Sign problem in the auxiliary field Quantum Monte Carlo algorithm


Time reversal invariant decomposition

. The notorious sign problem remains a major obstacle for quantum Monte-Carlo (QMC) simulations in fermionic systems. We (with S. C. Zhang ) examined this problem in the auxiliary field QMC method, finding the absence of the sign problem in a large class of models at any filling level and lattice geometry. We proved that if the fermion matrix is invariant under an anti-unitary transformation T satisfying $T^2 = -1$, then the statistical weights, i.e., the determinants of the fermion matrices, can be expressed as products of complex conjugate pairs of the eigenvalues, thus are positive definite. We emphasized that T does not necessarily need to be the explicit physical TR transformation.

Application

The interlayer staggered current phase Strongly interacting systems have been conjectured to spontaneously develop current carrying ground states under certain conditions. However, most results in 2D are based on mean field approximations whose validity is hard to justify. In contrast, we (with S. Capponi and S. C. Zhang) performed the QMC simulation to an extended bilayer Hubbard model without the sign problem, finding a commensurate staggered interlayer current phase. To our knowledge, it is the first work to conclusively demonstrate the existence of such a phase in 2D.


References and talks

  • Congjun Wu, and Shou-Cheng Zhang, "Sufficient condition for absence of the sign problem in the fermionic quantum Monte-Carlo algorithm", Phys. Rev. B 71, 155115 (2005), see pdf file .
  • Sylvain Capponi, Congjun Wu, and Shou-Cheng Zhang, "Current carrying ground state in a bi-layer model", Phys. Rev. B 70, 220505(R) (2004), see pdf file .
  • Center of Advanced Studies, Tsinghua University, Beijing, "T-invariant Decomposition and the Sign problem in Quantum Monte-Carlo simulation (PPT)", , Mar. 2007.

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    Last modified: July 15, 2007.