Submatrix updates for the continuous-time auxiliary-field algorithm

Gull, Emanuel; Staar, Peter; Fuchs, Sebastian; Nukala, Phani K. V. V.; Summers, Michael S.; Pruschke, Thomas; Schulthess, T. C.; Maier, Thomas

doi:10.1103/physrevb.83.075122

Cited by 91 publications

(92 citation statements)

References 44 publications

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“…We describe only a brief outline of CT-INT in this section. For efficient computation, we also employ the submatrix update algorithm 34,35) extended to CT-INT. 33) We divide the impurity Hamiltonian into two parts, H = H 0 + H i .…”

Section: Continuous Time Quantum Monte Carlo Methodsmentioning

confidence: 99%

“…Given this background, we analyze the one-particle spectrum of a single band model of a cuprate superconductor near the Fermi level using dynamical mean field theory (DMFT) 21) with two kinds of impurity solvers : iterated perturbation theory (IPT) [22][23][24][25][26][27][28][29] and continuous time quantum Monte Carlo (CT-QMC) [30][31][32][33][34][35] We find that the electron-hole asymmetry can exist even under common interaction strengths between the hole-and the electron-doped systems. The asymmetry of the spectrum already exists in the non-interacting case, but it is drastically enhanced, especially when the interaction is strong enough to make the non-doped case a Mott insulator.…”

Section: Introductionmentioning

confidence: 99%

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DMFT Study on the Electron–hole Asymmetry of the Electron Correlation Strength in the High T_c Cuprates

2017

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Recent experiments revealed a striking asymmetry in the phase diagram of the high temperature cuprate superconductors. The correlation effect seems strong in the hole-doped systems and weak in the electrondoped systems. On the other hand, a recent theoretical study shows that the interaction strengths (the Hubbard U ) are comparable in these systems. Therefore, it is difficult to explain this asymmetry by their interaction strengths. Given this background, we analyze the one-particle spectrum of a single band model of a cuprate superconductor near the Fermi level using the dynamical mean field theory. We find the difference in the "visibility" of the strong correlation effect between the hole-and electron-doped systems. This can explain the electron-hole asymmetry of the correlation strength without introducing the difference in the interaction strength.

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Section: Continuous Time Quantum Monte Carlo Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

DMFT Study on the Electron–hole Asymmetry of the Electron Correlation Strength in the High T_c Cuprates

2017

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“…More recent developments [18] have enabled researchers to access clusters large enough to obtain a reasonable picture of the N → ∞ limit [14,16,[47][48][49][50][51]. It has been found [16] that in DCA clusters of size N > 4 the Mott transition is multistaged, with the fully gapped Mott insulating state being separated from the Fermi liquid state by an intermediate phase, in which regions of momentum space near the (0, π)/(π, 0) point are gapped and regions of momentum space near (±π/2, ±π/2) are not.…”

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confidence: 99%

“…Specifics of our methods are given in the Supplemental Material; here we briefly note that a key aspect of our study is the use of recently developed "submatrix update" numerical techniques [17][18][19] which enable access to couplings strong enough to produce a pseudogap at temperatures low enough to construct the superconducting state for cluster size N large enough to reasonably represent the N → ∞ limit. Our key results are that the pseudogap and superconductivity are competing phases and that, remarkably, the onset of superconductivity within the pseudogap phase leads to a decrease in the excitation gap, in sharp contrast to conventional situations where the onset of superconductivity increases the gap.…”

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confidence: 99%

Superconductivity and the Pseudogap in the Two-Dimensional Hubbard Model

2013

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Recently developed numerical methods have enabled the explicit construction of the superconducting state of the Hubbard model of strongly correlated electrons in parameter regimes where the model also exhibits a pseudogap and a Mott insulating phase. d x 2 −y 2 symmetry superconductivity is found to occur in proximity to the Mott insulator, but separated from it by a pseudogapped nonsuperconducting phase. The superconducting transition temperature and order parameter amplitude are found to be maximal at the onset of the normal-state pseudogap. The emergence of superconductivity from the normal state pseudogap leads to a decrease in the excitation gap. All of these features are consistent with the observed behavior of the copper-oxide superconductors. where ε p = −2t(cos p x + cos p y ) + 4t ′ cos p x cos p y an electron dispersion and U > 0 a local interaction which disfavors double occupancy of a site.In the years since Anderson's paper, the interplay of the pseudogap and superconductivity and the relation of both to the Hubbard model have been of central interest to condensed matter physicists. The existence of dwave superconductivity in the Hubbard model has been demonstrated by perturbative analytic calculations [4] (later improved by renormalization group methods [5, 6]) and by numerics [7, 8]. The issue of the pseudogap has been more controversial. It has been variously argued that the pseudogap is a signature of unusual superconducting fluctuations [9][10][11], of a competing nonsuperconducting phase or regime [3, 12], or of physics not contained in the Hubbard model [13]. Theoretical determination of the interplay of the pseudogap and superconductivity in the Hubbard model is important in helping resolve this controversy, and will provide insight into the pseudogap phenomenon and into strongly correlated superconductivity more generally, but this requires access to intermediate or strong couplings for which perturbation theory is inadequate. The development of cluster dynamical mean field theory [15] has provided important nonperturbative information about the Hubbard model. Dynamical mean field theory approximates the electron self-energy in terms of a finite number of auxiliary functions determined from the solution of an N -site quantum impurity model and becomes exact as N tends to infinity. In this Letter we use dynamical mean field methods to determine the interplay of superconductivity and the pseudogap in the Hubbard model. This is challenging because the theory

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“…With the introduction of continuous-time Monte Carlo solvers [10][11][12][13][14], it has become possible to directly measure the self-energy on the Matsubara axis with unprecedented speed [15,16] and accuracy [17]. This motivated us to investigate the possibility of an analytic continuation of the self-energy directly in frequency space with the relationship (z) = 0 + 1 2π…”

Section: S = − Dωa(ω) − M(ω) − A(ω) Log[a(ω)/m(ω)] (3)mentioning

confidence: 99%

Continuous-pole-expansion method to obtain spectra of electronic lattice models

et al. 2014

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We present a new algorithm to analytically continue the self-energy of quantum many-body systems from Matsubara frequencies to the real axis. The method allows straightforward, unambiguous computation of electronic spectra for lattice models of strongly correlated systems from self-energy data that has been collected with state-of-the-art continuous time solvers within dynamical mean-field simulations. Using well-known analytical properties of the self-energy, the analytic continuation is cast into a constrained minimization problem that can be formulated as a quadratic programmable optimization with linear constraints. The algorithm is validated against exactly solvable finite-size problems, showing that all features of the spectral function near the Fermi level are very well reproduced and coarse features are reproduced for all energies. The method is applied to two well-known lattice problems, the two-dimensional Hubbard model at half filling, where the momentum dependence of the gap formation is studied, as well as a multiband model of NiO, for which the spectral function can be directly compared to experiment. Agreement with published results is very good.

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Submatrix updates for the continuous-time auxiliary-field algorithm

Cited by 91 publications

References 44 publications

DMFT Study on the Electron–hole Asymmetry of the Electron Correlation Strength in the High T_c Cuprates

DMFT Study on the Electron–hole Asymmetry of the Electron Correlation Strength in the High T_c Cuprates

Superconductivity and the Pseudogap in the Two-Dimensional Hubbard Model

Continuous-pole-expansion method to obtain spectra of electronic lattice models

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Submatrix updates for the continuous-time auxiliary-field algorithm

Cited by 91 publications

References 44 publications

DMFT Study on the Electron–hole Asymmetry of the Electron Correlation Strength in the High Tc Cuprates

DMFT Study on the Electron–hole Asymmetry of the Electron Correlation Strength in the High Tc Cuprates

Superconductivity and the Pseudogap in the Two-Dimensional Hubbard Model

Continuous-pole-expansion method to obtain spectra of electronic lattice models

Contact Info

Product

Resources

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DMFT Study on the Electron–hole Asymmetry of the Electron Correlation Strength in the High T_c Cuprates

DMFT Study on the Electron–hole Asymmetry of the Electron Correlation Strength in the High T_c Cuprates