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Physica C Superconductivity

A controlled route to the competing phases and the single-particle spectral function in the ground state of the 2D Hubbard model

Werner R. Hanke, Markus Aichhorn, Enrico Arrigoni, Michael Potthoff

Published Mar 21, 2007• 0 citations
Publisher
DOI
10.1016/j.physc.2007.03.019

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Abstract We study the electron spectral function of the antiferromagnetically ordered phase of the three dimensional Hubbard model, using recently formulated low‐energy theory based on the 2D half‐filled Hubbard model which describes both collective spin and charge fluctuations for arbitrary value of the Coulomb repulsion U. The model then is solved by a saddle‐point approximation within the CP1 representation for the Neel field. The single‐particle properties are obtained by writing the fermion field in terms of a U(1) phase, Schwinger boson SU(2) fields and a pseudofermion variables. We demonstrate that the appearance of a sharp peak in the electron spectral function in the antiferromagnetic state points to the emergence of the bosonic mode, which is associated with spin ordering.
We take an in depth look into the celebrated Fermi-Hubbard model for strongly interacting fermions, beginning with a two-site exact diagonalization demonstration of the Mott ground state. We continue with measurements of compressibility and susceptibility using Determinantal Quantum Monte Carlo (DQMC) methods on a larger square lattice 6x6 over the parameter space of interaction strength U/t and doping, controlled by the chemical potential, mu/t. We construct the Fermi surface for a 16x16 cluster size using the retarded Green's function and the single particle spectral function (derived from the Green's function using an analytic continuation procedure) and find conclusive evidence of Fermi surface restructuring (FSR) as a result of strong interactions freezing out states from contributing to the Luttinger count, n, at intermediate temperatures, T = t/2. FSR is found for strongly interacting, doped systems for dopings p < 0.2. This phase is dubbed the Luttinger's rule breaking (LB) phase, and we provide a discussion of the consequences of the deviation from Luttinger's theorem. We strongly suggest a topological nature underlying the restructuring of the Fermi surface by eliminating competing ordering in spin or charge channels.
We present a tangent-space Krylov method for efficient computation of zero-temperature real-frequency spectral functions on top of ground-state matrix product states obtained from the density matrix renormalization group. It relies on projecting the Hamiltonian to the tangent space of the ground-state matrix product states, where resolvents can be efficiently represented using Krylov space techniques. This enables direct computations of excitation energies and the corresponding spectral weights. We demonstrate the accuracy and efficiency of the tangent-space Krylov approach by showcasing spectral data for various models. These include the 1D Haldane-Shastry and Heisenberg models as benchmarks. As an interesting application, we study the Hubbard model on a cylinder at half filling, augmented by a density-assisted hopping (DAH) term. We find that DAH leads to particle-hole asymmetric single-particle mobilities and lifetimes in the resulting Mott insulator, and identify the responsible scattering processes. Furthermore, we find that DAH influences the dispersion of Green’s function zeros beyond its range, which has a frustrating effect on the Mott insulator studied here.