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Résumé |
Unbiased numerical approaches are essential for understanding strongly correlated quantum systems, but are often limited by the quantum Monte Carlo sign problem, particularly in frustrated spin systems and doped fermionic models. In this seminar, I will discuss two different quantum Monte Carlo strategies addressing these regimes.
I will first introduce the stochastic series expansion (SSE), a finite-temperature quantum Monte Carlo method based on a high-temperature expansion, and explain how cluster-based computational bases can reduce or eliminate sign problems in frustrated quantum magnets. As an illustration, I will present results for the spin-1/2 Heisenberg antiferromagnet on the diamond-decorated square lattice, a highly frustrated system of coupled orthogonal dimers.
I will then turn to diagrammatic Monte Carlo (DiagMC), in which thermodynamic observables are computed from perturbative expansions in terms of connected Feynman diagrams directly in the thermodynamic limit. I will introduce a recently developed DiagMC formalism that reorganizes these expansions around generic shifted quadratic reference points, and explain how automatic differentiation provides a systematic way to implement such shifted expansions. |
