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arXiv:cond-mat/0605007 · Physical Review B

Effect of frustration on charge dynamics for a doped two-dimensional triangular Hubbard lattice: Comparison with a square lattice

Takami Tohyama

Published Sep 21, 2006• 6 citations
arXivHTMLPDF

Abstract

We examine the optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ and the chemical potential $\ensuremath{\mu}$, together with the spin correlation, in the strong-coupling limit of a hole-doped two-dimensional triangular Hubbard model near half filling by using an exact diagonalization technique. In contrast to the case of a square lattice without frustration, the doping dependences of $\ensuremath{\mu}$ and the Drude weight indicate that the charge degree of freedom is weakly coupled to the spin degree of freedom. However, we find that $\ensuremath{\sigma}(\ensuremath{\omega})$ shows strong incoherent excitations extended to a higher energy region. This implies that geometrical frustration in strongly correlated electron systems influences incoherent charge dynamics.

DOI
10.1103/physrevb.74.113108

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We examine the optical conductivity \ensuremathσ(\ensuremathω)\ensuremath{\sigma}(\ensuremath{\omega})\ensuremathσ(\ensuremathω) and the chemical potential \ensuremathμ\ensuremath{\mu}\ensuremathμ, together with the spin correlation, in the strong-coupling limit of a hole-doped two-dimensional triangular Hubbard model near half filling by using an exact diagonalization technique. In contrast to the case of a square lattice without frustration, the doping dependences of \ensuremathμ\ensuremath{\mu}\ensuremathμ and the Drude weight indicate that the charge degree of freedom is weakly coupled to the spin degree of freedom. However, we find that \ensuremathσ(\ensuremathω)\ensuremath{\sigma}(\ensuremath{\omega})\ensuremathσ(\ensuremathω) shows strong incoherent excitations extended to a higher energy region. This implies that geometrical frustration in strongly correlated electron systems influences incoherent charge dynamics.
We examine the regular part of optical conductivity in the strong-coupling limit of a hole-doped two-dimensional triangular Hubbard model near half filling. A numerically exact diagonalization method based on the Lanczos technique is employed for a 21-site triangular lattice. The regular part is calculated by averaging over various twisted boundary conditions to reduce finite-size effects. We find that the spectra show strong incoherent excitations extended to a higher energy region irrespective of the sign of the hopping amplitude. This is in contrast to the case of a square lattice without frustration. The results imply that geometrical frustration in strongly correlated electron systems influences incoherent charge dynamics.
High-temperature bad-metal transport has been recently studied both theoretically and in experiments as one of the key signatures of strong electronic correlations. Here we use the dynamical mean field theory and its cluster extensions, as well as the finite-temperature Lanczos method to explore the influence of lattice frustration on the thermodynamic and transport properties of the Hubbard model at high temperatures. We consider the triangular and the square lattices at half-filling and at 15% hole doping. We find that for $T\ensuremath{\gtrsim}1.5t$ the self-energy becomes practically local, while the finite-size effects become small at lattice size $4\ifmmode\times\else\texttimes\fi{}4$ for both lattice types and doping levels. The vertex corrections to optical conductivity, which are significant on the square lattice even at high temperatures, contribute less on the triangular lattice. We find approximately linear temperature dependence of dc resistivity in doped Mott insulator for both types of lattices.
Dynamical properties are notoriously difficult to compute in numerical treatments of the Fermi-Hubbard model, especially in two spatial dimensions. However, they are essential in providing us with insight into some of the most important and less well-understood phases of the model, such as the pseudogap and strange metal phases at relatively high temperatures, or unconventional superconductivity at lower temperatures, away from the commensurate filling. Here, we use the numerical linked-cluster expansions to compute spin and charge optical conductivities of the model at different temperatures and strong interaction strengths via the exact real-time-dependent correlation functions of the current operators. We mitigate systematic errors associated with having a limited access to the long-time behavior of the correlators by introducing fits and allowing for non-zero Drude weights when appropriate. We compare our results to available data from optical lattice experiments and find that the Drude contributions can account for the theory-experiment gap in the DC spin conductivity of the model at half filling in the strong-coupling region. Our method helps paint a more complete picture of the conductivity in the two-dimensional Hubbard model and opens the door to studying dynamical properties of quantum lattice models in the thermodynamic limit.
We numerically study optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ near the ``antiferromagnetic'' phase transition in the square-lattice Hubbard model at half filling. We use a cluster dynamical mean field theory and calculate conductivity including vertex corrections and, to this end, we have reformulated the vertex corrections in the antiferromagnetic phase. We find that the vertex corrections change various important details in temperature and $\ensuremath{\omega}$ dependencies of conductivity in the square lattice, and this contrasts sharply the case of the Mott transition in the frustrated triangular lattice. Generally, the vertex corrections enhance variations in the $\ensuremath{\omega}$ dependence, and sharpen the Drude peak and a high-$\ensuremath{\omega}$ incoherent peak in the paramagnetic phase. They also enhance the dip in $\ensuremath{\sigma}(\ensuremath{\omega})$ at $\ensuremath{\omega}=0$ in the antiferromagnetic phase. Therefore, the dc conductivity is enhanced in the paramagnetic phase and suppressed in the antiferromagnetic phase, but this change occurs slightly below the transition temperature. We also find a temperature region above the transition temperature in which the dc conductivity shows an insulating behavior but $\ensuremath{\sigma}(\ensuremath{\omega})$ retains the Drude peak, and this region is stabilized by the vertex corrections. We also investigate which fluctuations are important in the vertex corrections and analyze momentum dependence of the vertex function in detail.
We investigate the effects of magnetic frustration on spin and charge dynamics in strongly correlated itinerant electron systems by using the exact diagonalization technique. A Hubbard model with adjustable degree of magnetic frustration is constructed. Static and dynamic spin and charge correlation functions show different dependence on the degree of magnetic frustration in the system. With increasing magnetic frustration, the spin and charge correlation function spectra become more sparse, indicating a decreased level of mixing of the spin and charge degrees of freedom or a partial spin-charge separation.
Unusual normal-state properties of strongly correlated electron materials have been discovered in recent years. They can not be explained by traditional theories. Much work has been devoted to exploring the physical insight into these properties. In the dissertation, the study of spin and charge response to magnetic frustration in the Hubbard Model is presented. Using exact diagonalization techniques, the eigenvalues and eigenvectors of a two-dimensional Hubbard model applied to a cluster with periodic boundary conditions have been obtained. Static and dynamic spin and charge correlation functions as well as one-particle excitation spectra have been calculated. The effects of magnetic frustration due to geometrical competition of different electron hopping terms are studied for various doping and short-range Coulomb interaction parameters. The calculated results are discussed in the framework of many-body physics.