Conductivity in the Square Lattice Hubbard Model at High Temperatures: Importance of Vertex Corrections

Vučičević, J.; Kokalj, Jure; Žitko, Rok; Wentzell, Nils; Tanasković, D.; Mravlje, Jernej

doi:10.1103/physrevlett.123.036601

Cited by 65 publications

(55 citation statements)

References 51 publications

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“…The control parameters of the calculations are most commonly the lattice size and the maximal perturbation order. Some algorithms [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] are very efficient for small systems but have not yet reached very large lattice sizes, while others [17][18][19][20][21][22][23][24] can address the thermodynamic limit directly but are limited in the number of perturbation orders that can be computed.…”

Section: Introductionmentioning

confidence: 99%

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Real-frequency diagrammatic Monte Carlo at finite temperature

Vučičević¹,

Ferrero

2020

Phys. Rev. B

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Diagrammatic expansions are a central tool for treating correlated electron systems. At thermal equilibrium, they are most naturally defined within the Matsubara formalism. However, extracting any dynamic response function from a Matsubara calculation ultimately requires the ill-defined analytical continuation from the imaginary-to the real-frequency domain. It was recently proposed [Phys. Rev. B 99, 035120 (2019)] that the internal Matsubara summations of any interactionexpansion diagram can be performed analytically by using symbolic algebra algorithms. The result of the summations is then an analytical function of the complex frequency rather than Matsubara frequency. Here we apply this principle and develop a diagrammatic Monte Carlo technique which yields results directly on the real-frequency axis. We present results for the self-energy Σ(ω) of the doped 32x32 cyclic square-lattice Hubbard model in a non-trivial parameter regime, where signatures of the pseudogap appear close to the antinode. We discuss the behavior of the perturbation series on the real-frequency axis and in particular show that one must be very careful when using the maximum entropy method on truncated perturbation series. Our approach holds great promise for future application in cases when analytical continuation is difficult and moderate-order perturbation theory may be sufficient to converge the result.

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Section: Introductionmentioning

confidence: 99%

“…Analytical continuation is a common hurdle in finitetemperature calculations, and it came up recently in the study of transport in the optical lattice realizations of the Hubbard model 16,27 . It turns out that the directcurrent resistivity is particularly difficult to extract from the imaginary-axis current-current correlation function.…”

Section: Introductionmentioning

confidence: 99%

Real-frequency diagrammatic Monte Carlo at finite temperature

Vučičević¹,

Ferrero

2020

Phys. Rev. B

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“…This discourages the application of the ladder DΓA and ladder dual fermion to transport phenomena, since the optical response is completely unaffected by the vertex corrections of the DMFT approximation [31]. In strongly correlated systems the full momentum-dependence of the vertex is however crucial for the optical conductivity, even at high temperature [11,12]. Due to the missing vertex corrections the ladder approximation is also thermodynamically inconsistent, which leads to multiple values of the total energy [32] and inconsistent critical behavior of single-and two-particle quantities [33].…”

Section: Introductionmentioning

confidence: 99%

Parquetlike equations for the Hedin three-leg vertex

Krien

Valli

2019

Phys. Rev. B

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Taking the competition and the mutual screening of various bosonic fluctuations in correlated electron systems into account requires an unbiased approach to the many-body problem. One such approach is the self-consistent solution of the parquet equations, whose numerical treatment in lattice systems is however prohibitively expensive. In a recent article it was shown that there exists an alternative to the parquet decomposition of the four-point vertex function, which classifies the vertex diagrams according to the principle of single-boson exchange (SBE) [F. Krien, A. Valli, and M. Capone, arXiv:1907.03581 (2019)]. Here we show that the SBE decomposition leads to a closed set of equations for the Hedin three-leg vertex, the polarization, and the electronic self-energy, which sums self-consistently the diagrams of the Maki-Thompson type. This circumvents the calculation of four-point vertex functions and the inversion of the Bethe-Salpeter equations, which are the two major bottlenecks of the parquet equations. The convergence of the calculation scheme starting from a fully irreducible vertex is demonstrated for the Anderson impurity model. arXiv:1909.02793v1 [cond-mat.str-el]

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“…Why has this not been realized before? This is because numerical methods such as quantum Monte Carlo [10] or exact diagonalization [12] suffer from the difficulty to analyze the underlying physical processes highlighted by the parquet decomposition, and analytical methods as e.g. RPA or FLEX [13] have been mostly biased with respect to certain channels such as the particle-hole (ph) channel in Fig.…”

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confidence: 99%

Generic Optical Excitations of Correlated Systems: π -tons

et al. 2020

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The interaction of light with solids gives rise to new bosonic quasiparticles, with the exciton being-undoubtedly-the most famous of these polaritons. While excitons are the generic polaritons of semiconductors, we show that for strongly correlated systems another polariton is prevalentoriginating from the dominant antiferromagnetic or charge density wave fluctuations in these systems. As these are usually associated with a wave vector (π, π, . . .) or close to it, we propose to call the derived polaritons π-tons. These π-tons yield the leading vertex correction to the optical conductivity in all correlated models studied: the Hubbard, the extended Hubbard model, the Falicov-Kimball, and the Pariser-Parr-Pople model, both in the insulating and in the metallic phase. arXiv:1902.09342v2 [cond-mat.str-el]

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Conductivity in the Square Lattice Hubbard Model at High Temperatures: Importance of Vertex Corrections

Cited by 65 publications

References 51 publications

Real-frequency diagrammatic Monte Carlo at finite temperature

Real-frequency diagrammatic Monte Carlo at finite temperature

Parquetlike equations for the Hedin three-leg vertex

Generic Optical Excitations of Correlated Systems: π -tons

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