In this manuscript, we study quantum criticality of Dirac fermions via large-scale numerical simulations, focusing on the Gross-Neveu (GN) chiral-Ising quantum critical point with critical bosonic modes coupled with Dirac fermions. We show that finite-size effects at this quantum critical point can be efficiently minimized via model design, which maximizes the ultraviolet cutoff and at the same time places the bare control parameters closer to the nontrivial fixed point to better expose the critical region. Combined with the efficient self-learning quantum Monte Carlo algorithm, which enables non-local update of the bosonic field, we find that moderatelylarge system size (up to 16 × 16) is already sufficient to produce robust scaling behavior and critical exponents. The conductance of the Dirac fermions is also calculated and its frequency dependence is found to be consistent with the scaling behavior predicted by the conformal field theory. The methods and model-design principles developed for this study can be generalized to other fermionic QCPs, and thus provide a promising direction for controlled studies of strongly-correlated itinerant systems. arXiv:1910.07430v3 [cond-mat.stat-mech]

Thanks to the development in quantum Monte Carlo technique, the compact U(1) lattice gauge theory coupled to fermionic matter at (2+1)D is now accessible with large-scale numerical simulations, and the ground state phase diagram as a function of fermion flavor (N f ) and the strength of gauge fluctuations is mapped out [1]. Here we focus on the large fermion flavor case (N f = 8) to investigate the dynamic properties across the deconfinement-to-confinement phase transition. In the deconfined phase, fermions coupled to the fluctuating gauge field to form 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 phase with translational symmetry breaking and gapped spectra. The dynamical behaviors provide supporting evidence for the existence of the U(1) deconfined phase and could shine light on the nature of the U(1)-to-VBS phase transition which is of the QED 3 -Gross-Neveu chiral O(2) universality whose properties still largely unknown.