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Journal of Superconductivity and Novel Magnetism

Dual Fermion Approach to High-Temperature Superconductivity

Hartmut Hafermann, M. Kecker, S. Brener, Alexey N. Rubtsov, Mikhail I. Katsnelson, Alexander I. Lichtenstein

Published Oct 29, 2008• 7 citations
Publisher
DOI
10.1007/s10948-008-0361-9

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Abstract We study the physics of high-temperature cuprate superconductors starting from the highly degenerate four-site plaquette of the t−t′−Ut-t^{\prime} -Ut−t′−U t − t ′ − U Hubbard model as a reference system. The degeneracy causes strong fluctuations when a lattice of plaquettes is constructed. We show that there is a large binding energy between holes when a set of four plaquettes is considered. The next-nearest-neighbour hopping t′t^{\prime}t′ t ′ plays a crucial role in the formation of these strongly bound electronic bipolarons whose coherence at lower temperature could be the explanation for superconductivity. A complementary approach is cluster dual fermion starting from a single degenerate plaquette, which contains the relevant short-ranged fluctuations from the beginning. It gives d-wave superconductivity as the leading instability under a reasonably broad range of parameters. The origin of the pseudogap is also discussed in terms of the coupling of degenerate plaquettes. Thus, some of the essential elements of cuprate superconductivity appear from the local plaquette physics.
Motivated by the intriguing physics of quasi-two-dimensional fermionic systems, such as high-temperature superconducting oxides, layered transition metal chalcogenides, or surface or interface systems, the development of many-body computational methods geared at including both local and nonlocal electronic correlations has become a rapidly evolving field. It has been realized, however, that the success of such methods can be hampered by the emergence of noncausal features in the effective or observable quantities involved. Here, we present an approach wherein local many-body techniques such as dynamical mean-field theory (DMFT) are extended to nonlocal correlations and interactions, which preserves causality and has a physically intuitive interpretation. Our strategy has implications for the general class of DMFT-inspired many-body methods and can be adapted to cluster, dual boson, or dual fermion techniques with minimal effort.
The dual fermion approach provides a formally exact prescription for calculating properties of a correlated electron system in terms of a diagrammatic expansion around dynamical mean-field theory (DMFT). Most practical implementations, however, neglect higher-order interaction vertices beyond two-particle scattering in the dual effective action and further truncate the diagrammatic expansion in the two-particle scattering vertex to a leading-order or ladder-type approximation. In this work, we compute the dual fermion expansion for the two-dimensional Hubbard model including all diagram topologies with two-particle interactions to high orders by means of a stochastic diagrammatic Monte Carlo algorithm. We benchmark the obtained self-energy against numerically exact diagrammatic determinant Monte Carlo simulations to systematically assess convergence of the dual fermion series and the validity of these approximations. We observe that, from high temperatures down to the vicinity of the DMFT N\'eel transition, the dual fermion series converges very quickly to the exact solution in the whole range of Hubbard interactions considered ($4\ensuremath{\le}U/t\ensuremath{\le}12$), implying that contributions from higher-order vertices are small. As the temperature is lowered further, we observe slower series convergence, convergence to incorrect solutions, and ultimately divergence. This happens in a regime where magnetic correlations become significant. We find, however, that the self-consistent particle-hole ladder approximation yields reasonable and often even highly accurate results in this regime.