Dirac Eigenvalue Spectrum In Nonzero Magnetic Fields From Lattice QCD

As strong magnetic fields may appear in the early universe,heavy-ion collisions and magnetars,the properties of strong interacting matter in external magnetic fields have attracted a lot of studies.At the same time,chiral condensate is a very im-portant physical quantity in the theory of quantum chromodynamics,and it is often calculated by the stochastic noise estimator method in lattice quantum chromody-namics.In order to explore the microscopic nature,another method for calculating chiral condensate through Dirac eigenvalue spectrum has been proposed.Eigenvalue filtering technology and random estimate of mode number method are used in this paper to calculate the Dirac eigenvalue spectrum under non-zero magnetic field and explore other magnetic field-related behaviors.In this thesis,firstly,the research background and current research status of QCD under finite magnetic field,as well as the related knowledge of lattice quantum chromodynamics,are introduced.Secondly,two methods calculating chiral condense,direct calculation method and calculation by eigenvalue spectrum method,are de-scribed in details.Thirdly,we use the highly improved staggered quark(HISQ)to simulate the(2+1)flavor QCD.In the simulation,the spatial size is 32 and temporal sizes are 6,8,10,12,and 14,respectively with corresponding temperatures ranging in 120.3MeV-280MeV.The magnetic field quantization number Nb is 0,12,24 and 32.The mass of the strange quark is fixed to its physical mass,and the mass of the light quark is ml=msphy/10.In the continuity limit,the mass of pion is 220 MeV.Lastly,based on the existing GPU code to compute the Dirac Eigenvalue spectrum,we implemented the magnetic field in the computation,which is performed on the GPU cluster at CCNU.We calculate the chiral condensate using the Dirac eigenvalue spectrum obtained by the eigenvalue filter,and compare the result obtained by the direct calculation method(using the stochastic noise estimation method to calculate the inverse of the Fermi matrix).It is found that the chiral condensates obtained by using these two algorithms are consistent.In addition,we also explored the dependence of the Dirac eigenvalue spectrum on temperature,the magnetic field,and flavor species.It is found that as the temperature decreases,the eigenvalue spectrum increases near ??0.In addition,the magnetic catalysis and inverse magnetic catalysis near the critical temperature have been observed.Finally,the dependence of eigenvalue spectral density at ??0 on temperature and magnetic field is also studied.