Identification of non-Fermi liquid fermionic self-energy from quantum Monte Carlo data

Abstract: Quantum Monte Carlo (QMC) simulations of correlated electron systems provide unbiased information about system behavior at a quantum critical point (QCP) and can verify or disprove the existing theories of non-Fermi liquid (NFL) behavior at a QCP. However, simulations are carried out at a finite temperature, where quantum-critical features are masked by finite temperature effects. Here we present a theoretical framework within which it is possible to separate thermal and quantum effects and extract the information about NFL physics at $T=0$. We demonstrate our method for a specific example of 2D fermions near a Ising-ferromagnetic QCP. We show that one can extract from QMC data the zero-temperature form of fermionic self-energy $\Sigma (\omega)$ even though the leading contribution to the self-energy comes from thermal effects. We find that the frequency dependence of $\Sigma (\omega)$ agrees well with the analytic form obtained within the Eliashberg theory of dynamical quantum criticality, and obeys $\omega^{2/3}$ scaling at low frequencies. Our results open up an avenue for QMC studies of quantum-critical metals.