Unconventional Properties of Mott Insulators from the Ghost Gutzwiller Approximation

This Thesis demonstrates that an accurate description of a symmetry-invariant single-band Mott insulator within the ghost-Gutzwiller approximation necessitates the existence of in-gap single-particle modes that are strictly pinned at the chemical potential and carry no spectral weight in the physical single-particle excitation. Throughout the Thesis, we have endeavored to demonstrate that these zero-weight modes, rather than being a mere technical artifact of the variational construction, behave as genuine hidden quasiparticles, with measurable consequences whenever the insulator is perturbed, and which can be legitimately regarded as the sought- after Anderson’s spinons. Two case studies substantiate this claim. First, at the interface between a paramagnetic Mott insulator and a metal, these spinons reacquire charge and thereby spectral weight, hybridize with the metal and form heavy-fermion bands confined to a surface layer whose depth diverges with a mean-field critical exponent on approaching the Mott transition. This behavior is consistent with photoemission evidence of ambipolar in-gap states induced by surface doping of Ca2 RuO4 . Second, we have demonstrated that the symmetry-invariant Mott insulator stabilized within the ghost-Gutzwiller approximation exhibits a paramagnetic response in the presence of a Zeeman spin-splitting field. Remarkably, the spin magnetization m is carried entirely by the zero-weight modes, while the Hubbard bands remain unpolarized. The quadratic rise of the total energy, E(m) − E(0) ∼ m2 , suggests that these hidden quasiparticles indeed possess a bandwidth that becomes the antiferromagnetic exchange J = 4t2 /U in the strong coupling limit, as expected for the spinons. Conversely, when symmetry is allowed to spontaneously break, and the single-band model allowed to become the expected antiferromagnetic insulator, the above exotic insulator gives way to a more conventional Hartree-Fock-like band insulator. Nevertheless, we can still stabilize antiferromagnetic solutions with tunable deviation from the Hartree-Fock limit, quantified through the local mutual information, which might better represent realistic antiferromagnets where quantum fluctuations are not negligible. Taken together, these results demonstrate the ghost-Gutzwiller approach as a feasible variational method to explore the hidden excitations of Mott insulators, paving the way for future research into their unique properties.