Intrinsic Cluster-Shaped Density Waves in Cellular Dynamical Mean-Field Theory

Abstract

It is well known that cellular dynamical mean-field theory (CDMFT) leads to the artificial breaking of translation invariance. In spite of this, it is one of the most successful methods to treat strongly correlated electrons systems. Here, we investigate in more detail how this broken translation invariance manifests itself. This allows to disentangle artificial broken translation invariance effects from the genuine strongly correlated effects captured by CDMFT. We report artificial density waves taking the shape of the cluster---cluster density waves---in all our zero temperature CDMFT solutions, including pair density waves in the superconducting state. We discuss the limitations of periodization regarding this phenomenon, and we present mean-field density-wave models that reproduce CDMFT results at low energy in the superconducting state. We then discuss how these artificial density waves help the agreement of CDMFT with high temperature superconducting cuprates regarding the low-energy spectrum, in particular for subgap structures observed in tunnelling microscopy. We relate these subgap structures to nodal and anti-nodal gaps in our results, similar to those observed in photoemission experiments. This fortuitous agreement suggests that spatial inhomogeneity may be a key ingredient to explain some features of the low-energy underdoped spectrum of cuprates with strongly correlated methods. This work deepens our understanding of CDMFT and clearly identifies signatures of broken translation invariance in the presence of strong correlations.

14 pages, 7 figures

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• Single-particle spectral function formulated and calculated by variational Monte Carlo method with application to $d$-wave superconducting state
• Doping and temperature evolution of pseudogap and spin-spin correlations in the two-dimensional Hubbard model
• Fermi Arcs From Dynamical Variational Monte Carlo
• Spin texture in a bilayer high-temperature cuprate superconductor
• Charge- and pair-density-wave orders in the one-band Hubbard model with dynamical mean field theory
• Superconductivity in the two-dimensional Hubbard model with cellular dynamical mean-field theory: a quantum impurity model analysis
• Fermi arcs vs hole pockets: periodization of a cellular two-band model
• Pseudogap in the lightly hole-doped triangular-lattice moiré Hubbard model