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Register a new userIdentification of non-Fermi liquid fermionic self-energy from quantum Monte Carlo data
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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.
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This review summarizes recent developments in the study of fermionic quantum criticality, focusing on new progress in numerical methodologies, especially quantum Monte Carlo methods, and insights that emerged from recently large-scale numerical simulations. Quantum critical phenomena in fermionic systems have attracted decades of extensive research efforts, partially lured by their exotic properties and potential technology applications and partially awaked by the profound and universal fundamental principles that govern these quantum critical systems. Due to the complex and non-perturbative nature, these systems belong to the most difficult and challenging problems in the study of modern condensed matter physics, and many important fundamental problems remain open. Recently, new developments in model design and algorithm improvements enabled unbiased large-scale numerical solutions to be achieved in the close vicinity of these quantum critical points, which paves a new pathway towards achieving controlled conclusions through combined efforts of theoretical and numerical studies, as well as possible theoretical guidance for experiments in heavy-fermion compounds, Cu-based and Fe-based superconductors, ultra-cold fermionic atomic gas, twisted graphene layers, etc., where signatures of fermionic quantum criticality exist.
We describe an open-source implementation of the continuous-time interaction-expansion quantum Monte Carlo method for cluster-type impurity models with onsite Coulomb interactions and complex Weiss functions. The code is based on the ALPS libraries.
According to Landaus Fermi liquid theory, the main properties of the quasiparticle excitations of an electron gas are embodied in the effective mass $m^*$, which determines the energy of a single quasiparticle, and the Landau interaction function, which indicates how the energy of a quasiparticle is modified by the presence of other quasiparticles. This simple paradigm underlies most of our current understanding of the physical and chemical behavior of metallic systems. The quasiparticle effective mass of the three-dimensional homogeneous electron gas has been the subject of theoretical controversy and there is a lack of experimental data. In this work, we deploy diffusion Monte Carlo (DMC) methods to calculate $m^*$ as a function of density for paramagnetic and ferromagnetic three-dimensional homogeneous electron gases. The DMC results indicate that $m^*$ decreases when the density is reduced, especially in the ferromagnetic case. The DMC quasiparticle energy bands exclude the possibility of a reduction in the occupied bandwidth relative to that of the free-electron model at density parameter $r_s=4$, which corresponds to Na metal.
A path-integral representation is constructed for the Jahn-Teller polaron (JTP). It leads to a perturbation series that can be summed exactly by the diagrammatic Quantum Monte Carlo technique. The ground-state energy, effective mass, spectrum and density of states of the three-dimensional JTP are calculated with no systematic errors. The band structure of JTP interacting with dispersionless phonons, is found to be similar to that of the Holstein polaron. The mass of JTP increases exponentially with the coupling constant. At small phonon frequencies, the spectrum of JTP is flat at large momenta, which leads to a strongly distorted density of states with a massive peak at the top of the band.
We investigate the quantum phase transitions of a disordered nanowire from superconducting to metallic behavior by employing extensive Monte Carlo simulations. To this end, we map the quantum action onto a (1+1)-dimensional classical XY model with long-range interactions in imaginary time. We then analyze the finite-size scaling behavior of the order parameter susceptibility, the correlation time, the superfluid density, and the compressibility. We find strong numerical evidence for the critical behavior to be of infinite-randomness type and to belong to the random transverse-field Ising universality class, as predicted by a recent strong disorder renormalization group calculation.
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