Abstract
We propose a new strategy to evaluate the partition function of lattice QCD with Wilson gauge action coupled to staggered fermions, based on a strong coupling expansion in the inverse bare gauge coupling $\beta= 2N/g^{2}$. Our method makes use of the recently developed formalism to evaluate the ${\rm SU}(N)$ $1-$link integrals and consists in an exact rewriting of the partition function in terms of a set of additional dual degrees of freedom which we call "Decoupling Operator Indices" (DOI). The method is not limited to any particular number of dimensions or gauge group ${\rm U}(N)$, ${\rm SU}(N)$. In terms of the DOI the system takes the form of a Tensor Network which can be simulated using Worm-like algorithms. Higher order $\beta$-corrections to strong coupling lattice QCD can be, in principle, systematically evaluated, helping to answer the question whether the finite density sign problem remains mild when plaquette contributions are included. Issues related to the complexity of the description and strategies for the stochastic evaluation of the partition function are discussed.
Highlights
Lattice QCD at finite baryon density suffers from the notorious sign problem [1]
Our ultimate goal is to find a dual representation for lattice QCD: we propose a new approach based on a combined expansion of the Wilson plaquette action and of the staggered action to all orders
We proposed a new strategy for the evaluation of higher order contributions in the strong coupling expansion of lattice QCD with staggered fermion discretization
Summary
Lattice QCD at finite baryon density suffers from the notorious sign problem [1]. In a nutshell, the numerical sign problem arises because the weights of the partition function are not positive definite, prohibiting importance sampling in Monte Carlo simulations. To name some approaches that are in the spirit of a dual representation: the three-dimensional effective theory [26,27] (a joint strong coupling and hopping parameter expansion that can be mapped to SU(3) spin model), decoupling the gauge links using HubbardStratonovich transformations [28], “induced QCD” based on an alternative discretization of Yang Mills Theory [29,30]. All these approaches have their shortcomings, and a method that allows to simulate lattice QCD at finite density has not yet been established.
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