One-dimensional Hubbard model with pair-hopping term: Pair-density wave, pair-superconductor and orthogonal metal

TL;DR

This paper analyzes a one-dimensional Hubbard model with pair-hopping, revealing quantum liquid phases like pair-density wave and pair-superconductor, and discusses implications for higher-dimensional systems and exotic metallic states.

Contribution

It provides an analytical study of the 1D Hubbard model with pair-hopping, identifying novel quantum liquid phases and discussing their potential relevance to higher-dimensional phenomena.

Findings

Identified pair-density wave and pair-superconducting phases in the 1D model.

Discussed the limitations of 1D systems as precursors for orthogonal metals.

Suggested implications of these phases for 2D high-temperature superconductors.

Abstract

As the simplest non-Fermi liquids, orthogonal metals have gapped single-particle excitations but show normal metallic behaviors in thermodynamic and transport quantities. Such an exotic metallic state could be realized in a Hubbard model with pair-hopping term. However, it is difficult to solve this model in higher dimension, here we focus on its one-dimension version, in which a powerful U(1) abelian bosonization technique is available to capture \textit{analytically} its universal low-energy physics. It is found that the one-dimensional system is unable to provide an appropriate precursor for the desirable orthogonal metals in higher dimension and the occurrence of the featureless orthogonal metallic phase needs \textit{at least} a quasi-one-dimensional multi-leg ladder model. Nevertheless, two interesting quantum liquid phases are identified for the present one-dimensional model, namely, pair-density wave (PDW) state and pair-superconducting (PSC) state. The former describes the charge-density-wave order of cooper pairs while the latter shows the superfluidity of two cooper pairs. Needing not any explicit calculation, these two phases could have further implications in the two-dimensional case, namely, the PDW state may give rise to quantum electron liquid crystal states, which is believed to be responsible for the complex pseudogap phase in cuprate, and the PSC state with charge 4e can be related to certain nematic superconducting state. These predications call for further investigation on this model in higher dimension by available analytical methods and/or numerical calculations.