Phase diagram of dynamical twisted-mass Wilson fermions at finite isospin chemical potential

Abstract

Abstract. We consider the phase diagram of twisted mass Wilson fermions of twoflavor QCD in the parameter space of the quark mass, the isospin chemical potential, the twist angle and the lattice spacing. This work extends earlier studies in the continuum and those at zero chemical potential. We evaluate the phase diagram as well as the spectrum of the (pseudo-)Goldstone bosons using the chiral Lagrangian for twisted mass Wilson fermions at non-zero isospin chemical potential. The phases are obtained from a mean field analysis. At zero twist angle we find that already an infinitesimal isospin chemical potential destroys the Aoki phase. The reason is that in this phase we have massless Goldstone bosons with a non-zero isospin charge. At finite twist angle only two different phases are present, one phase which is continuously connected to the Bose condensed phase at non-zero chemical potential and another phase which is continuously connected to the normal phase. For either zero or maximal twist the phase diagram is more complicated as the saddle point equations allow for more solutions.

Simulating twisted mass fermions at physical light, strange, and charm quark masses

“…The occurrence of instabilities of the simulations at β = 1.726 when approaching the physical pion mass is, in fact, not unexpected. With twisted mass fermions, going to sufficiently small values of the light twisted mass parameter at a fixed lattice spacing one either enters the Aoki [40] or the Sharpe-Singleton [41] regime, see for an recent overview [42]. For the Sharpe-Singleton case, which is realized in our unquenched simulations, a sizable O(a 2 ) negative shift of the neutral pion mass occurs.…”

Cold QCD at finite isospin density: Confronting effective models with recent lattice data

“…On the contrary to what happens at finite baryonic density, systems with finite isospin density does not suffer with the sign problem and hence are easily accessible to lattice QCD based calculations. Initial results of lattice QCD at finite temperature and isospin density appeared in early 2000's [6,7] and they were also investigated by other available techniques, such as chiral perturbation theory (χPT) [8][9][10][11][12][13][14][15][16][17], Hard Thermal Loop perturbation theory (HTLPt) [18], Nambu-Jona-Lasinio (NJL) model [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] and its Polyakov loop extended version PNJL [36,37], quark meson model (QMM) [38][39][40][41] and the results were largely in qualitative agreement. However, all of the early lattice QCD calculations have been done considering unphysical pion masses and/or an unphysical flavour content.…”

Wilson chiral perturbation theory for dynamical twisted mass fermions vs lattice data—A case study

“…We refer the reader to [13] for a detailed and pedagogical introduction to Wilson χPT. Moreover, one can study the intricate phase diagram of twisted mass fermions in analytical mean field studies employing Wilson χPT [14,15,16,17,18]. When m ∝ a 2 , one has two possibilities, that of a second order phase transition to the so called Aoki phase [19] or a first order scenario (the Sharpe-Singleton scenario) [10].…”

“…[20]. By the same token, one can describe within Wilson χPT the changes in the orientation of the chiral condensate [14,13,18]. The chiral condensate changes promptly from -1 to +1 in the first order scenario, while it changes in a continuous manner in the Aoki phase.…”