Canonical simulations of supersymmetric SU(N) Yang-Mills quantum mechanics

Abstract

The fermion loop formulation naturally separates partition functions into their canonical sectors. Here we discuss various strategies to make use of this for supersymmetric SU(N) Yang-Mills quantum mechanics obtained from dimensional reduction in various dimensions and present numerical results for the separate canonical sectors with fixed fermion numbers. We comment on potential problems due to the sign of the contributions from the fermions and due to flat directions.

The Hubbard model in the canonical formulation

“…The canonical transfer matrices can be constructed for a large class of quantum field theories. In some supersymmetric Yang-Mills gauge theories, for example, the canonical formulation has been shown to lead to a solution of the fermion sign problem [1,2], based on the construction of the transfer matrices in and the close connection of the canonical formulation with the (dual) fermion loop or worldline formulation [3]. This, in turn, allows for the construction of efficient simulation algorithms, such as fermion bag [4,5] and fermion worm algorithms [6].…”

“…Indeed, in sector N σ the number of states N states = Ls Nσ is equal to the number of principal minors of order N σ . At half-filling, this number grows exponentially with L s , however, it can efficiently be evaluated stochastically with Monte Carlo methods, as for example in [1,2].…”