Lattice Green function in uniform magnetic fields

Ueta, Tsuyoshi

doi:10.1088/0305-4470/30/15/020

Cited by 7 publications

(6 citation statements)

References 22 publications

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“…As pointed out above, the effect of the magnetic field is contained in the local Green's function G ll , therefore, the strategy to solve the DMFT problem is to compute the eigenvalues of the non-interacting lattice in the presence of uniform magnetic field and use them in the selfconsistency loop. There are numerous methods to solve the non-interacting case 3,24,25 . For the numerical example presented below, we take the case of a uniform magnetic field perpendicular to a square lattice and we compute the energy level of Bloch electrons by solving an almost Mathieu equation named Harper equation 26 for rational ratios of magnetic flux, i.e.…”

Section: Methods and Modelmentioning

confidence: 99%

Orbital effect of the magnetic field in dynamical mean-field theory

2017

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The availability of large magnetic fields at international facilities and of simulated magnetic fields that can reach the flux-quantum-per-unit-area level in cold atoms, calls for systematic studies of orbital effects of the magnetic field on the self-energy of interacting systems. Here we demonstrate theoretically that orbital effects of magnetic fields can be treated within single-site dynamical meanfield theory with a translationally invariant quantum impurity problem. As an example, we study the one-band Hubbard model on the square lattice using iterated perturbation theory as an impurity solver. We recover the expected quantum oscillations in the scattering rate and we show that the magnetic fields allow the interaction-induced effective mass to be measured through the singleparticle density of states accessible in tunneling experiments. The orbital effect of magnetic fields on scattering becomes particularly important in the Hofstadter butterfly regime. II. THE DYNAMICAL MEAN-FIELD EQUATIONS WITH MAGNETIC FIELDHere we derive 17 the DMFT equations when the orbital effect of the magnetic field is taken into account in arXiv:1710.01396v1 [cond-mat.str-el]

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Section: Methods and Modelmentioning

confidence: 99%

Orbital effect of the magnetic field in dynamical mean-field theory

2017

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“…Recently, the Green function obtained for the tight-binding model on a square lattice in the applied magnetic field has been expressed by means of continued fractions by Ueta [8]. However, the derived expressions are more complicated, and therefore, as stated by the author, for large values of q (q > 5) are difficult to solve.…”

Section: If One Is Interested In G ð0þmentioning

confidence: 99%

Lattice Green function for electrons in magnetic field

Maśka

2003

Physica Status Solidi (b)

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The energy spectrum of electrons on a square lattice in an applied magnetic field composes the famous Hofstadter butterfly with a recursive internal subband structure. An effective method for calculating the Green function for such a system is proposed. The standard approach requires an explicit knowledge of the eigenstates and eigenenergies of the system; here we derive a Harper-like equation, that allows us to calculate the Green function for the lattice electrons in the field directly. The method is particularly useful in the weak-field regime, where the standard calculations are cumbersome.Introduction The problem of two-dimensional Bloch electrons in an applied magnetic field has been intensively studied for several decades. Besides exhibiting an extremely rich energy band structure, it can be related to various phenomena such as the quantum Hall effect or superconductivity in the presence of magnetic field [1]. The energy spectrum of a system of tightly bound electrons on a square lattice in a perpendicular uniform magnetic field exhibits interesting, multifractal properties. It is described by a model commonly referred as the Hofstadter or Azbel-Hofstadter model [2,3]. The band spectrum for rational values of the magnetic flux through an elementary plaquete F is known as the ''Hofstadter butterfly" [2]. In spite of the academic character of the model, experiments have been performed to uncover the multifractal structure [4]. This paper provides explicit expressions for the lattice Green functions in the presence of a magnetic field, that are convenient for both analytical and numerical calculations.Following Hofstadter, we start from the Schraedinger equation, where the tight-binding Hamiltonian is given by

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“…(28) in Ref. 13), it is possible to write the eigenvalue of T n (0) as From the above, the equation for the energy band structure is obtained as Hence, the problem of determination of the energy band is reduced to that of ∆ n (x), or a n , b n , c n , and d n .…”

Section: Formulation Of Inverse Problemmentioning

confidence: 99%

Determination of a structure of one‐dimensional dual‐periodic photonic crystal from an energy spectrum

Ueta

2002

Electron Comm Jpn Pt II

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SUMMARYAn inverse problem is treated for determination of the structure of a one-dimensional dual-periodic photonic crystal from the optical characteristics specified for practice. Under the assumption that the light is localized in the higher permittivity layer, a general formulation is obtained for determining the permittivity in the modulated high-permittivity layer from the structure of the energy spectrum by means of the tight-binding approximation. The problem is reduced to an algebraic equation. Numerical examples are given for determination of the permittivity.

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Lattice Green function in uniform magnetic fields

Cited by 7 publications

References 22 publications

Orbital effect of the magnetic field in dynamical mean-field theory

Orbital effect of the magnetic field in dynamical mean-field theory

Lattice Green function for electrons in magnetic field

Determination of a structure of one‐dimensional dual‐periodic photonic crystal from an energy spectrum

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