The topological Lifshitz phase transition is studied systematically within an effective model of QCD, in which the chiral symmetry, broken at zero temperature, is not restored at high temperature and/or baryon chemical potential. It is found that during phase transition the quark system undergoes a first-order transition from low density fully-gapped state to high density state with Fermi sphere which is protected by momentum-space topology. The Lifshitz phase diagram in the plane of temperature and baryon chemical potential is established. The critical behaviors of various equations of state are determined. | Communications in Physics, Vol. 23, No. 4 (2013), pp. 289-300 TOPOLOGICAL LIFSHITZ PHASE TRANSITION IN EFFECTIVE MODEL OF QCD WITH CHIRAL SYMMETRY NON-RESTORATION TRAN HUU PHAT Vietnam Atomic Energy Institute, 59 Ly Thuong Kiet, Hanoi, Vietnam. Center for Advance Study, Dong Do University, 170 Pham Van Dong, Hanoi, Vietnam Email: PHUNG THI THU HA Institute of Physics, 10 Dao Tan, Hanoi, Vietnam Vietnam Atomic Energy Institute, 59 Ly Thuong Kiet, Hanoi, Vietnam Email: NGUYEN TUAN ANH Electric Power University, 235 Hoang Quoc Viet, Hanoi, Vietnam Email: Received 25 September 2013 Accepted for publication 22 October 2013 Abstract. The topological Lifshitz phase transition is studied systematically within an effective model of QCD, in which the chiral symmetry, broken at zero temperature, is not restored at high temperature and/or baryon chemical potential. It is found that during phase transition the quark system undergoes a first-order transition from low density fully-gapped state to high density state with Fermi sphere which is protected by momentum-space topology. The Lifshitz phase diagram in the plane of temperature and baryon chemical potential is established. The critical behaviors of various equations of state are determined. I. INTRODUCTION Quantum Chromodynamics (QCD) is actually considered to be the theory of strongly interacting systems of quarks and gluons. At finite baryon chemical potential the theory also provides information on nuclear properties. We have expected that QCD at finite temperature T and baryon chemical potential µ has a very rich phase structure [1] such as the chiral symmetry restoration at high temperature and/or baryon chemical potential, the thermal phase transition from the Nambu-Goldstone phase to quark - gluon plasma, the phase transition from the Nambu-Goldstone phase to the color superconductivity at low T and so on. The experimental exploration of these phase transitions is being actively carried out in RHIC (Relativistic .
