Spin functional renormalization group for the $J_1{J}_2{J}_3$ quantum Heisenberg model

Abstract

We use our recently developed functional renormalization group (FRG) approach for quantum spin systems to investigate the phase diagram of the frustrated $J_1{J}_2{J}_3$ quantum Heisenberg model on a cubic lattice. From a simple truncation of the hierarchy of FRG flow equations for the irreducible spin-vertices which retains only static spin fluctuations and neglects the flow of the four-spin interaction, we can estimate the critical temperature with a similar accuracy as the numerically more expensive pseudofermion FRG. In the regime where the ground state exhibits either ferromagnetic or antiferromagnetic order, a more sophisticated truncation including the renormalization of the four-spin interaction as well as dynamic spin fluctuations reveals the underlying renormalization group fixed point and yields critical temperatures which deviate from the accepted values by at most 4 %.

18 pages, 12 figures, corrected mistakes described in erratum: 10.1103/PhysRevB.107.019904

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• Spectral representation of Matsubara n-point functions: Exact kernel functions and applications
• Recursive algorithm for generating high-temperature expansions for spin systems and the chiral non-linear susceptibility
• Functional renormalization group without functional integrals: implementing Hilbert space projections for strongly correlated electrons via Hubbard X-operators