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Register a new userA Dynamical Quantum Cluster Approach to Two-Particle Correlation Functions in the Hubbard Model
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We investigate the charge- and spin dynamical structure factors for the 2D one-band Hubbard model in the strong coupling regime within an extension of the Dynamical Cluster Approximation (DCA) to two-particle response functions. The full irreducible two-particle vertex with three momenta and frequencies is approximated by an effective vertex dependent on the momentum and frequency of the spin/charge excitation. In the spirit of the DCA, the effective vertex is calculated with quantum Monte Carlo methods on a finite cluster. On the basis of a comparison with high temperature auxiliary field quantum Monte Carlo data we show that near and beyond optimal doping, our results provide a consistent overall picture of the interplay between charge, spin and single-particle excitations.
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Cluster Perturbation Theory (CPT) is a computationally economic method commonly used to estimate the momentum and energy resolved single-particle Greens function. It has been used extensively in direct comparisons with experiments that effectively measure the single-particle Greens function, e.g., angle-resolved photoemission spectroscopy. However, many experimental observables are given by two-particle correlation functions. CPT can be extended to compute two-particle correlation functions by approximately solving the Bethe-Salpeter equation. We implement this method and focus on the transverse spin-susceptibility, measurable via inelastic neutron scattering or with optical probes of atomic gases in optical lattices. We benchmark the method with the one-dimensional Fermi-Hubbard model at half filling by comparing with known results.
We explore the Matsubara quasiparticle fraction and the pseudogap of the two-dimensional Hubbard model with the dynamical cluster quantum Monte Carlo method. The character of the quasiparticle fraction changes from non-Fermi liquid, to marginal Fermi liquid to Fermi liquid as a function of doping, indicating the presence of a quantum critical point separating non-Fermi liquid from Fermi liquid character. Marginal Fermi liquid character is found at low temperatures at a very narrow range of doping where the single-particle density of states is also symmetric. At higher doping the character of the quasiparticle fraction is seen to cross over from Fermi Liquid to Marginal Fermi liquid as the temperature increases.
The nonequilibrium variational-cluster approach is applied to study the real-time dynamics of the double occupancy in the one-dimensional Fermi-Hubbard model after different fast changes of hopping parameters. A simple reference system, consisting of isolated Hubbard dimers, is used to discuss different aspects of the numerical implementation of the approach in the general framework of nonequilibrium self-energy functional theory. Opposed to a direct solution of the Euler equation, its time derivative is found to serve as numerically tractable and stable conditional equation to fix the time-dependent variational parameters.
We examine a central approximation of the recently introduced Dynamical Cluster Approximation (DCA) by example of the Hubbard model. By both analytical and numerical means we study non-compact and compact contributions to the thermodynamic potential. We show that approximating non-compact diagrams by their cluster analogs results in a larger systematic error as compared to the compact diagrams. Consequently, only the compact contributions should be taken from the cluster, whereas non-compact graphs should be inferred from the appropriate Dyson equation. The distinction between non-compact and compact diagrams persists even in the limit of infinite dimensions. Non-local corrections beyond the DCA exist for the non-compact diagrams, whereas they vanish for compact diagrams.
As a measure to ascertain whether a system is metallic or insulating, localization length $lambda_N$, which represents the spread of electron distribution, can be a useful quantity, especially for approaching a metal-insulator transition from the insulator side. We try to calculate $lambda_N$ using a variational Monte Carlo method for normal (paramagnetic), superconducting and antiferromagnetic states in the square-lattice Hubbard model. It is found that the behavior of $lambda_N$ is consistent with what is expected from other quantities, and gives information complementary to another measure, the Drude weight.
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