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We present a quantum Monte Carlo method which allows calculations on many-fermion systems at finite temperatures without any sign decay. This enables simulations of the grand-canonical ensemble at large system sizes and low temperatures. Both diagonal and off-diagonal expectations can be computed straightforwardly. The sign decay is eliminated by a constraint on the fermion determinant. The algorithm is approximate. Tests on the Hubbard model show that accurate results on the energy and correlation functions can be obtained.

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