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arXiv:1908.04776 · Physical review. B./Physical review. B

Dynamical charge susceptibility in the Hubbard model

Xinyang Dong, Xi Chen, Emanuel Gull

Published Dec 5, 2019• 22 citations
arXivHTMLPDF

Abstract

We compute the dynamical charge susceptibility in the two-dimensional Hubbard model within the dynamical cluster approximation. In order to understand the connection between charge susceptibility and pseudogap, we investigate the momentum, doping, and temperature dependence. We find that as a function of frequency, the dynamical charge susceptibility is well represented by a single peak at a characteristic frequency. It shows little momentum or temperature dependence, while the doping dependence is more evident, and no clear signature of the pseudogap is observed. Data for the doping evolution of the static susceptibility and for fluctuation diagnostics are presented. Our susceptibilities should be directly measurable in future Momentum-resolved electron energy-loss spectroscopy experiments.

DOI
10.1103/physrevb.100.235107

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The doping and temperature dependencies of the electronic structure and the dynamic spin susceptibility of the Hubbard model on a square lattice are studied within cluster perturbation theory (CPT). The most general features of both electronic and spin spectra qualitatively agree with the experimental data on cuprates. Generalized mean-field calculations of the electronic structure using static short-range magnetic correlations from CPT are also implemented and compared with the results of CPT, allowing us to discuss the role of short-range antiferromagnetism in the formation of the pseudogap.
We compute unbiased spectral functions of the two-dimensional Hubbard model by extrapolating Green functions, obtained from determinantal quantum Monte Carlo simulations, to the thermodynamic and continuous time limits. Our results clearly resolve the pseudogap at weak to intermediate coupling, originating from a momentum selective opening of the charge gap. A characteristic pseudogap temperature T∗{T}^{*}T∗, determined consistently from the spectra and from the momentum dependence of the imaginary-time Green functions, is found to match the dynamical mean-field critical temperature, below which antiferromagnetic fluctuations become dominant. Our results identify a regime where pseudogap physics is within reach of experiments with cold fermions on optical lattices.
We investigate charge fluctuations in the two-dimensional Hubbard model as a function of doping, interaction strength, next-nearest-neighbor hopping, and temperature within the eight-site dynamical cluster approximation. In the regime of intermediate interaction strengths, we find that ddd density wave fluctuations, which had previously been postulated using analytical arguments, are present and strong but cannot be interpreted as the cause of the pseudogap in the model, due to their evolution with doping and interaction strength. For all parameters away from half filling, the charge fluctuations investigated, including ddd density wave fluctuations, are weaker than ddd-wave superconducting fluctuations.
We study the normal-state, doping-driven phase diagram of the square-lattice Hubbard model using the dynamical cluster approximation combined with the numerical renormalization group as a cluster solver, which gives direct access to real-frequency dynamics at essentially zero temperature. In a parameter regime relevant for cuprates, U=7tU=7tU=7t and t′=−0.3tt'=-0.3tt′=−0.3t, we find a critical doping p∗p^{\ast}p∗ that marks a continuous quantum phase transition between a pseudogap metal and a normal Fermi liquid. The transition is identified by a continuous collapse, from both sides, of the Fermi-liquid scale extracted from charge, spin, and dx2−y2d_{x^2-y^2}dx2−y2​-wave pairing susceptibilities. This collapse produces a non-Fermi-liquid regime at intermediate energy scales, which appears to extend to arbitrarily low scales at p∗p^{\ast}p∗. As p∗p^{\ast}p∗ is crossed from the normal Fermi liquid at p>p∗p>p^{\ast}p>p∗ into the pseudogap metal at $p
We consider the dynamic charge susceptibility and the charge density waves in strongly-correlated electronic systems within the two-dimensional t-J-V model. Using the equation of motion method for the relaxation functions in terms of the Hubbard operators, we calculate the static susceptibility and the spectrum of charge fluctuations as functions of doped hole concentrations and temperature. Charge density waves emerge for a sufficiently strong intersite Coulomb interaction. Calculation of the dynamic charge susceptibility reveals a strong damping of charge density waves for a small hole doping and propagating high-energy charge excitations at large doping.