Determinant Monte Carlo Simulation On Quantum Critical Points

In the study of Strongly correlated system,Quantum critical points(QCPs)in the presence of fermionic fluctuations are the intriguing and challenging topics.Due to strong fluctuations near QCPs,many exotic physical phenomenon beyond the Landau theory are observed such as new universality class,unconventional superconductor,non-fermi liquid and pseudogap.Meanwhile Quantum Monte Carlo(QMC)gradually became effective tool to understand fermionic QCPs with development of numerical method and computing power in recent years.In this thesis,two types of fermionic QCPs are simulated by QMC;The first is the Dirac fermion QCPs,the model have been designed for minimizing finite-size effect and maximizing the ultraviolet cutoff.The robust scaling behavior and critical exponents are observed clearly in the moderately large size(up to 16×16×2).The conductance of Dirac fermions is also calculated and its frequency dependence is consistent with scaling behavior predicted by comformal field theory.At the same time,another Dirac fermion model is calculated to study that fluctuations of massless fermion influence on QCPs.Its result shows that Dirac fermion will enhance first-order transition which is contrary to the theorical prediction of inducing continuous phase transition.It reflects competition between finite-size effect and critical fluctuations that can be qualitatively understood by mean-field theory.We also study the scaling behavior at the separation point between the first-order and continuous phase transition belonging to the chiral tricritical Gross-Neveu university.The second is ferromagnetic itinerant fermionic QCPs,non-fermi liquid behavior is exhibited in the model of coupling between 2D quantum rotor and itinerant fermions which does not agree with theorical prediction of Hertz-Mills-Moriya(HMM)theory.In HMM theory,the scaling of fermionic self energy near QCP is Σ～ω2/3 and dynamical critical exponent is z=3,but in our simulation,non-fermi liquid have the scaling of self energy∑～ω1/2 and dynamical critical exponent z=2 which is very similar to antiferromagnetic itinerant QCPs.We argue that the phenomenon is associated with the fact that total spin is by itself not a conserved quantity due to fermion-boson coupling and the part of Landau damping 1/q is replaced by constant.