Strong coupling lattice QCD in the continuous time limit

Abstract

We present results for lattice QCD with staggered fermions in the limit of infinite gauge coupling, obtained from a worm-type Monte Carlo algorithm on a discrete spatial lattice but with continuous Euclidean time. This is obtained by sending both the anisotropy parameter ξ ¼ a σ =a τ and the number of time slices N τ to infinity, keeping the ratio aT ¼ ξ=N τ fixed. The obvious gain is that no continuum extrapolation N τ → ∞ has to be carried out. Moreover, the algorithm is faster, and the sign problem disappears. We derive the continuous time partition function and the corresponding Hamiltonian formulation. We compare our computations with those on discrete lattices and study both zero and finite temperature properties of lattice QCD in this regime.

Hamiltonian Lattice QCD from Strong Coupling Expansion

“…All results presented here are valid in the chiral limit. We have argued in [1] that also a Hamiltonian formulation at finite quark mass 𝑎𝑚 𝑞 is well-defined, which extends this approach to staggered lattice QCD further. We are preparing Quantum Monte Carlo simulations that will help to obtain the QCD phase diagram on the lattice in the parameter space (𝑎𝑇, 𝑎𝜇 𝐵 , 𝑎𝜇 𝐼 , 𝑎𝑚 𝑞 , 𝛽) in lattice units or in units of the baryon mass 𝑎𝑚 𝐵 .…”

“…The Hamiltonian formulation of lattice QCD has been discussed in detail in [1] in the strong coupling limit for 𝑁 𝑓 = 1. In contrast to Hamiltonian formulations in the early days of lattice QCD [2] this formulation is based on the dual representation that is obtained when integrating out the gauge links first, and then the Grassmann-valued fermions [3].…”

“…The 𝑁 𝑓 = 1 formulation at strong coupling has many similarities with full QCD, and via Quantum Monte Carlo the grand-canonical and canonical phase diagram could be determined [1]. The nuclear interactions are of entropic nature: the nucleons, which are point-like in the strong coupling limit, attract each other due to the modification of the pion bath that surrounds them.…”

QCD at high temperature and density: selected highlights

“…Recent developments in strong coupling methods [48], based on a character expansion of the gauge field action, have allowed simulations to be carried out for heavy quarks (using a hopping parameter expansion) [53] as well as for light quarks (using a dual formulation) [54,55]. Recently, a continuous-time formulation for staggered fermions has been developed [52]. Figure 3 using this formulation, exhibiting a first-order nuclear gas-nuclear liquid phase transition including a critical endpoint.…”

“…Left: Fermion density as function of chemical potential from complex Langevin with N f = 2 Wilson fermions[51], at temperatures ranging from 100 MeV (N t = 32) to 800 MeV (N t = 4). Right: Energy density as a function of temperature and chemical potential in the strong coupling expansion, from[52]. A first order nuclear gas-liquid transition with a critical endpoint is observed.…”