Lattice QCD Phase Diagram In and Away from the Strong Coupling Limit

We study lattice QCD with four flavors of staggered quarks. In the limit of infinite gauge coupling, “dual” variables can be introduced, which render the finite-density sign problem mild and allow a full determination of the $\mu -T$ phase diagram by Monte Carlo simulations, also in the chiral limit. However, the continuum limit coincides with the weak coupling limit. We propose a strong-coupling expansion approach towards the continuum limit. We show first results, including the phase diagram and its chiral critical point, from this expansion truncated at next-to-leading order.

Figure 1

Left: Lattice QCD phase diagram in the strong coupling limit, setting $a/a_t={\gamma }^2$ following mean field. Different results are obtained for different numbers $N_t$ of time slices $N_t=2$, $N_t=4$ [7], $N_t=6$, and $N_t=\infty$ (i.e., continuous Euclidean time) [18]. Right: Same, with corrected anisotropy [19].

Figure 2

Polyakov loop $\frac{1}{3}⟨\mathrm{tr}L⟩$ and average spatial and temporal plaquette $\frac{1}{3}⟨\mathrm{tr}{P}_s⟩$, $\frac{1}{3}⟨\mathrm{tr}{P}_t⟩$ as a function of ($\mu$, $T$) on a ${16}^3\times 4$ lattice at $\beta =0$. The colors label successive values of $\mu /T$, and the $x$ axis is $\rho \equiv a\sqrt{{\mu }^2+T^2}$. At the tricritical point, ${\rho }_T=1.10(2)$. Wilson loops are sensitive to the chiral transition and develop a discontinuity as the transition turns first order. $⟨\mathrm{tr}{P}_s⟩$ varies oppositely to $⟨\mathrm{tr}{P}_t⟩$, and remains very small.

Figure 3

The $\mu =0$ transition temperature $a{T}_c$ from finite-size scaling of the chiral susceptibility on $N_t=4$ lattices. Left: $\beta =0$. Right: $\beta =0.02$. The arrow marks the shift in $a{T}_c$.

Figure 4

Phase boundary in $\beta -aT$ plane at $\mu =0$. Left: linear extrapolation. Right: exponential extrapolation. The boundary coincides very well with conventional Hybrid Monte Carlo data at large $\beta$. Also, the phase boundary is rather similar to the one obtained via a mean field theory approach without [27] and with Polyakov loop effects [28].

Figure 5

Phase boundary in the $\mu -T$ plane in the strong coupling limit and extrapolated to finite $\beta$, comparing linear and exponential extrapolation. We do not observe a shift of the chiral tricritical point. The nuclear critical end point (CEP), determined from the reweighted baryon density, moves down along the first order line (extrapolated to $T=0$ to guide the eye) as $\beta$ is increased.