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arXiv:1812.01795 · Physical review. B./Physical review. B

Fractionalized long-range ordered state in a Falicov-Kimball model

Minh-Tien Tran

Published Apr 3, 2019• 3 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.99.165104

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•Apr 20, 2005•0 citations
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.
Quantum Monte Carlo simulations reveal an exotic metallic phase with a single-particle gap but gapless spin and charge excitations and a nonsaturating resistivity in a two-dimensional SU(2) Falicov-Kimball model. An exact duality between this model and an unconstrained slave-spin theory leads to a classification of the phase as a fractionalized or orthogonal metal whose low-energy excitations have different quantum numbers than the original electrons. Whereas the fractionalized metal corresponds to the regime of disordered slave spins, the regime of ordered slave spins is a Fermi liquid. At a critical temperature, an Ising phase transition to a spontaneously generated constrained slave-spin theory of the Hubbard model is observed.
The two-dimensional Falicov-Kimball (FK) model is analyzed using the Monte Carlo method. In the case of concentrations of both itinerant and localized particles equal to 0.5 we determine temperature dependence of specific heat, charge density wave susceptibility, and density-density correlation function. In the weak interaction regime we find a first order transition to the ordered state and anomalous temperature dependence of the correlation function. We construct the phase diagram of half-filled FK model. Also, the role of next-nearest-neighbor hopping on the phase diagram is analyzed. Lastly, we discuss the density of states and the spectral functions for the mobile particles in weak and strong interaction regime.
In this work, we study the extended Falicov-Kimball model at half-filling within the Hartree-Fock approach (HFA) (for various crystal lattices) and compare the results obtained with the rigorous ones derived within the dynamical mean field theory (DMFT). The model describes a system, where electrons with spin-↓ are itinerant (with hopping amplitude t), whereas those with spin-↑ are localized. The particles interact via on-site U and intersite V density-density Coulomb interactions. We show that the HFA description of the ground state properties of the model is equivalent to the exact DMFT solution and provides a qualitatively correct picture also for a range of small temperatures. It does capture the discontinuous transition between ordered phases at U = 2V for small temperatures as well as correct features of the continuous order-disorder transition. However, the HFA predicts that the discontinuous boundary ends at the isolated-critical point (of the liquid-gas type) and it does not merge with the continuous boundary. This approach cannot also describe properly a change of order of the continuous transition for large V as well as various metal-insulator transitions found within the DMFT.
The Falicov-Kimball model supplemented with the Ising-type Hund coupling describes charge and magnetic order induced by on-site, charge-, and spin-dependent interactions between itinerant electrons and localized ions. Motivated by a discovery of the rich structure of ground-state phase diagrams containing various charge and magnetic superstructures, we analyze the energy spectrum and determine numerically finite temperature properties of the model on the square $4\ifmmode\times\else\texttimes\fi{}4$ cluster at half filling. For the density of magnetic ions equal to 1 and 1/2 and not too small coupling constants we show that many-electron collective excitations derived from changes in positions of the ions or inversions their spins have much lower energy than single-electron excitations. From an analysis of the excitation spectrum structure we derive effective interactions between the ions. When the coupling constants are large enough the interactions reduce to two-body forces between ions occupying the nearest-neighboring sites. Finite-temperature characteristics and temperatures of transformation from charge or magnetically ordered to disordered phases are determined in the wide range of the interaction couplings.
The Falicov-Kimball model was introduced in 1969 as a statistical model for metal-insulator transitions; it includes itinerant and localized electrons that mutually interact with a local Coulomb interaction and is the simplest model of electron correlations. It can be solved exactly with dynamical mean-field theory in the limit of large spatial dimensions, which provides an interesting benchmark for the physics of locally correlated systems. In this review, the authors develop the formalism for solving the Falicov-Kimball model from a path-integral perspective and provide a number of expressions for single- and two-particle properties. Many important theoretical results are examined that show the absence of Fermi-liquid features and provide a detailed description of the static and dynamic correlation functions and of transport properties. The parameter space is rich and one finds a variety of many-body features like metal-insulator transitions, classical valence fluctuating transitions, metamagnetic transitions, charge-density-wave order-disorder transitions, and phase separation. At the same time, a number of experimental systems have been discovered that show anomalies related to Falicov-Kimball physics [including YbInCu4,{\mathrm{YbInCu}}_{4},YbInCu4​, ${\mathrm{EuNi}}_{2}({\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{Ge}}_{x}{)}_{2},$ NiI2,{\mathrm{NiI}}_{2},NiI2​, and TaxN].{\mathrm{Ta}}_{x}\mathrm{N}].Tax​N].
The two-dimensional Falicov-Kimball (FK) model is analyzed using Monte Carlo method. In the case of concentrations of both itinerant and localized particles equal to 0.5 we determine temperature dependence of specific heat, charge density wave susceptibility and density-density correlation function. In the weak interaction regime we find a first order transition to the ordered state and anomalous temperature dependence of the correlation function. We construct the phase diagram of half-filled FK model. Also, the role of next-nearest-neighbor hopping on the phase diagram is analyzed. Lastly, we discuss the density of states and the spectral functions for the mobile particles in weak and strong interaction regime.