Self-energy and Fermi surface of the two-dimensional Hubbard model

Eder, R.; Seki, Koh‐ichi; Ohta, Y.

doi:10.1103/physrevb.83.205137

Cited by 34 publications

(30 citation statements)

References 68 publications

(109 reference statements)

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“…, which obviously provides a reasonable, if not perfect, fit to the zeros of the calculated Green function. This form, which resembles an inverted free-electron dispersion with a renormalised hopping parameter, is quite similar to the results obtained by exact diagonalisation [24], except in that the effective hopping is smaller.…”

Section: Luttinger Volumesupporting

confidence: 84%

“…The shifting of spectral weight between Hubbard bands signals that the real part of the electron Green function changes sign between ( ) 0, 0 and p p ( ) , , which implies that the self-energy diverges and the Green function has a zero surface falling within this region [64]. The importance of zeros and poles of the Green function has been stressed by many authors [24,[64][65][66][67]87] in the discussion of Mott physics, particularly in the context of pseudogap phenomena in the doped system. We defer a discussion of the zero surface of the electron Green function to section 5.…”

Section: Spectral Function 41 Derivation and Calculationmentioning

confidence: 99%

“…However, this change of sign is not always connected with an infinity. It may also occur through zeros of the Green function [24,[64][65][66][67]87], and in fact these are the relevant quantities for insulating systems, where there is no Fermi surface. By contrast, all systems have a Luttinger surface, and this may be defined from the zeros.…”

Section: Luttinger Volumementioning

confidence: 99%

“…For the intermediate-coupling regime, where no well-controlled theoretical solution exists, many numerical methods have been applied to the two-dimensional (2D) Hubbard model, including exact diagonalisation [20][21][22][23][24], quantum Monte Carlo [25][26][27][28][29][30][31][32], cluster perturbation theory [33][34][35][36][37][38], the variational cluster approximation [39][40][41][42][43] and cluster DMFT [44][45][46][47][48][49]. A detailed review, including further results from density-matrix renormalisation-group (DMRG) calculations, may be found in [50].…”

Section: Introductionmentioning

confidence: 99%

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Charge dynamics of the antiferromagnetically ordered Mott insulator

Han

Liu

et al. 2016

New J. Phys.

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We introduce a slave-fermion formulation in which to study the charge dynamics of the half-filled Hubbard model on the square lattice. In this description, the charge degrees of freedom are represented by fermionic holons and doublons and the Mott-insulating characteristics of the ground state are the consequence of holon-doublon bound-state formation. The bosonic spin degrees of freedom are described by the antiferromagnetic Heisenberg model, yielding long-ranged (Néel) magnetic order at zero temperature. Within this framework and in the self-consistent Born approximation, we perform systematic calculations of the average double occupancy, the electronic density of states, the spectral function and the optical conductivity. Qualitatively, our method reproduces the lower and upper Hubbard bands, the spectral-weight transfer into a coherent quasiparticle band at their lower edges and the renormalisation of the Mott gap, which is associated with holon-doublon binding, due to the interactions of both quasiparticle species with the magnons. The zeros of the Green function at the chemical potential give the Luttinger volume, the poles of the self-energy reflect the underlying quasiparticle dispersion with a spin-renormalised hopping parameter and the optical gap is directly related to the Mott gap. Quantitatively, the square-lattice Hubbard model is one of the best-characterised problems in correlated condensed matter and many numerical calculations, all with different strengths and weaknesses, exist with which to benchmark our approach. From the semi-quantitative accuracy of our results for all but the weakest interaction strengths, we conclude that a self-consistent treatment of the spin-fluctuation effects on the charge degrees of freedom captures all the essential physics of the antiferromagnetic Mott-Hubbard insulator. We remark in addition that an analytical approximation with these properties serves a vital function in developing a full understanding of the fundamental physics of the Mott state, both in the antiferromagnetic insulator and at finite temperatures and dopings.

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Section: Luttinger Volumesupporting

confidence: 84%

Section: Spectral Function 41 Derivation and Calculationmentioning

confidence: 99%

Section: Luttinger Volumementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Charge dynamics of the antiferromagnetically ordered Mott insulator

Han

Liu

et al. 2016

New J. Phys.

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“…Note that S(k, ω) 0 because A(k, ω) 0. The divergence of S(k, ω) corresponds to the zero of A(k, ω), thus implying the presence of the single-particle gap [88,[123][124][125]. In practice, the divergence of S(k, ω) appears as the peak due to the finite η.…”

Section: The Third Law Of Thermodynamics In Sftmentioning

confidence: 99%

Variational cluster approach to thermodynamic properties of interacting fermions at finite temperatures: A case study of the two-dimensional single-band Hubbard model at half filling

2018

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We formulate a finite-temperature scheme of the variational cluster approximation (VCA) particularly suitable for an exact-diagonalization cluster solver. Based on the analytical properties of the single-particle Green's function matrices, we explicitly show the branch-cut structure of logarithm of the complex determinant functions appearing in the self-energy-functional theory (SFT) and whereby construct an efficient scheme for the finite-temperature VCA. We also derive the explicit formulas for entropy and specific heat within the framework of the SFT. We first apply the method to explore the antiferromagnetic order in a half-filled Hubbard model by calculating the entropy, specific heat, and single-particle excitation spectrum for different values of on-site Coulomb repulsion U and temperature T . We also calculate the T dependence of the single-particle excitation spectrum in the strong coupling region, and discuss the overall similarities to and the fine differences from the spectrum obtained by the spin-density-wave mean-field theory at low temperatures and the Hubbard-I approximation at high temperatures. Moreover, we show a necessary and sufficient condition for the third law of thermodynamics in the SFT. On the basis of the thermodynamic properties, such as the entropy and the double occupancy, calculated via the T and/or U derivative of the grand potential, we obtain a crossover diagram in the (U, T )-plane which separates a Slater-type insulator and a Mott-type insulator. Next, we demonstrate the finite-temperature scheme in the cluster-dynamical-impurity approximation (CDIA), i.e., the VCA with noninteracting bath orbitals attached to each cluster, and study the paramagnetic Mott metal-insulator transition in the half-filled Hubbard model. Formulating the finite-temperature CDIA, we first address a subtle issue regarding the treatment of the artificially introduced bath degrees of freedom which are absent in the originally considered Hubbard model. We then apply the finite-temperature CDIA to calculate the finite-temperature phase diagram in the (U, T )-plane. Metallic, insulating, coexistence, and crossover regions are distinguished from the bathcluster hybridization-variational-parameter dependence of the grand-potential functional. We find that the Mott transition at low temperatures is discontinuous, and the coexistence region of the metallic and insulating states persists down to zero temperature. The result obtained here by the finite-temperature CDIA is complementary to the previously reported zero-temperature CDIA phase diagram. arXiv:1808.03807v3 [cond-mat.str-el]

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Probing Phase Coherence Via Density of States for Strongly Correlated Excitons

Apinyan

Kopeć

2015

J Low Temp Phys

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We present the calculation of the coherent spectral functions and density of states (DOS) for excitonic systems in the frame of the three-dimensional extended Falicov-Kimball model. Using gage-invariant U(1) transformation to the usual fermions, we represent the electron operator as a fermion attached to the U(1) phase-flux tube. The emergent bosonic gage field, related to the phase variables, is crucial for the Bose-Einstein condensation (BEC) of excitons. Employing the path-integral formalism, we manipulate the bosonic and fermionic degrees of freedom to obtain the effective actions related to fermionic and bosonic sectors. Considering the normal and anomalous excitonic Green functions, we calculate the spectral functions, which have the forms of convolutions in the reciprocal space between bosonic and fermionic counterparts. For the fermionic incoherent part of the DOS, we have found the strong evidence of the hybridization gap in DOS spectra. Furthermore, considering Bogoliubov coherence mechanism, we calculate the coherent DOS spectra. For the coherent normal fermionic DOS, there is no hybridization gap found in the system due to strong coherence effects and phase stiffness. The similar behavior is observed also for the condensate part of the anomalous excitonic DOS spectra. We show that for small values of the Coulomb interaction the fermionic DOS exhibits a Bardeen-Cooper-Schrieffer (BCS)-like double-peak structure. In the BEC region of the BCS-BEC crossover, the double-peak structure disappears totally for both: coherent and incoherent DOS spectra. We discuss also the temperature dependence of DOS functions.

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Self-energy and Fermi surface of the two-dimensional Hubbard model

Cited by 34 publications

References 68 publications

Charge dynamics of the antiferromagnetically ordered Mott insulator

Charge dynamics of the antiferromagnetically ordered Mott insulator

Variational cluster approach to thermodynamic properties of interacting fermions at finite temperatures: A case study of the two-dimensional single-band Hubbard model at half filling

Probing Phase Coherence Via Density of States for Strongly Correlated Excitons

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