Weak coupling analysis of the optical conductivity of the two dimensional Hubbard model

Brenig, Wilhelm

doi:10.1007/bf01320935

Cited by 11 publications

(6 citation statements)

References 23 publications

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“…Therefore, one is interested in the integrated weight of this singularity -the so called Drude weight -in the thermodynamic limit. The appearance of a nonzero Drude weight is often ascribed to the influence of conservation laws on transport properties 30,38,43,46,47 . For example, in the case of the Heisenberg chain the energy-current operator is conserved 30,48 implying a nonzero thermal Drude weight at all temperatures.…”

Section: Introductionmentioning

confidence: 99%

Zero-frequency transport properties of one-dimensional spin-12systems

et al. 2003

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We report a detailed analysis of the Drude weights for both thermal and spin transport in one dimensional spin-1/2 systems by means of exact diagonalization and analytic approaches at finite temperatures. Transport properties are studied first for the integrable XXZ model and second for various nonintegrable systems such as the dimerized chain, the frustrated chain, and the spin ladder. We compare our results obtained by exact diagonalization and mean-field theory with those of the Bethe ansatz, bosonization and other numerical studies in the case of the anisotropic Heisenberg model both in the gapless and gapped regime. In particular, we find indications that the Drude weight for spin transport is finite in the thermodynamic limit for the isotropic chain. For the nonintegrable models, a finite-size analysis of the numerical data for the Drude weights is presented covering the entire parameter space of the dimerized and frustrated chain. We also discuss which conclusions can be drawn from bosonization regarding the question of whether the Drude weights are finite or not. One of our main results is that the Drude weights vanish in the thermodynamic limit for nonintegrable models. I. INTRODUCTIONDue to their relevance for modeling the magnetic properties of several quasi-one-dimensional materials, dimerized and frustrated spin-1/2 chains and ladders are models of great and current interest. Recently, growing experimental evidence has been found that magnetic excitations can contribute significantly to the thermal conductivity of various quasi-one and quasi-two-dimensional materials [1][2][3][4][5][6][7][8][9][10][11] . Stimulated by these observations, many theoretical activities have addressed the issue of heat transport in one-dimensional spin systems [12][13][14][15][16][17][18][19][20][21][22] . While spin transport has been a topic of numerous theoretical investigations , the theory of thermal transport is less well understood. One of the key questions is to understand under which conditions transport is ballistic, i.e., dissipationless. The criterion for this is the existence of a singularity at zero frequency in the real part of the conductivity. Therefore, one is interested in the integrated weight of this singularity -the so called Drude weight -in the thermodynamic limit. The appearance of a nonzero Drude weight is often ascribed to the influence of conservation laws on transport properties 30,38,43,46,47 . For example, in the case of the Heisenberg chain the energy-current operator is conserved 30,48 implying a nonzero thermal Drude weight at all temperatures. Another widely discussed and related issue is the difference between transport in integrable models compared to nonintegrable ones 15,17,20,27,33,41,43 . The purpose of the present paper is to provide a systematic study of both the Drude weight for spin and thermal transport at finite temperatures by means of exact diagonalization on finite systems and analytic methods. The dependence on exchange coupling anisotropy, frustration and dimerization ...

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Section: Introductionmentioning

confidence: 99%

Zero-frequency transport properties of one-dimensional spin-12systems

et al. 2003

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“…An analytical analysis of the frequency dependent conductivity has been given by perturbation method in weak-coupling limit [16,17] and by applying the memory function technique in terms of the Hubbard operators [7]. Recently the optical conductivity has been investigated within the dynamical mean-field approach [6].…”

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“…However, for the realistic planar Hubbard model non-local corrections to the transport vertices and the self-energy are important [6]. Beyond this, vertex corrections are crucial to satisfy the relevant Ward-Takahashi identities [17].…”

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The conductivity tensor for the Hubbard model

Mancini

Villani

1999

Physics Letters A

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“…Hubbard model [1] is the simplest model describing the essential physics of materials with strong electron correlations and is used intensively. Theoretical investigations of the conductivity in the Hubbard model last for many decades, by both analytical [2][3][4] and numerical [5,6] methods. Extensive investigations of ferromagnetic properties of the model have been done (see [7,8] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Mott Transition, Ferromagnetism and Conductivity in the Generalized Hubbard Model

et al. 2007

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The electron correlations in narrow energy bands are examined within the framework of the Hubbard model, generalized by taking into account the correlated hopping of electrons. Electronic conductivity and ferromagnetic ordering stabilization in the system with various forms of electronic density of states are studied. The influence of magnetic field, temperature and the form of density of states on concentration dependence of conductivity and magnetization is investigated. The correlated hopping is shown to cause the electron-hole asymmetry of transport and ferromagnetic properties of narrow band materials.

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Weak coupling analysis of the optical conductivity of the two dimensional Hubbard model

Cited by 11 publications

References 23 publications

Zero-frequency transport properties of one-dimensional spin-12systems

Zero-frequency transport properties of one-dimensional spin-12systems

The conductivity tensor for the Hubbard model

Mott Transition, Ferromagnetism and Conductivity in the Generalized Hubbard Model

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