A two-dimensional Falicov-Kimball model, equivalent to the Hubbard model in an unconstrained slave-spin representation, is studied by quantum Monte Carlo simulations. The focus is on a fractionalized metallic phase that is characterized in terms of spectral, thermodynamic, and transport properties, including a comparison to the half-filled Hubbard model. The properties of this phase, most notably a single-particle gap but gapless spin and charge excitations, can in principle be understood in the framework of orthogonal metals. However, important and interesting differences arise in the present setting compared to single-particle mean-field theories and other models. We also discuss the role of the local constraints from the slave-spin representation within an extended phase diagram that includes the spatial dimension as a parameter, thereby making contact with previous work in infinite dimensions. Finally, we highlight the absence of $\ensuremath{\pi}$-flux configurations in the slave-spin formulation, in particular in the context of topologically ordered fractional phases predicted at the mean-field level.
We present a fractionalized metallic phase which is indistinguishable from the Fermi liquid in conductivity and thermodynamics, but is sharply distinct in one-electron properties, such as the electron spectral function. We dub this phase the ``orthogonal metal.'' The orthogonal metal and the transition to it from the Fermi liquid are naturally described using a slave-particle representation wherein the electron is expressed as a product of a fermion and a slave Ising spin. We emphasize that when the slave spins are disordered, the result is not a Mott insulator (as erroneously assumed in the prior literature), but rather the orthogonal metal. We construct prototypical ground-state wave functions for the orthogonal metal by modifying the Jastrow factor of Slater-Jastrow wave functions that describe ordinary Fermi liquids. We further demonstrate that the transition from the Fermi liquid to the orthogonal metal can, in some circumstances, provide a simple example of a continuous destruction of a Fermi surface with a critical Fermi surface appearing right at the critical point. We present exactly soluble models that realize an orthogonal metal phase, and the phase transition to the Fermi liquid. These models thus provide valuable solvable examples for phase transitions associated with the death of a Fermi surface.
A Falicov-Kimball model which thermodynamically reduces the local Coulomb interaction of particles to attraction or repulsion is studied within the dynamical mean-field theory. In the strong interaction regime a fractionalization of particles into charge and spin objects, the physical properties of which are different from the whole particles, is observed in both high- and low-temperature phases. At high temperature and strong interaction the single-particle density of states opens an excitation gap, but the charge compressibility and the spin susceptibility exhibit the features of gapless excitations. The low-temperature phase has a long-range order, and the single-particle spectra are always gapped, while the charge and spin excitations are gapless in the strong interaction regime. In the fractionalized long-range ordered phase both the charge compressibility and the spin susceptibility are universal scaling functions of temperature.
We describe the phases of a solvable $t\text{\ensuremath{-}}J$ model of electrons with infinite-range, and random, hopping, and exchange interactions, similar to those in the Sachdev-Ye-Kitaev models. The electron fractionalizes, as in an ``orthogonal metal,'' into a fermion
f, which carries both the electron spin and charge, and a boson $\ensuremath{\phi}$. Both
f and $\ensuremath{\phi}$ carry emergent
Z2 gauge charges. The model has a phase in which the $\ensuremath{\phi}$ bosons are gapped, and the
f fermions are gapless and critical, and so the electron spectral function is gapped. This phase can be considered as a toy model for the underdoped cuprates, without spatial structure. The model also has an extended, critical, ``quasi-Higgs'' phase where both $\ensuremath{\phi}$ and
f are gapless, and the electron operator $\ensuremath{\sim}f\ensuremath{\phi}$ has a Fermi liquid-like $1/\ensuremath{\tau}$ propagator in imaginary time, $\ensuremath{\tau}$. So while the electron spectral function has a Fermi liquid form, other properties are controlled by
Z2 fractionalization and the anomalous exponents of the
f and $\ensuremath{\phi}$ excitations. This quasi-Higgs phase is proposed as a toy model of the overdoped cuprates. We also describe the critical state separating these two phases.
The finite-temperature properties of the three-dimensional Falicov-Kimball model are studied in the symmetric case using the classical Monte-Carlo method. Analysing the temperature dependence of the specific heat C V,N we have found that the system exhibits the phase transition from the low-temperature ordered phase to the high-temperature disordered phase. The critical temperature of the phase transition is calculated numerically from the position of the maximum of C V,N and it is shown that its value in the three-dimensional case is considerably enhanced in comparison to the two-dimensional case. In addition, the temperature dependence of the itinerant electron density of states (DOS) is analysed. For very low-temperatures we have observed a formation of fine structure inside the principal gap that transforms to a pseudo-gap at higher temperatures and becomes temperature independent for sufficiently large temperatures. In this temperature region we have calculated DOS for different Coulomb interactions and found the Mott-Hubbard metal-insulator transition.
The spin-
21 Falicov-Kimball model is solved exactly on an infinite-coordination-number Bethe lattice in the thermodynamic limit. This model is a paradigm for a charge-transfer metal-insulator transition, where the occupancy of localized and delocalized electronic orbitals rapidly changes at the metal-insulator transition (rather than the character of the electronic states changing from insulating to metallic as in a Mott-Hubbard transition). The exact solution displays both continuous and discontinuous (first-order) transitions.