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-
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.