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Sign Problems in Quantum Monte Carlo and Meron Cluster Algorithms
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Ab-initio studies of strongly correlated systems at finite densities
and at real-times are hindered by the infamous sign problem. In this
discussion, we analyze the problem for fermionic many-body quantum
systems (quantum field theories on the lattice) and discuss criteria
for solving such a sign problem. Meron cluster algorithms are then
introduced and discussed taking the example of the fermionic t-V model.
The algorithms can be generalized to simulate Abelian gauge theories
(realized as quantum link models) coupled to fermions in any space-time
dimension.
References:
1. Computational complexity and fundamental limitations to fermionic
quantum Monte Carlo simulations, Matthias Troyer, Uwe-Jens Wiese,
Phys.Rev.Lett. 94 (2005) 170201.
2. Meron cluster approach to systems of strongly correlated electrons,
S. Chandrasekharan, J. Cox, J.C. Osborn, U-.J. Wiese,
Nucl.Phys.B 673 (2003) 405-436