Exact Integration of the High Energy Scale in Doped Mott Insulators

TL;DR

This paper develops an exact low-energy theory for doped Mott insulators by integrating out high-energy degrees of freedom, revealing new charge bosonic fields that influence spectral properties and symmetry features.

Contribution

It introduces a novel exact method to derive low-energy theories that include emergent charge bosons not obtainable by projection, advancing understanding of Mott insulators.

Findings

Emergence of a charge ±2e bosonic field at low energies.

Preservation of the Luttinger surface through these bosonic excitations.

Bosonic degrees of freedom influence the Kondo effect in impurity models.

Abstract

We expand on our earlier work (cond-mat/0612130, Phys. Rev. Lett. {\bf 99}, 46404 (2007)) in which we constructed the exact low-energy theory of a doped Mott insulator by explicitly integrating (rather than projecting) out the degrees of freedom far away from the chemical potential. The exact low-energy theory contains degrees of freedom that cannot be obtained from projective schemes. In particular a new charge $\pm 2e$ bosonic field emerges at low energies that is not made out of elemental excitations. Such a field accounts for dynamical spectral weight transfer across the Mott gap. At half-filling, we show that two such excitations emerge which play a crucial role in preserving the Luttinger surface along which the single-particle Green function vanishes. In addition, the interactions with the bosonic fields defeat the artificial local SU(2) symmetry that is present in the Heisenberg model. We also apply this method to the Anderson-U impurity and show that in addition to the Kondo interaction, bosonic degrees of freedom appear as well. Finally, we show that as a result of the bosonic degree of freedom, the electron at low energies is in a linear superposition of two excitations--one arising from the standard projection into the low-energy sector and the other from the binding of a hole and the boson.