New dual representation for staggered lattice QCD

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 β = 2N/g 2 . Our method makes use of the recently developed formalism to evaluate the 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 U(N ), SU(N ). In terms of the DOI the system takes the form of a Tensor Network which can be simulated using Wormlike algorithms. Higher order β-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.

Strong coupling lattice QCD in the continuous time limit

“…Some first steps to extend our Hamiltonian formulation to more flavors and finite quark mass are presented in the Appendix E. We plan to include the gauge corrections from the Wilson gauge action in continuous time in a similar way as we have already successfully implemented in discrete time [15,17,67]. As the continuous time limit is well defined also at finite lattice gauge coupling β, we may improve on the phase diagram by reducing the spatial lattice spacing directly in the continuous time limit via quantum Monte Carlo simulations.…”

“…where we have used the definition of T , Eq. (17). This result is explicitly temperature dependent, with N τ quantifying the cutoff dependence.…”

“…We will now neglect the subleading terms; i.e., we will only keep terms that survive in the limit Eq. (17). For any temperature, the average contribution per time location is 1=γ 2 .…”

“…The first task that is also relevant to define the temperature and chemical potential nonperturbatively [Eqs. (17) and (18)] is to determine the anisotropy correction factor κ, see Eq. (12).…”

“…The method of dual variables has been successfully used in models with Abelian gauge symmetry [11,12]; there have been attempts to dualize non-Abelian gauge theories [13,14], but it has not yet been possible to overcome the finite density sign problem. Our own approach discussed in [15][16][17] is based on the strong coupling expansion, i.e., an expansion in the inverse gauge coupling β ¼ 2N c g 2 . It is in principle possible to sample partition functions that include all orders via Monte Carlo, in the spirit of [18,19].…”