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arXiv:1106.5136 · Condensed Matter Physics

Spectral densities and diagrams of states of one-dimensional ionic Pauli conductor

Stasyuk, Vorobyov, Stetsiv

Published Jan 1, 2011• 1 citation
arXivHTMLPDF

Abstract

We focus on the features of spectra and diagrams of states obtained via exact diagonalization technique for finite ionic conductor chain in periodic boundary conditions.One dimensional ionic conductor is described with the lattice model where ions are treated within the framework of "mixed" Pauli statistics.The ion transfer and nearest-neighbour interaction between ions are taken into account.The spectral densities and diagrams of states for various temperatures and values of interaction are obtained.The conditions of transition from uniform (Mott insulator) to the modulated (charge density wave state) through the superfluid-like state (similar to the state with the Bose-Einstein condensation observed in hard-core boson models) are analyzed.

DOI
10.5488/cmp.14.23702

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We focus on the features of spectra and diagrams of states obtained via exact diagonalization technique for finite ionic conductor chain in periodic boundary conditions.One dimensional ionic conductor is described with the lattice model where ions are treated within the framework of "mixed" Pauli statistics.The ion transfer and nearest-neighbour interaction between ions are taken into account.The spectral densities and diagrams of states for various temperatures and values of interaction are obtained.The conditions of transition from uniform (Mott insulator) to the modulated (charge density wave state) through the superfluid-like state (similar to the state with the Bose-Einstein condensation observed in hard-core boson models) are analyzed.
We study the one-dimensional Bose-Hubbard model using the density-matrix renormalization group. For the cases of on-site interactions and additional nearest-neighbor interactions the phase boundaries of the Mott insulators and charge-density wave phases are determined. We find a direct phase transition between the charge-density wave phase and the superfluid phase, and no supersolid or normal phases. In the presence of nearest-neighbor interaction the charge density wave phase is completely surrounded by a region in which the effective interactions in the superfluid phase are repulsive. In this region a single impurity causes the system to be insulating. An even bigger region of the superfluid phase is driven into a Bose-glass phase by any finite quenched disorder. We determine the boundaries of both regions in the phase diagram. The ac conductivity of the superfluid phase in the attractive and the repulsive region is calculated, and a big superfluid stiffness is found in the attractive as well as the repulsive region.
We investigate the ground-state phase diagram of the one-dimensional 'ionic' Hubbard model with an alternating periodic potential at half-filling by numerical diagonalization of finite systems with the Lanczos and density matrix renormalization group methods. We identify an insulator–insulator phase transition from a band to a correlated insulator with simultaneous charge and bond-charge order. The transition point is characterized by the vanishing of the optical excitation gap while simultaneously the charge and spin gaps remain finite and equal. Indications for a possible second transition into a Mott-insulator phase are discussed.
By means of the density matrix renormalization group technique, we accurately determine the zero-temperature phase diagram of the one-dimensional extended Bose–Hubbard model with on-site and nearest-neighbor interactions. We analyze the scaling of the charge and of the neutral ground-state energy gaps, as well as of various order parameters. In this way we come to an accurate location of the boundaries between the superfluid and the insulating phases. In this last region, we are able to distinguish between the conventional Mott insulating and density-wave phases and the Haldane insulator phase displaying long-range string ordering, as originally predicted by Dalla Torre et al (2006 Phys. Rev. Lett. 97 260401).
We investigate three different types of quantum phase transition occurring in quasi one-dimensional systems theoretically and numerically. First, we study the band-insulator to Mott-insulator transition occurring in charge-transfer complexes, for which the half-filled one-dimensional ionic Hubbard model is considered to be the prototype model. The study is carried out by first deriving an effective spin-one model, and then studying the model numerically using the density matrix renormalization group. We perform a careful finite-size scaling analysis of the mass gaps, order-parameters, and relative susceptibility. We confirm the existence of two quantum critical points. Analysis of the critical exponents confirms that the band-insulator-to-spontaneously-dimerized phase transition belong to the 2D Ising class. The spontaneously dimerized phase undergoes a phase transition to the Mott-insulator which is an infinite-order. Second, we investigate the Mott metal-insulator transition for the half-filled Hubbard model with both nearest-neighbor t and next-nearest-neighbor t′ hopping terms. We study the model using the bosonization approach and density matrix renormalization group simulations. An effective low-energy Hamiltonian that describes the insulator-metal transition is derived. We present results of density matrix renormalization group calculations of spin and charge distribution in various sectors of the phase diagram. The numerical results support the picture derived from the effective theory and give evidence for the complete separation of the transitions involving the spin and the charge degrees of freedom. Finally, we investigate quantum phase transitions phases in low-dimensional fermionic and spin models that go from uniform to spatially inhomogeneous, i.e., dimerized, trimerized, or incommensurate, phases. We propose a new approach based on studying the length dependence of the von Neumann entropy and its corresponding Fourier spectrum for finite segments in the ground state of finite chains. Peaks at a nonzero wave vector are indicators of oscillatory behavior in decaying correlation functions and also provide significant information about certain relevant features of the excitation spectrum; in particular, they can identify the wave vector of soft modes in critical models.
We carry out an extensive study of the phase diagrams of the extended Bose Hubbard model, with a mean filling of one boson per site, in one dimension by using the density matrix renormalization group and show that it contains Superfluid (SF), Mott-insulator (MI), density-wave (DW) and Haldane-insulator (HI) phases. We show that the critical exponents and central charges for the HI-DW, MI-HI and SF-MI transitions are consistent with those for models in the two-dimensional Ising, Gaussian, and Berezinskii-Kosterlitz-Thouless (BKT) universality classes, respectively; and we suggest that the SF-HI transition may be more exotic than a simple BKT transition. We show explicitly that different boundary conditions lead to different phase diagrams.
Exact ground states, charge densities, and excitation energies are found using valence bond methods for N-site modified Hubbard models with uniform spacing. At the neutral-ionic transition (NIT), the ground state has a symmetry crossover in 4n4n4n and 4n+24n+24n+2 rings with periodic and antiperiodic boundary conditions, respectively. Large site energies $\ensuremath{\Delta}$ stabilize a paired state of the half-filled chain, while large U stabilizes a covalent state. Finite-transfer integrals t shift the NIT to the covalent side of $U\ensuremath{-}2\ensuremath{\Delta}.$ Exact results to N=16N=16N=16 in the full basis and to N=22N=22N=22 in a restricted basis for large U and $\ensuremath{\Delta}$ are extrapolated to obtain the crossover and charge density of extended chains. The modified Hubbard model has a continuous NIT between a diamagnetic band insulator on the paired side and a paramagnetic Mott insulator on the covalent side. The singlet-triplet (ST), singlet-singlet (SS), and charge gaps for finite N indicate that the ST and SS gaps close at the NIT with increasing U, and that the charge gap vanishes only there. Finite-N excitations constrain all singularities to $\ifmmode\pm\else\textpm\fi{}0.1t$ of the symmetry crossover. The NIT is interpreted as a localized ground state (GS) with finite gaps on the paired side and an extended GS with vanishing ST and SS gaps on the covalent side. The charge gap and charge stiffness indicate a metallic GS at the transition that, however, is unconditionally unstable to dimerization. Finite $\ensuremath{\Delta}$ breaks electron-hole $(e\ensuremath{-}h)$ symmetry, but the modified Hubbard model has an extended $e\ensuremath{-}h$ symmetry, and a strong mixing of spin and charge excitations is limited to a few t's about the NIT. Exact finite-size results complement other approaches to valence or ferroelectric transitions in organic charge-transfer salts or in inorganic oxides, and to electron-vibration coupling and structural instabilities in one-dimensional systems.