Inhomogeneous chiral condensates and non-analyticity under an external magnetic field

Abstract

We investigate inhomogeneous chiral condensates, such as the so-called dual chiral density wave of dense quark matter, under an external magnetic field at finite real and imaginary chemical potentials. In a model-independent manner, we find that analytic continuation from imaginary to real chemical potential is not possible due to the singularity induced by inhomogeneous chiral condensates at zero chemical potential. From the discussion on the non-analyticity and methods used in lattice QCD simulations, e.g., Taylor expansion, and the analytic continuation with an imaginary chemical potential, it turns out that information on an inhomogeneous chiral condensed phase is missed in the lattice simulations at finite baryon chemical potentials unless the non-analyticity at zero chemical potential is correctly considered. We also discuss an exceptional case without such non-analyticity at zero chemical potential.

Topological feature and phase structure of QCD at complex chemical potential

“…(II) The analytic continuation in QCD from the imaginary to the real chemical potential is usually performed on the µ 2 plane. In the continuation, we may miss some information such as an inhomogeneous condensate [34]. The analytic continuation on the complex chemical potential plane may restore the information missing.…”

Symmetry breaking effect on the inhomogeneous chiral transition in the magnetic field

“…In Ref. [40], the case with the singular line at µ = 0 is discussed. Though the existence of the line is pointed out by the generalized GL expansion with B in the chiral limit [19], such a singular line, that is, the phase boundary is moved to µ = 0 region due to the current quark mass.…”

“…The possibility of the observation is also discussed in the lattice QCD simulations, based on Ref. [40], where non-analyticity of the partition function is studied in the DCDW phase. Sect.…”

Magnetic-field induced critical endpoint

“…The current understanding is that an inhomogeneous phase is present in this region of the phase diagram [34][35][36][37][38][39][40][41][42][43]. The influence of a magnetic field on these phases was discussed in [44][45][46][47][48][49][50][51][52].…”