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 an Ising ferromagnetic QCP. We show that one can extract from QMC data the zero-temperature form of fermionic self-energy Σ(ω) even though the leading contribution to the self-energy comes from thermal effects. We find that the frequency dependence of Σ(ω) agrees well with the analytic form obtained within the Eliashberg theory of dynamical quantum criticality, and obeys ω2/3 scaling at low frequencies. Our results open up an avenue for QMC studies of quantum critical metals.

How non-Fermi liquids cure their infrared divergences

“…The second regime in (III.23) was also recently found in [17], where it was argued to be relevant for matching quantum Monte Carlo results [27]. We should also verify our assumption that A(ω m ) vq in the second line of (III.14), which allowed us to replace that term by Σ NFL (ω n ) of (II.16).…”

“…The title of our work is motivated by[5] 2. While we were finishing this manuscript, Refs [16,17]. appeared, which have some overlaps with the results in Sec.…”

“…Furthermore, while we have argued that superconductivity becomes irrelevant above N c = 8, we plan to present a detailed analysis at finite temperature in future work, finding the solutions to the corrected Eliashberg equations and revisiting the role of the first Matsubara frequencies [15,23,24]. Another direction recently explored in [16,17] is the relevance of thermal effects to numerical quantum Monte Carlo results [28][29][30][31], something that deserves further study both at finite but small temperature and including the effects of pairing interactions. Finally, the methods of this paper for a z b = 3 bosonic scaling could be extended to more general z b > 1.…”

“…1 In contrast, much less is known about infrared problems at finite density. Work in this area, both in the condensed matter and high energy fields, includes [6][7][8][9][10][11][12][13][14][15][16][17].…”

Measuring Rényi entanglement entropy with high efficiency and precision in quantum Monte Carlo simulations

“…Here we show that previously difficult EE measurements can be greatly optimized and improved via the nonequilibrium increment method, and in this way, one can investigate the scaling behavior of EE in many (2 + 1)d quantum many-body systems with unprecedentedly large system sizes, controlled errorbars and minimal computational costs. Starting from the three representative cases shown here, one can foresee the implementation and measurement of EE via the Qiu Ku algorithm for other topological ordered phases and phase transitions, interacting fermionic systems such as the Gross-Neveu QCPs with critical Dirac fermions [83], the deconfined QED 3 problems of gauge fields coupled to fermion matter fields [84][85][86] and the more complicated situations of non-Fermi-liquid and quantum critical metals [87][88][89][90][91][92][93][94][95] and hopefully make further suggestions to the on-going experimental search for these strongly entangled quantum matter.…”