Some Studies On Fermion-Boson Coupled System

Fermion-Boson coupled models can be used to study the strongly correlated quan-tum many-body systems.Such models are designed from the coupling between free Fermion and critical Bosonic modes,such that the quantum fluctuations of bosonic or-der parameters would mediate strong interactions among the Fermions.In this thesis we study two Fermion-Boson coupled models,i.e.the 3D compact quantum electro-dynamics(c QED₃)coupled with Fermion lattice model and the Yukawa-SYK model with finite temperature determinantal quantum Monte Carlo method.In these works,two kinds of strongly correlated electron problems-deconfined phase transition and non-Fermi liquid are well revealed.Firstly we study the deconfinement-to-confinement phase transition induced by the fluctuation of the gauge field in the c QED₃model.The phase diagram as a function of fermion flavors and the strength of gauge fluctuations has been mapped out.These phase transitions are beyond the Landau-Ginzburg-Wilson frame and the existence of the de-confined phase is confirmed in the quantum Monte Carlo calculation.When tuning the fluctuations of the gauge field,the deconfinement-to-confinement phase transitions emerge with the associated spontaneous-symmetry breaking.The properties of the U(1)deconfined phase are well studied and the universality class(dubbed QED₃-GN-XY)of these phase transitions(U1D-VBS)are determined.Also we focus on the large fermion flavor case(₁)=8)to investigate the dynamic properties across the deconfinement-to-confinement phase transition.In the deconfined phase,fermions coupled to the fluc-tuating gauge field form a U(1)spin liquid with continua in both spin and dimer spectral functions,and in the confined phase fermions are gapped out into valence bond solid(VBS)phase with translational symmetry breaking and gapped spectra.Secondly,we consider a Sachdev-Ye-Kitaev(SYK)-like model with random Yukawa interaction between critical bosons and fermions(dubbed the Yukawa-SYK model).Our simulation demonstrates that the Yukawa-SYK model features“self-tuned quantum crit-icality”,i.e.,the system is critical independent of the bosonic bare mass.We put these results to the test at finite,and our unbiased numerics reveal clear evidence of these exotic quantum critical non-Fermi liquid(n FL)properties—the power-law behavior in the Green's function of fermions and bosons.Meanwhile we present the global phase diagram as a function of chemical potential?and temperatureof the Yukawa-SYK model.Up to a critical value in the chemical potential,a finite temperature phase transition from n FL to superconductivity is observed.Our results provide the model realization of the transitions of n FL towards superconductivity and insulating states,therefore offer a controlled platform for future investigations of the generic phase di-agram that hosts n FL,insulator and superconductor and their phase transitions.Also our study builds relationship between zero temperature lagre-and finite temperature finiteof this model,which can give a well way to extend these conclusions at the limit of analytic calculation to realistic physical system.