Non-conservation of Fermionic Degrees of Freedom at Low-energy in Doped Mott Insulators

TL;DR

This paper demonstrates that in doped Mott insulators, low-energy fermionic degrees of freedom are dynamically generated and not conserved, leading to a breakdown of the traditional electron-hole correspondence and affecting experimental interpretations.

Contribution

It explicitly shows how the spectrum in the lower Hubbard band should be partitioned to account for dynamically generated charge degrees of freedom and corroborates this with the low-energy Hubbard model theory.

Findings

Low-energy fermionic degrees of freedom are dynamically generated in doped Mott insulators.

The Landau one-to-one correspondence between electrons and effective fermions breaks down.

Experimental probes should consider the total dynamically generated hole number, not just the bare value.

Abstract

Hall and optical conductivity experiments on the cuprates indicate that the low-energy fermionic degrees of freedom in a doped Mott insulator posess a component that is dynamcially generated and hence determined by the temperature. We show explicitly how the spectrum in the lower Hubbard band should be partitioned to describe such dynamically generated charge degrees of freedom and corroborate this picture with the results from the exact low-energy theory of the Hubbard model. A consequence of such dynamics is that the Landau one-to-one correspondence between bare electrons and the effective fermionic degrees of freedom at low energies breaks down explicitly. This state of affairs obtains because the total hole number is not conserved as it contains a dynamical contribution. We propose that any experimental probe that couples to the low-energy dynamics of a doped Mott insulator, quantum oscillation experiments included, should be interpreted in terms of the total dynamically generated hole number rather than the bare value.