ﻻ يوجد ملخص باللغة العربية
QCD is expected to have a rich phase structure. It is empirically known to be difficult to access low temperature and nonzero chemical potential $mu$ regions in lattice QCD simulations. We address this issue in a lattice QCD with the use of a dimensional reduction formula of the fermion determinant. We investigate spectral properties of a reduced matrix of the reduction formula. Lattice simulations with different lattice sizes show that the eigenvalues of the reduced matrix follow a scaling law for the temporal size $N_t$. The properties of the fermion determinant are examined using the reduction formula. We find that as a consequence of the $N_t$ scaling law, the fermion determinant becomes insensitive to $mu$ as $T$ decreases, and $mu$-independent at T=0 for $mu<m_pi/2$. The $N_t$ scaling law provides two types of the low temperature limit of the fermion determinant: (i) for low density and (ii) for high-density. The fermion determinant becomes real and the theory is free from the sign problem in both cases. In case of (ii), QCD approaches to a theory, where quarks interact only in spatial directions, and gluons interact via the ordinary Yang-Mills action. The partition function becomes exactly $Z_3$ invariant even in the presence of dynamical quarks because of the absence of the temporal interaction of quarks. The reduction formula is also applied to the canonical formalism and Lee-Yang zero theorem. We find characteristic temperature dependences of the canonical distribution and of Lee-Yang zero trajectory. Using an assumption on the canonical partition function, we discuss physical meaning of those temperature dependences and show that the change of the canonical distribution and Lee-Yang zero trajectory are related to the existence/absence of $mu$-induced phase transitions.
A three-dimensional effective lattice theory of Polyakov loops is derived from QCD by expansions in the fundamental character of the gauge action, u, and the hopping parameter, kappa, whose action is correct to kappa^n u^m with n+m=4. At finite baryo
The properties of matter at finite baryon densities play an important role for the astrophysics of compact stars as well as for heavy ion collisions or the description of nuclear matter. Because of the sign problem of the quark determinant, lattice Q
Lattice QCD with heavy quarks reduces to a three-dimensional effective theory of Polyakov loops, which is amenable to series expansion methods. We analyse the effective theory in the cold and dense regime for a general number of colours, $N_c$. In pa
After combined character and hopping expansions and integration over the spatial gauge links, lattice QCD reduces to a three-dimensional $SU(3)$ Polyakov loop model with complicated interactions. A simple truncation of the effective theory is valid f
In this paper we carry out a low-temperature scan of the phase diagram of dense two-color QCD with $N_f=2$ quarks. The study is conducted using lattice simulation with rooted staggered quarks. At small chemical potential we observe the hadronic phase