One dimensional continuum Falicov-Kimball model in the strongly correlated limit (original) (raw)
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Ground-State Energy and Low-Temperature Behavior of the One-Dimensional Falicov-Kimball Model
Europhysics Letters (EPL), 1993
We consider the Falicov-Kimball model in the case of an equal number of classical > and quantum <> with Fermi statistics. In one dimension we find an exact formula for the leading behavior of the ground-state energy as a function of the attractive potential U between electrons and nuclei. For U > U, the system forms <<atoms. which have an effective repulsion between them. Similar results hold for a continuum model provided there is a sufficiently large hard core between the nuclei. Some low-temperature properties are also discussed. We consider the Falicov-Kimball model as a very primitive model of matter which retains two basic features of electrons and nuclei: the two types of constituents attract each other and the .electrons>> are subject to the Pauli principle. The auclei>> are considered as classical particles with a <<hard core),, occupying the sites of a lattice Z d. The electrons and nuclei interact by an attractive on-site potential. The kinetic energy of an electron is given by the lattice Laplacian Kq =-81i-jl, + 2d8ij. For a given configuration of M nuclei the single-electron Hamiltonian has the matrix elements h, = Kq-Unidq, U > 0, ni = 1, 0
Thermodynamics of the two-dimensional Falicov-Kimball model: A classical Monte Carlo study
Physical Review B, 2006
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.
Thermodynamic Properties of the Generalized Falicov–Kimball Model
Journal of Superconductivity, 2000
The thermodynamic properties: specific heat and magnetization are studied as a function of temperature, doping, and interlevel spacing within the two-dimensional extended Falicov-Kimball model for spinless fermions. It was recently shown that the strong coupling limit of the above model possesses electronically driven ferroelectric order. Thermodynamic quantities are calculated using the finite-temperature Lanczos method with additional phase-averaging for a system of 4 × 4 sites. Our results indicate that valence transition exists in the extended Falicov-Kimball model.
Exact solution of the multicomponent Falicov-Kimball model in infinite dimensions
Philosophical Magazine Part B, 2001
The exact solution for the thermodynamic and dynamic properties of the infinite-dimensional multi-component Falicov-Kimball model for arbitrary concentration of d-and f-electrons is presented. The emphasis is on a descriptive derivation of important physical quantities by the equation of motion technique. We provide a thorough discussion of the f-electron Green function and of the susceptibility to spontaneous hybridization. The solutions are used to illustrate different physical systems ranging from the high-temperature phase of the YbInCu 4 family of materials to an examination of classical intermediate valence systems that can develop a spontaneous hybridization at T = 0.
Thermodynamic studies of the two dimensional Falicov-Kimball model on a triangular lattice
The European Physical Journal B, 2011
Thermodynamic properties of the spinless Falicov-Kimball model are studied on a triangular lattice using numerical diagonalization technique with Monte-Carlo simulation algorithm. Discontinuous metal-insulator transition is observed at finite temperature. Unlike the case of square lattice, here we observe that the finite temperature effect is not able to smear out the discontinuous metal-insulator transition seen in the ground state. Calculation of specific heat (Cv) shows single and double peak structures for different values of parameters like on-site correlation strength (U), f −electron energy (E f) and temperature.
Universal correlations of one-dimensional interacting electrons in the gas phase
Physics Letters A, 1999
We consider dynamical correlation functions of short range interacting electrons in one dimension at finite temperature. Below a critical value of the chemical potential there is no Fermi surface anymore, and the system can no longer be described as a Luttinger liquid. Its low temperature thermodynamics is that of an ideal gas. We identify the impenetrable electron gas model as a universal model for the gas phase and present exact and explicit expressions for the asymptotics of correlation functions at small temperatures, in the presence of a magnetic field.
Exact dynamical mean-field theory of the Falicov-Kimball model
Reviews of Modern Physics, 2003
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 YbInCu 4 , EuNi 2 (Si 1Ϫx Ge x ) 2 , NiI 2 , and Ta x N].
Charge-density-wave order parameter of the Falicov-Kimball model in infinite dimensions
2003
In the large-U limit, the Falicov-Kimball model maps onto an effective Ising model, with an order parameter described by a BCS-like mean-field theory in infinite dimensions. In the small-U limit, van Dongen and Vollhardt showed that the order parameter assumes a strange non-BCS-like shape with a sharp reduction near T ≈ Tc/2. Here we numerically investigate the crossover between these two regimes and qualitatively determine the order parameter for a variety of different values of U . We find the overall behavior of the order parameter as a function of temperature to be quite anomalous. 71.30.+h, Dynamical mean field theory 1 has been widely used to study electron correlations in a variety of different interacting systems. Much work has focused on the "paramagnetic" metal-insulator transition, on transport properties in the normal state, and on determining phase diagrams to ordered phases via a susceptibility analysis or a Maxwell construction. The properties of the ordered phase have been less studied, yet there is much interesting physics to examine there. For example, one might have thought that since the system is infinite-dimensional, both the critical behavior and the order parameter as a function of temperature would be determined by a BCSlike mean-field picture. Indeed, the critical exponents are always mean-field like, but the order parameter can have quite anomalous behavior as a function of temperature. This anomalous behavior is amplified for small correlation strength, since many models map onto effective spin models for large correlations, and the order parameter of an infinite-dimensional spin model is always mean-fieldlike. In this contribution, we examine in detail the case of a commensurate (two-sublattice) charge-density-wave (CDW) phase in the spinless Falicov-Kimball model at half filling. Analytical work in the large and small-U limits has already been carried out 2,3 .
Physical Review B, 2003
Specific heat and charge susceptibility are computed for the Falicov-Kimball model with two spinless impurities embedded in a fermionic bath. The model takes into account the Coulomb scattering and hybridization between local levels and conduction states. The numerical renormalization group with two discretization parameters is used to obtain the spectrum of the model, from which the thermodynamic is obtained. We discuss the importance of going beyond the usual approximation that projects all momenta at the Fermi level.
Thermodynamical Limit of the Lipkin-Meshkov-Glick Model
Physical Review Letters, 2007
A method based on the analyzis of the Majorana polynomial roots is introduced to compute the spectrum of the Lipkin-Meshkov-Glick model in the thermodynamical limit. A rich structure made of four qualitatively different regions is revealed in the parameter space whereas the ground state study only distinguishes between two phases.