Exact Classical Effective Potential
Abstract
A quantum spin system can be modelled by an equivalent classical system, with an effective Hamiltonian obtained by integrating all non-zero frequency modes out of the path integral. The effective Hamiltonian Heff(Si) derived from the coherent-state integral is highly singular: the quasiprobability density exp(-beta Heff), a Wigner function, imposes quantisation through derivatives of delta functions. This quasiprobability is the distribution of the time-averaged lower symbol of the spin in the coherent-state integral. We relate the quantum Monte Carlo minus-sign problem to the non-positivity of this quasiprobability, both analytically and by Monte Carlo integration.
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