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001037656 1001_ $$0P:(DE-Juel1)165594$$aGäntgen, Christoph$$b0$$eCorresponding author$$ufzj
001037656 245__ $$aFermionic sign problem minimization by constant path integral contour shifts
001037656 260__ $$aWoodbury, NY$$bInst.$$c2024
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001037656 520__ $$aThe path integral formulation of quantum mechanical problems including fermions is often affected by a severe numerical sign problem. We show how such a sign problem can be alleviated by a judiciously chosen constant imaginary offset to the path integral. Such integration contour deformations introduce no additional computational cost to the Hamiltonian Monte Carlo algorithm, while its effective sample size is greatly increased. This makes otherwise unviable simulations efficient for a wide range of parameters. Applying our method to the Hubbard model, we find that the sign problem is significantly reduced. Furthermore, we prove that it vanishes completely for large chemical potentials, a regime where the sign problem is expected to be particularly severe without imaginary offsets. In addition to a numerical analysis of such optimized contour shifts, we analytically compute the shifts corresponding to the leading and next-to-leading order corrections to the action. We find that such simple approximations, free of significant computational cost, suffice in many cases. We present a simulation of C60 fullerenes (buckyballs) that are successful over a wide parameter range.
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001037656 7001_ $$0P:(DE-Juel1)188583$$aBerkowitz, Evan$$b1$$ufzj
001037656 7001_ $$0P:(DE-Juel1)159481$$aLuu, Thomas$$b2
001037656 7001_ $$00000-0001-7641-8030$$aOstmeyer, Johann$$b3
001037656 7001_ $$0P:(DE-Juel1)185942$$aRodekamp, Marcel$$b4
001037656 773__ $$0PERI:(DE-600)2844160-6$$a10.1103/PhysRevB.109.195158$$gVol. 109, no. 19, p. 195158$$n19$$p195158$$tPhysical review / B$$v109$$x2469-9950$$y2024
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