Derivation of exact flow equations from the self-consistent parquet relations. New Journal of Physics, 20(12):123029, Dec 2018.