Finite-temperature investigation of quarter filled ladder systems

Abstract

We investigate charge ordering in a quarter-filled ladder at finite temperature by determinantal Quantum Monte Carlo. The sign problem is moderate in a wide range of model parameters relevant for NaV2O5. The charge order parameter exhibits a crossover as a function of inverse temperature β on finite systems. Above a critical nearest neighbor Coulomb repulsion Vc, the correlation length grows exponentially with β, indicative of the ordered phase at β = ∞. We find a clear single-particle gap manifesting itself in a flat n(µ) dependence at large nearest neighbor Coulomb repulsion V . Key words:quarter-filled ladders, charge ordering, quantum Monte CarloThe inorganic ladder compound NaV2O5 has attracted great attention in recent years. This interest was triggered by magnetic susceptibility measurements [1], which show a phase transition at T = 34 K into a low-temperature spin-gapped phase. This transition is accompanied by charge ordering, as observed in NMR measurements [2], where the valence of the vanadium sites changes from V 4.5 to V 4.5±δ , with δ the amount of charge disproportion. This transition has been studied theoretically by several techniques at T = 0 [3].On a microscopic level the system can be described by an extended Hubbard modelat quarter filling n = 0.5, with hopping matrix elements tij = tx along the ladder and tij = ty within a rung, and chemical potential µ. We state all energies in units of ty. These hopping parameters as well as the onsite Coulomb interaction can be extracted from firstprinciple calculations [4]. The hopping along chains * Corresponding author: e-mail: evertz@tugraz.at tx ≃ 0.5ty is weaker than along rungs. This strongly influences the physics of the ladder, for which a spingap seems to appear at tx > ∼ ty [3]. We used tx = 0.5 and U = 8. Since the non-local Coulomb interaction V cannot be determined properly by band-structure calculations, we used V as a free parameter of the Hamiltonian. The charge order parameter is ∆ 2 co = 1 2L n ij e iQ(r i −r j ) (ni − n )(nj − n ) with Q = (π, π), which is unity for complete ordering.We performed grand canonical calculations by determinantal quantum Monte Carlo. These are often very difficult for doped systems because of a sign problem. Fortunately, the average sign is favorably large in the relevant parameter range of tx/ty = 0.5 and large V (Fig. 1). In the opposite case of isotropic tx = ty at small V , sign becomes very small. The charge order parameter exhibits similar behavior, but it is less strongly dependent on tx/ty. Charge order grows with increasing V . Fig. 2 shows the charge correlation length ξcc. At small interactions, V = 1.5 and 2.0, the correlation length seems to saturate, but for V = 2.5 and 3.0 it increases exponentially with β, with a V -dependent slope. This behavior is consistent with the 1D Ising model in a transverse field (IMTF) [5], which is equiv-

Charge order induced by electron-lattice interaction inNaV2O5

“…The properties of the EHM without electron-lattice coupling were studied using mean field approaches, 35 and Cluster Perturbation Theory. 36 De-tailed studies of the EHM were also performed using the DMRG, 37,38 but not at specific values of the coupling parameters appropriate for NaV 2 O 5 .…”

Single-particle spectral function of quarter-filled ladder systems

“…As discussed below, in all our calculations we found a well established gap between the PES and IPES states yielding a constant density n in a reasonably large neighborhood of the physical chemical potential µ, in agreement with quantum Monte Carlo calculations. 35 Therefore µ ED gives a reasonable approximation for our calculations.…”