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

TL;DR

This paper investigates how cellular dynamical mean-field theory (CDMFT) introduces artificial density waves due to broken translation invariance, and how these artifacts relate to real physical phenomena in high-temperature superconductors.

Contribution

It identifies and analyzes artificial cluster-shaped density waves in CDMFT solutions, clarifies their impact on interpreting strongly correlated electron systems, and connects these artifacts to experimental observations in cuprates.

Findings

Artificial density waves are inherent in zero-temperature CDMFT solutions.

Mean-field models can replicate low-energy CDMFT results, including density waves.

Artificial density waves may explain certain experimental features in cuprate superconductors.

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.