Numerical study of dense adjoint matter in two color QCD

Abstract

We identify the global symmetries of SU(2) lattice gauge theory with N flavors of staggered fermion in the presence of a quark chemical potential µ, for fermions in both fundamental and adjoint representations, and anticipate likely patterns of symmetry breaking at both low and high densities. Results from numerical simulations of the model with N = 1 adjoint flavor on a 4 3 × 8 lattice are presented, using both hybrid Monte Carlo and Two-Step Multi-Boson algorithms. It is shown that the sign of the fermion determinant starts to fluctuate once the model enters a phase with non-zero baryon charge density. HMC simulations are not ergodic in this regime, but TSMB simulations retain ergodicity even in the dense phase, and in addition appear to show superior decorrelation. The HMC results for the equation of state and the pion mass show good quantitative agreement with the predictions of chiral perturbation theory, which should hold only for N ≥ 2. The TSMB results incorporating the sign of the determinant support a delayed onset transition, consistent with the pattern of symmetry breaking expected for N = 1.

Characteristics of the eigenvalue distribution of the Dirac operator in dense two-color QCD

“…The twocolor determinant, however, buries a nice property of respective eigenvalues under the product. We can prove that, if λ i = m q + iλ ′ i is an eigenvalue of the Dirac determinant in two-color QCD, there appear m q − iλ ′ i , m q + iλ ′ * i , and m q − iλ ′ * i simultaneously in the eigenvalue spectrum [11,25,32]. The proof may break down when iλ ′ i is a real number; the eigenvectors for m q + iλ ′ i and m q − iλ ′ * i could not be independent.…”

“…We immediately hit on several reasons why we can believe so: First of all, numerous works on dense two-color QCD have almost established a firm understanding on the ground state of two-color QCD by the analytical approach as well as the Monte-Carlo simulation [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31]. Second, the notorious sign problem of the Dirac determinant at µ = 0 (where µ is the quark chemical potential) is not so harmful as genuine QCD, which makes it viable to perform the Monte-Carlo integration [1,11,25,32]. Third, dense two-color matter realizes a bosonic baryon system leading to the Bose-Einstein condensation of the color-singlet diquark [6,7].…”

Can we study quark matter in the quenched approximation?

“…In the limit µ → µ o+ the matter in the ground state becomes arbitrarily dilute, weakly-interacting, and non-relativistic, and is a textbook example of Bose-Einstein condensation. This scenario was subsequently confirmed by simulations with staggered lattice fermions [5,9]. More recent simulations have found evidence for a second transition at larger µ to a deconfined phase, as evidenced by a non-vanishing Polyakov loop [11] and by a fall in the topological susceptibility [12].…”

“…2,6. This approximate linear behaviour is once again a prediction of χPT [5,9,13], and is to be contrasted with the n q ∝ µ 3 behaviour expected of a deconfined theory where baryons can be identified with degenerate quark states occupying a Fermi sphere of radius k F ≈ µ. The absence of this scaling is a further reason to conclude that the reconstructed model does not describe deconfined physics.…”

“…For QCD this scale is m N /3, where m N is the nucleon mass; for a theory with conjugate quarks the onset scale is m π /2. Only cancellations among configurations due to a complex-valued measure detM can ensure that the fake signal for n q > 0 vanishes in the range m π /2 < µ < m N /3 [5]. A recent analytic demonstration has been given, once again in the context of a random matrix model, in [6].…”