Chiral symmetry and density waves in quark matter

Abstract

A density wave in quark matter is discussed at finite temperature, which occurs along with the chiral condensation, and is described by a dual standing wave in scalar and pseudo-scalar condensates on the chiral circle. The mechanism is quite similar to that for the spin density wave suggested by Overhauser, and entirely reflects many-body effects. It is found within a mean-field approximation for NJL model that the chiral condensed phase with the density wave develops at a high-density region just outside the usual chiral-transition line in phase diagram. A magnetic property of the density wave is also elucidated.

Inhomogeneous chiral condensates

“…Subsequent refinements on this study, focusing on the competition of this kind of inhomogeneous phase with color-superconductivity, have been discussed by Shuster and Son [38], Park et al [39] as well as by Rapp, Shuryak and Zahed [40]. Model analyses of inhomogeneous chiral symmetry breaking started in the early 1990s by Kutschera et al [41] and have become increasingly systematic, particularly thanks to seminal papers by Nakano and Tatsumi [42] and Nickel [43,44].…”

“…(CDW) or "dual chiral density wave" (DCDW), where "dual" refers to the presence of two (scalar and pseudoscalar) standing waves [86,42]. 9 The ansatz is also sometimes called "chiral spiral" because M ( x) describes a spiral in the complex plane, when going along the q direction.…”

“…A common choice employed by several authors (for more details, see e.g. [42]) is to act only on the vacuum contributions to Ω kin and impose a sharp cutoff g(τ ) = θ(τ − 1/Λ 2 ) on the lower bound of integration in Eq. (28).…”

Multi-Dimensional Structure of Crystalline Chiral Condensates in Quark Matter

“…In the study with TFA, spatial derivative terms of the condensate are required in the model, but the conventional NJL model does not have such terms. Hence, in the formula for quark energies, we need to effectively extract derivative coupling terms by a good scale transformation, as in the case where the momentum-dependent interaction term was derived via the Weinberg transformation [4]. Here, in order to calculate the free energy (thermodynamic potential), it is necessary to know the quark energy eigenvalues E n of the eigenstates n of the effective Dirac Hamiltonian,…”

“…For a one-dimensional (1D) spatial modulation, there are two well-known ground states of inhomogeneous phases, as in superconductivity: one is the Fulde-Ferrell type characterized by the modulated phase with constant amplitude (i.e., ϕ(z) = ∆e iθ(z) ), and the other is the Larkin-Ovchinnikov type characterized by the modulated amplitude (i.e., ϕ(z) = ∆(z)). In the context of iCPs, the former corresponds to the dual chiral density wave (DCDW) [4], while the latter the real kink crystal (RKC) [5]. These structures are based on analytically known solutions in 1+1D systems [6].…”