We study quantum critical behavior in three dimensional lattice Gross-Neveu models containing two massless Dirac fermions. We focus on two models with SU (2) flavor symmetry and either a Z2 or a U (1) chiral symmetry. Both models could not be studied earlier due to sign problems. We use the fermion bag approach which is free of sign problems and compute critical exponents at the phase transitions. We estimate ν = 0.83(1), η = 0.62(1), η ψ = 0.38(1) in the Z2 and ν = 0.849(8), η = 0.633(8), η ψ = 0.373(3) in the U (1) model.
The recently proposed fermion-bag approach is a powerful technique to solve some four-fermion lattice field theories. Because of the existence of a duality between strong and weak couplings, the approach leads to efficient Monte Carlo algorithms in both these limits. The new method allows us for the first time to accurately compute quantities close to the quantum critical point in the three dimensional lattice Thirring model with massless fermions on large lattices. The critical exponents at the quantum critical point are found to be ν=0.85(1), η=0.65(1), and η(ψ)=0.37(1).
In a progress toward searching for the QCD critical point, we study the finite density phase transition of N f = 4 and 2 lattice QCD at finite temperature with the canonical ensemble approach.We develop a winding number expansion method to accurately project out the particle number from the fermion determinant which greatly extends the applicable range of baryon number sectors to make the study feasible. Our lattice simulation was carried out with the clover fermions and improved gauge action. For a given temperature, we calculate the baryon chemical potential from the canonical approach to look for the mixed phase as a signal for the first order phase transition.In the case of N f = 4, we observe an "S-shape" structure in the chemical potential-density plane due to the surface tension of the mixed phase in a finite volume which is a signal for the first order phase transition. We use the Maxwell construction to determine the phase boundaries for three temperatures below T c . The intersecting point of the two extrapolated boundaries turns out to be at the expected first order transition point at T c with µ = 0. This serves as a check for our method of identifying the critical point. We also studied the N f = 2 case, but do not see a signal of the mixed phase for temperature as low as 0.83 T c .
The overlap fermion propagator is calculated on 2 + 1 flavor domain wall fermion gauge configurations on 16 3 × 32, 24 3 × 64 and 32 3 × 64 lattices. With HYP smearing and low eigenmode deflation, it is shown that the inversion of the overlap operator can be expedited by ∼ 20 times for the 16 3 × 32 lattice and ∼ 80 times for the 32 3 × 64 lattice. The overhead cost for calculating eigenmodes ranges from 4.5 to 7.9 propagators for the above lattices. Through the study of hyperfine splitting, we found that the O(m 2 a 2 ) error is small and these dynamical fermion lattices can adequately accommodate quark mass up to the charm quark. A preliminary calculation of the low energy constant ∆ mix which characterizes the discretization error of the pion made up of a pair of sea and valence quarks in this mixed action approach is carried out via the scalar correlator with periodic and anti-periodic boundary conditions. It is found to be small which shifts a 300 MeV pion mass by ∼ 10 to 19 MeV on these sets of lattices. We have studied the signal-to-noise issue of the noise source for the meson and baryon. We introduce a new algorithm with Z 3 grid source and low eigenmode substitution to study the the many-to-all meson and baryon correlators. It is found to be efficient in reducing errors for the correlators of both mesons and baryons. With 64-point Z 3 grid source and low-mode substitution, it can reduce the statistical errors of the light quark (m π ∼ 200 − 300 MeV) meson and nucleon correlators by a factor of ∼ 3 − 4 as compared to the point source. The Z 3 grid source itself can reduce the errors of the charmonium correlators by a factor of ∼ 3.
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