Meron-Cluster Solution of Fermion Sign Problems

Abstract

We present a general strategy to solve the notorious fermion sign problem using cluster algorithms. The method applies to various systems in the Hubbard model family as well as to relativistic fermions. Here it is illustrated for non-relativistic lattice fermions. A configuration of fermion world-lines is decomposed into clusters that contribute independently to the fermion permutation sign. A cluster whose flip changes the sign is referred to as a meron. Configurations containing meron-clusters contribute 0 to the path integral, while all other configurations contribute 1. The cluster representation describes the partition function as a gas of clusters in the zero-meron sector.Comment: 4 pages, ReVTe

Numerical study of dense adjoint matter in two color QCD

“…The sign problem is well-known [26] and can be addressed, at least in principle, by including the sign of detM with the observable as in (1.1); this may be expected to be effective provided the average sign is significantly different from zero. The problem with ergodicity is less well-known -it can be anticipated in any model where M is real but its eigenvalues λ complex; another example which would be interesting to study is the lattice Gross-Neveu model with discrete Z 2 chiral symmetry [27].…”

Introduction to quantum Monte Carlo simulations for fermionic systems

“…In the meron-cluster approach [44], HS fields are introduced in all sites as usual, but during the sampling process (1) the configurations are decomposed into clusters which can be flipped independently, and (2) a matching between positive-and negative-weighted configurations is sought; see Ref. [44] for details, and Ref. [45] for another grouping strategy.…”

Towards quantum simulating QCD

“…This does not exclude that specific sign problems may indeed be solvable on classical computers. In fact, several severe sign or complex action problems have been solved with the meron-cluster algorithm [2,3,4] or with the fermion bag approach [5,6,7]. Even the real-time evolution of a large strongly coupled quantum spin system, whose dynamics is entirely driven by measurements, has recently been simulated successfully with a cluster algorithm [8].…”