We show that doped Mott insulators exhibit a collective degree of freedom, not made out of the elemental excitations, because the number of single-particle addition states at low energy per electron per spin is greater than one. The presence of such a collective degree of freedom which is not a consequence of proximity to a phase transition is a consequence of dynamical spectral weight transfer from high to low energies. This physics is captured by the charge
2e boson that emerges by explicitly integrating out the high-energy scale in the Hubbard model. The charge
2e boson binds to a hole, thereby mediating new charge
e states at low energy. It is the presence of such charge
e states which have no counterpart in the non-interacting system that provides the general mechanism for the breakdown of Fermi liquid theory in doped Mott insulators. The relationship between the charge
2e boson formulation and the standard perturbative treatment is explained.
We expand on our earlier work [R. G. Leigh et al., Phys. Rev. Lett. 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 charge $\ifmmode\pm\else\textpm\fi{}2e$ bosonic field that is not made out of elemental excitations emerges at low energies. 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's 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.
We construct the low-energy theory of a doped Mott insulator, such as the high-temperature superconductors, by explicitly integrating over the degrees of freedom far away from the chemical potential. For either hole or electron doping, a charge 2e bosonic field emerges at low energy. The charge 2e boson mediates dynamical spectral weight transfer across the Mott gap and creates a new charge e excitation by binding a hole. The result is a bifurcation of the electron dispersion below the chemical potential as observed recently in angle-resolved photoemission on Pb-doped Bi2Sr2CaCu2O8+delta (Pb2212).
We show here that many of the normal state properties of the cuprates can result from the new charge
2e bosonic field which we have recently [Phys. Rev. Lett. 99, 046404 (2007); Phys. Rev. B 77, 014512 (2007)] shown to exist in the exact low-energy theory of a doped Mott insulator. In particular, the (1) midinfrared band including the nonvanishing of the restricted
f-sum rule in the Mott insulator, (2)
T2 contribution to the thermal conductivity, (3) pseudogap, (4) bifurcation of the electron spectrum below the chemical potential, as recently seen in angle-resolved photoemission, (5) insulating behavior away from half-filling, (6) high- and low-energy kinks in the electron dispersion, and (7)
T-linear resistivity all derive from the charge
2e bosonic field. We also calculate the inverse dielectric function and show that it possesses a sharp quasiparticle peak and a broad particle-hole continuum. The sharp peak is mediated by a new charge
e composite excitation formed from the binding of a charge
2e boson and a hole and represents a distinctly new prediction of this theory. It is this feature that is responsible for the dynamical part of the spectral weight transferred across the Mott gap. We propose that electron-energy loss spectroscopy at finite momentum and frequency can be used to probe the existence of such a sharp feature.
By bosonizing the electronic t-J model exactly on any two-dimensional (2D) lattices, and integrating out the gauge fluctuations combined to slave particles beyond mean fields, we obtain a theory in terms of physical Cooper pair and spin condensates. In the sense of mutual Berry phase they turn out to be dual to each other. The mutual duality is the missing key in the resonant-valance-bond idea [Science 235, 1196 (1987)]] to work as a paradigm of doped 2D Mott insulators. We argue that the essential aspects of high-T(c) phenomenology can be explained in the present framework.