Bold Diagrammatic Monte Carlo technique for frustrated spin systems

Abstract

Using fermionic representation of spin degrees of freedom within the Popov-Fedotov approach we develop an algorithm for Monte Carlo sampling of skeleton Feynman diagrams for Heisenberg type models. Our scheme works without modifications for any dimension of space, lattice geometry, and interaction range, i.e. it is suitable for dealing with frustrated magnetic systems at finite temperature. As a practical application we compute uniform magnetic susceptibility of the antiferromagnetic Heisenberg model on the triangular lattice and compare our results with the best available high-temperature expansions. We also report results for the momentum-dependence of the static magnetic susceptibility throughout the Brillouin zone.

arXiv comment15 pages, 16 figures

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• Taming pseudo-fermion functional renormalization for quantum spins: Finite-temperatures and the Popov-Fedotov trick
• Thermodynamic description of the Ising antiferromagnet on triangular lattice with selective dilution by modified Pair Approximation method
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• Taming spin susceptibilities in frustrated quantum magnets: Mean-field form and approximate nature of the quantum-to-classical correspondence
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• Auxiliary-Field Monte Carlo for lattice bosons: tackling strong interactions and frustration
• Majorana Diagrammatics for Quantum Spin-1/2 Models
• Global sampling of Feynman's diagrams through Normalizing Flow