Dual Formulation and Phase Diagram of Lattice QCD in the Strong Coupling Regime

Abstract

We present the computation of invariants that arise in the strong coupling expansion of lattice QCD. These invariants are needed for Monte Carlo simulations of Lattice QCD with staggered fermions in a dual, color singlet representation. This formulation is in particular useful to tame the finite density sign problem. The gauge integrals in this limiting case β → 0 are well known, but the gauge integrals needed to study the gauge corrections are more involved. We discuss a method to evaluate such integrals. The phase boundary of lattice QCD for staggered fermions in the µB − T plane has been established in the strong coupling limit. We present numerical simulations away from the strong coupling limit, taking into account the higher order gauge corrections via plaquette occupation numbers. This allows to study the nuclear and chiral transition as a function of β.Speaker,

New dual representation for staggered lattice QCD

“…A great simplification occurring, is that the strong coupling contributions always decouple from those corresponding to non-zero {n p ,n p }. As we showed in [40], at strong coupling the tensors T ρ have only one non-zero element. Although for baryon fluxes (f x,µ = ±N ) this is a trivial statement as there is only one possible DOI per link, in the case of dimer contributions it is a consequence of the structure of the Decoupling Operators.…”

“…A dual representation of lattice QCD has only been derived in the strong coupling regime: the classical arXiv:1911.08389v1 [hep-lat] 19 Nov 2019 formulation in terms of a monomer-dimer-polymer system has been both addressed via mean-field [31][32][33][34] and Monte Carlo [35][36][37][38] and is valid only in the strong coupling limit. More recently also the leading order gauge corrections have been included [39,40]. At strong coupling, also the fermion bag approach has been used [41,42] and continuous time methods have been applied [43,44].…”

Towards a Dual Representation of Lattice QCD

“…This dual formulation has the advantage that the sign problem induced by a baryon-chemical potential is mild enough so that the phase boundaries can be mapped out using standard reweighting in the sign. Incorporating leading order β-correction is also possible, by computing the modified weights induced by a single plaquette excitation [5], whereas in [7] gauge contributions produced by plaquette-surfaces have been taken into account. Going beyond these approximations is very challenging.…”

Thermodynamics at strong coupling on anisotropic lattices

“…An immediate question one can ask is: do the nuclear and chiral transition split at sufficiently large β ? New simulations obtained by sampling plaquette contributions directly via world sheets did not indicate any splitting [6]. We may have to consider the possibility that in the chiral limit, both transitions are on top even in the continuum limit.…”