Reentrant Charge Order Transition in the Extended Hubbard Model

Abstract

We study the extended Hubbard model with both on-site and nearest neighbor Coulomb repulsion (U and V , respectively) in the Dynamical Mean Field theory. At quarter filling, the model shows a transition to a charge ordered phase with different sublattice occupancies nA = nB. The effective mass increases drastically at the critical V and a pseudo-gap opens in the single-particle spectral function for higher values of V . The Vc(T )-curve has a negative slope for small temperatures, i.e. the charge ordering transition can be driven by increasing the temperature. This is due to the higher spin-entropy of the charge ordered phase.PACS 71.10.Fd, 71.27.+a, 71.45.Lr The possibility of crystallization of electrons due to their long-range Coulomb repulsion was first proposed by Wigner [1]. He considered an electron system in a uniform positive background at sufficiently low densities. The Wigner lattice is formed when the gain in Coulomb energy due to the localization of the electrons exceeds the gain in kinetic energy for the homogeneous electron distribution. It is experimentally realized in the two dimensional electron gas in a GaAs/AlGaAs heterostructure [2]. Due to the reduced dimensionality, the effect of the Coulomb interaction is enhanced so that the transition to the ordered state occurs at experimentally accessible electron densities.Crystallization of charge carriers (charge ordering) can also be observed in three dimensional systems, even at very high densities [3]. Here the kinetic energy of the electrons or holes has to be reduced drastically for the charge ordered state to become possible. In 4f-electron systems it is the small hybridization of the well localized 4f-orbitals that leads to a reduced kinetic energy. An example is Yb 4 As 3 where a first order charge ordering transition occurs at T c ≈ 295K [4,5]. The carrier concentration in Yb 4 As 3 (approximately one hole per four Yb ions) is considerably larger than typical values for a Wigner lattice. The kinetic energy of the electrons can also be reduced by the interaction with lattice and spin degrees of freedom. An interplay of these mechanisms is responsible for the charge order transition occurring in a variety of rare earth manganites (e.g., in La 1−x Ca x MnO 3 for x ≥ 0.5 [6]).In all examples mentioned so far, the charge ordered phase is the ground state. However, a melting of the charge ordered state on decreasing the temperature (i.e. a reentrant transition) has been found recently in In this Letter, we investigate the simplest model which allows for a charge ordering transition due to the competition between kinetic and Coulomb energy. The extended Hubbard model [9]describes fermions on a lattice with an on-site Coulomb repulsion U , a nearest neighbor Coulomb repulsion V and a hopping matrix element t. The c † iσ (c iσ ) denote creation (annihilation) operators for a fermion at site i with spin σ, the n i are defined as n i = n i↑ + n i↓ where n iσ = c † iσ c iσ and <ij> indicates the sum over nearest neighbors.In the following we study ...

Finite-temperature numerical renormalization group study of the Mott transition

“…The above-mentioned restrictions concerning the value of U and T , or the low energy resolution, do not apply to the numerical renormalization group method (NRG) [11,12] which has only recently been used to investigate lattice models within the DMFT [13][14][15][16][17]. The NRG as well has its drawbacks, which will be discussed in Sec.…”

“…Applications of the NRG within the DMFT include the investigation of the Mott-transition [13][14][15], the problem of charge ordering in the extended Hubbard model [16], and the formation of the heavy-fermion liquid in the periodic Anderson model [17]. In all these investigations, the temperature was restricted to T = 0.…”

Theory of the reentrant charge-order transition in the manganites

“…Previous work [12] solved this model in infinite spatial dimensions, resulting in finite entropy (due to the spins) at T = 0 in the CO phase, so a reentrant transition was guaranteed to be found. In the infinite two-dimensional square lattice, the spins will order into a Néel state with zero entropy at T = 0.…”

“…The lowest temperature phase is metallic, and the CO insulator is only observed at intermediate temperatures. A reentrant transition has been obtained theoretically using extended Hubbard models both with electron-phonon interactions [11] and without electron-phonon interactions [12].…”

Theories on Frustrated Electrons in Two-Dimensional Organic Solids

“…One example can be found on a square lattice (V = 0). Dynamical mean-field theory (DMFT) [41,47] and the exact diagonalization [48] show that the extended Hubbard model at quarter-filling exhibits a charge ordered metallic phase-a Fermi liquid state, but with considerably large degree of charge disproportionation breaking the translational symmetry-in a very narrow range (∼ O(t/10)) in the vicinity of the insulating phase. This metallic state itself is not directly related to the frustration effect.…”