Brillouin-zone integration scheme for many-body density of states: Tetrahedron method combined with cluster perturbation theory

Seki, Koh‐ichi; Yunoki, Seiji

doi:10.1103/physrevb.93.245115

Cited by 10 publications

(8 citation statements)

References 70 publications

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“…This is consistent with the interpretation that an atomic impurity deposited in an AB or BA region must necessarily have non-negligible projection on the host Wannier orbital and the three nearest-neighbor Wannier states. We confirm this with numerical simulation of the LDOS induced by an atomic impurity using the tetrahedron method applied to the full continuum model [29]. The results are shown in Fig.…”

supporting

confidence: 78%

Obstruction and Interference in Low Energy Models for Twisted Bilayer Graphene

Phong,

Mele

2020

Preprint

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The electronic bands of twisted bilayer graphene (TBLG) with a large-period moiré superlattice fracture to form narrow Bloch minibands that are spectrally isolated by forbidden energy gaps from remote dispersive bands. When these gaps are sufficiently large, one can study a band-projected Hamiltonian that correctly represents the dynamics within the minibands. This inevitably introduces nontrivial geometrical constraints that arise from the assumed form of the projection. Here we show that this choice has a profound consequence in a low-energy experimentally-observable signature which therefore can be used to tightly constrain the analytic form of the appropriate low-energy theory. We find that this can be accomplished by a careful analysis of the electron density produced by backscattering of Bloch waves from an impurity potential localized on the moiré superlattice scale. We provide numerical estimates of the effect that can guide experimental work to clearly discriminate between competing models for the low-energy band structure.

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supporting

confidence: 78%

Obstruction and Interference in Low Energy Models for Twisted Bilayer Graphene

Phong,

Mele

2020

Preprint

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“…This already suggests that det G(z) has a form shown in Eqs. (23) and (26). In the following, we shall show that zeros of det G(z) are all on the real-frequency axis.…”

Section: Determinant Of Single-particle Green's Functionmentioning

confidence: 89%

Topological interpretation of the Luttinger theorem

Seki

Yunoki

2017

Phys. Rev. B

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Based solely on the analytical properties of the single-particle Green's function of fermions at finite temperatures, we show that the generalized Luttinger theorem inherently possesses topological aspects. The topological interpretation of the generalized Luttinger theorem can be introduced because i) the Luttinger volume is represented as the winding number of the single-particle Green's function and thus ii) the deviation of the theorem, expressed with a ratio between the interacting and noninteracting single-particle Green's functions, is also represented as the winding number of this ratio. The formulation based on the winding number naturally leads to two types of the generalized Luttinger theorem. Exploring two examples of single-band translationally invariant interacting electrons, i.e., simple metal and Mott insulator, we show that the first type falls into the original statement for Fermi liquids given by Luttinger, where poles of the single-particle Green's function appear at the chemical potential, while the second type corresponds to the extended one for non metallic cases with no Fermi surface such as insulators and superconductors generalized by Dzyaloshinskii, where zeros of the single-particle Green's function appear at the chemical potential. This formulation also allows us to derive a sufficient condition for the validity of the Luttinger theorem of the first type by applying the Rouche's theorem in complex analysis as an inequality. Moreover, we can rigorously prove in a non-perturbative manner, without assuming any detail of a microscopic Hamiltonian, that the generalized Luttinger theorem of both types is valid for generic interacting fermions as long as the particle-hole symmetry is preserved. Finally, we show that the winding number of the single-particle Green's function can also be associated with the distribution function of quasiparticles, and therefore the number of quasiparticles is equal to the Luttinger volume. This implies that the fundamental hypothesis of the Landau's Fermi-liquid theory, the number of fermions being equal to that of quasiparticles, is guaranteed if the Luttinger theorem is valid since the theorem states that the number of fermions is equal to the Luttinger volume. All these general statements are made possible because of the finding that the Luttinger volume is expressed as the winding number of the single-particle Green's function at finite temperatures, for which the complex analysis can be readily exploited.

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“…Further analytical properties of the single-particle Green's function matrix can be found, for example, in Refs. [43,[86][87][88]. Notice in Eqs.…”

Section: Remarks On Branch Cutsmentioning

confidence: 99%

“…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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Brillouin-zone integration scheme for many-body density of states: Tetrahedron method combined with cluster perturbation theory

Cited by 10 publications

References 70 publications

Obstruction and Interference in Low Energy Models for Twisted Bilayer Graphene

Obstruction and Interference in Low Energy Models for Twisted Bilayer Graphene

Topological interpretation of the Luttinger theorem

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

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