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arXiv:1404.2995 · International Conference on Strongly Correlated Electron Systems (SCES)

Variational Approach to Localization Length for Two-Dimensional Hubbard Model

Shun Tamura, Hisatoshi Yokoyama

Published Jun 16, 2014• 2 citations
arXivHTMLPDF

Abstract

As a measure to ascertain whether a system is metallic or insulating, localization length $λ_N$, 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 $λ_N$ 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 $λ_N$ is consistent with what is expected from other quantities, and gives information complementary to another measure, the Drude weight.

DOI
10.7566/jpscp.3.013003

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As a measure to ascertain whether a system is metallic or insulating, localization length λNλ_NλN​, 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 λNλ_NλN​ 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 λNλ_NλN​ is consistent with what is expected from other quantities, and gives information complementary to another measure, the Drude weight.
Density functional and quantum Monte Carlo methods are used to examine the behaviour of the many-electron localization length near band insulator-to-metal transitions in various one- and two-dimensional model systems. The many-electron localization length is infinite in metals and finite in insulators, and is normally assumed to diverge as an insulator-to-metal transition is approached from the insulating side. Our results show that this is not the case: the band insulator-to-metal transition is normally first order and not associated with a diverging length scale. We also identify examples where the localization length diverges but the system is insulating on both sides of the divergence. The usefulness of the localization length as an indicator of the approach of an insulator-to-metal transition is therefore limited. A comparison of our quantum Monte Carlo and density functional results allows us to draw some general conclusions about the effect of correlation on localization.
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Abstract. We investigate the phase diagram of the square lattice bilayer Hubbard model at half filling with the variational Monte Carlo method for both the magnetic and the paramagnetic case as a function of the interlayer hopping t ⊥ and on-site Coulomb repulsion U. With this study we resolve some discrepancies in previous calculations based on the dynamical mean field theory, and we are able to determine the nature of the phase transitions between metal, Mott insulator and band insulator. In the magnetic case we find only two phases: An antiferromagnetic Mott insulator at small t ⊥ for any value of U and a band insulator at large t⊥. At large U values we approach the Heisenberg limit. The paramagnetic phase diagram shows at small t ⊥ a metal to Mott insulator transition at moderate U values and a Mott to band insulator transition at larger U values. We also observe a re-entrant Mott insulator to metal transition and metal to band insulator transition for increasing t ⊥ in the range of 5.5t < U < 7.5t. Finally, we discuss the obtained phase diagrams in relation to previous studies based on different many-body approaches. PACS numbers: 71.10.Fd, 71.27.+a, 71.30.+h 1.
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