Evaluating second-order phase transitions with Diagrammatic Monte Carlo:\n N\\'{e}el Transition in the doped three-dimensional Hubbard model

Abstract

Diagrammatic Monte Carlo -- the technique for numerically exact summation of\nall Feynman diagrams to high orders -- offers a unique unbiased probe of\ncontinuous phase transitions. Being formulated directly in the thermodynamic\nlimit, the diagrammatic series is bound to diverge and is not resummable at the\ntransition due to the non-analyticity of physical observables. This enables the\ndetection of the transition with controlled error bars from an analysis of the\nseries coefficients alone, avoiding the challenge of evaluating physical\nobservables near the transition. We demonstrate this technique by the example\nof the N\\'eel transition in the $3d$ Hubbard model. At half-filling and higher\ntemperatures, the method matches the accuracy of state-of-the-art finite-size\ntechniques, but surpasses it at low temperatures and allows us to map the phase\ndiagram in the doped regime, where finite-size techniques struggle from the\nfermion sign problem. At low temperatures and sufficient doping, the transition\nto an incommensurate spin density wave state is observed.\n