Inhomogeneous condensation in effective models for QCD using the finite-mode approach

Abstract

We use a numerical method, the finite-mode approach, to study inhomogeneous condensation in effective models for QCD in a general framework. Former limitations of considering a specific ansatz for the spatial dependence of the condensate are overcome. Different error sources are analyzed and strategies to minimize or eliminate them are outlined. The analytically known results for 1 + 1 dimensional models (such as the Gross-Neveu model and extensions of it) are correctly reproduced using the finite-mode approach. Moreover, the NJL model in 3 + 1 dimensions is investigated and its phase diagram is determined with particular focus on the inhomogeneous phase at high density.

Consistent regularization and renormalization in models with inhomogeneous phases

“…The idea of inhomogeneous phases is rather old going back to the work of Fulde and Ferrell as well as by Larkin and Ovchinikov in the context of superconductors [1,2], density waves in nuclear matter by Overhauser [3], and pion condensation by Migdal [4]. In recent years, inhomogeneous phases have been studied in, for example, cold atomic gases [5], color superconducting phases [6][7][8], quarkyonic phases [9,10], as well as chiral condensates [11][12][13][14][15][16][17][18][19][20][21][22]; see Refs. [23,24] for recent reviews.…”

Chiral density wave versus pion condensation in the ( 1+1 )-dimensional NJL model

“…The idea of inhomogeneous phases at low temperature and high density dates back to the work by Fulde and Ferrell, and by Larkin and Ovchinnikov in the context of superconductors [3,4], density waves in nuclear matter by Overhauser [5], and pion condensation by Migdal [6]. In recent years, inhomogeneous phases have been studied in, for example, cold atomic gases [7], color superconducting phases [8][9][10], quarkyonic phases [11,12], pion condensates [13,14] as well as chiral condensates [15][16][17][18][19][20][21][22][23][24][25][26]; see Refs. [27,28] for recent reviews.…”

Inhomogeneous chiral condensate in the quark-meson model

“…To be specific, we focus on a chiral-density wave (CDW). The problem of inhomogeneous phases has been addressed before in the context of the Ginzburg-Landau approach [16][17][18][19], the NJL [20][21][22][23][24][25] and PNJL models [26,27], the QM model [22,28,29], and the nonlocal chiral quark model [30]. Numerical methods for the calculation of the phase diagram for a general inhomogeneous condensate are available [31,32], but we resort to a chiral-density wave ansatz in order to present analytical results.…”