Practical consequences of the Luttinger-Ward functional multivaluedness for cluster DMFT methods

Vučičević, J.; Wentzell, Nils; Ferrero, Michel; Parcollet, Olivier

doi:10.1103/physrevb.97.125141

Cited by 60 publications

(59 citation statements)

References 90 publications

(110 reference statements)

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“…Depending on the interaction strength and doping level, the generalized impurity susceptibility may have egivenvalues with negative real part but their zero-crossing occurs at finite imaginary part, leading to a smooth irreducible charge vertex. For small U , the eigenvalues remain real for a small range of doping 88 .…”

Section: Dynamical Vertexmentioning

confidence: 96%

Charge fluctuations in lightly hole-doped cuprates: Effect of vertex corrections

2019

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Identification of the electronic state that appears upon doping a Mott insulator is important to understand the physics of cuprate high-temperature superconductors. Recent scanning tunneling microscopy of cuprates provides evidence that a charge-ordered state emerges before the superconducting state upon doping the parent compound. We study this phenomenon by computing the charge response function of the Hubbard model including frequency-dependent local vertex corrections that satisfy the compressibility sum-rule. We find that upon approaching the Mott phase from the overdoped side, the charge fluctuations at wave vectors connecting hot spots are suppressed much faster than at the other wave-vectors. It leads to a momentum dependence of the dressed charge susceptibility that is very different from either the bare susceptibility or from the susceptibility obtained from the random phase approximation. We also find that the paramagnetic lightly hole-doped Mott phase at finite-temperature is unstable to charge ordering only at zero wave-vector, confirming the results previously obtained from the compressibility. Charge order is driven by the frequency-dependent scattering processes that induce an attractive particle-hole interaction at large interaction strength and small doping.

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Section: Dynamical Vertexmentioning

confidence: 96%

Charge fluctuations in lightly hole-doped cuprates: Effect of vertex corrections

2019

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“…Furthermore, the two-particle self-energy γ (irreducible vertex) also shows divergences, sometimes located in the vicinity of the Mott insulator [46], but they also arise in systems without Mott localization [49] and even in the atomic limit [50]. Divergences of the two-particle self-energy have been related to the multivaluedness of the Luttinger-Ward functional [51][52][53].…”

Section: Introductionmentioning

confidence: 99%

Two-particle Fermi liquid parameters at the Mott transition: Vertex divergences, Landau parameters, and incoherent response in dynamical mean-field theory

Krien

Loon²,

Katsnelson³

et al. 2019

Phys. Rev. B

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We consider the interaction-driven Mott transition at zero temperature from the viewpoint of microscopic Fermi liquid theory. To this end, we derive an exact expression for the Landau parameters within the dynamical mean-field theory (DMFT) approximation to the single-band Hubbard model. At the Mott transition the symmetric and the anti-symmetric Landau parameter diverge. The vanishing compressibility at the Mott transition directly implies the divergence of the forward scattering amplitude in the charge sector, which connects the proximity of the Mott phase to a tendency towards phase separation. We verify the expected behavior of the Landau parameters in a DMFT application to the Hubbard model on the triangular lattice at finite temperature. Exact conservation laws and the Ward identity are crucial to capture vertex divergences related to the Mott transition. We furthermore generalize Leggett's formula for the static susceptibility of the Fermi liquid to the static fermion-boson response function. In the charge sector the limits of small transferred momentum and frequency of this response function commute at the Mott transition. arXiv:1811.00362v4 [cond-mat.str-el]

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“…Recently, a lot of attention has been directed towards the properties of the generalized susceptibilities as they, unexpectedly, can become singular 11,[19][20][21][22][23][24] in the intermediately-to-strongly correlated or disordered regime. The singular points are directly linked to eigenvalues of χ νν ω r , for a fixed bosonic frequency ω, that go from positive to negative when the interaction or disorder increases, and thus cross zero 11,22 .…”

Section: Introductionmentioning

confidence: 99%

Analytical investigation of singularities in two-particle irreducible vertex functions of the Hubbard atom

et al. 2018

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Two-particle generalized susceptibilities and their irreducible vertex functions play a prominent role in the quantum many-body theory for correlated electron systems. They act as basic building blocks in the parquet formalism which provides a flexible scheme for the calculation of spectral and response functions. The irreducible vertices themselves have recently attracted increased attention as unexpected divergences in these functions have been identified. Remarkably, such singularities appear already for one of the simplest strongly interacting systems: the atomic limit of the half-filled Hubbard model (Hubbard atom). In this paper, we calculate the analytical expressions for all twoparticle irreducible vertex functions of the Hubbard atom in all scattering channels as well as the fully irreducible two-particle vertices. We discuss their divergences and classify them by the eigenvalues and eigenvectors of the corresponding generalized susceptibilities. In order to establish a connection to the recently found multivaluedness of the exact self-energy functional Σ[G], we show that already an approximation akin to iterated perturbation theory is sufficient to capture, qualitatively, the divergent structure of the vertex functions. Finally, we show that the localized divergences in the disordered binary mixture model are directly linked to a minimum in the single-particle Matsubara Green's function.

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Practical consequences of the Luttinger-Ward functional multivaluedness for cluster DMFT methods

Cited by 60 publications

References 90 publications

Charge fluctuations in lightly hole-doped cuprates: Effect of vertex corrections

Charge fluctuations in lightly hole-doped cuprates: Effect of vertex corrections

Two-particle Fermi liquid parameters at the Mott transition: Vertex divergences, Landau parameters, and incoherent response in dynamical mean-field theory

Analytical investigation of singularities in two-particle irreducible vertex functions of the Hubbard atom

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