Density matrix renormalisation group for a quantum spin chain at non-zero temperature

We apply a recent adaptation of White's density matrix renormalisation group (DMRG) method to a simple quantum spin model, the dimerised $XY$ chain, in order to assess the applicabilty of the DMRG to quantum systems at non-zero temperature. We find that very reasonable results can be obtained for the thermodynamic functions down to low temperatures using a very small basis set. Low temperature results are found to be most accurate in the case when there is a substantial energy gap.Comment: 6 pages, Standard Latex File + 7 PostScript figures available on reques

Can Quantum Lattice Fluctuations Destroy the Peierls Broken Symmetry Ground State?

The study of bond alternation in one-dimensional electronic systems has had a long history. Theoretical work in the 1930s predicted the absence of bond alternation in the limit of infinitely long conjugated polymers; a result later contradicted by experimental investigations. When this issue was re-examined in the 1950s it was shown in the adiabatic limit that bond alternation occurs for any value of electron-phonon coupling. The question of whether this conclusion remains valid for quantized nuclear degrees of freedom was first addressed in the 1980s. Since then a series of numerical calculations on models with gapped, dispersionless phonons have suggested that bond alternation is destroyed by quantum fluctuations below a critical value of electron-phonon coupling. In this work we study a more realistic model with gapless, dispersive phonons. By solving this model with the DMRG method we show that bond alternation remains robust for any value of electron-phonon coupling

Density Matrices for a Chain of Oscillators

We consider chains with an optical phonon spectrum and study the reduced density matrices which occur in density-matrix renormalization group (DMRG) calculations. Both for one site and for half of the chain, these are found to be exponentials of bosonic operators. Their spectra, which are correspondingly exponential, are determined and discussed. The results for large systems are obtained from the relation to a two-dimensional Gaussian model.Comment: 15 pages,8 figure

Quantum transfer matrix method for one-dimensional disordered electronic systems

We develop a novel quantum transfer matrix method to study thermodynamic properties of one-dimensional (1D) disordered electronic systems. It is shown that the partition function can be expressed as a product of $2\times2$ local transfer matrices. We demonstrate this method by applying it to the 1D disordered Anderson model. Thermodynamic quantities of this model are calculated and discussed.Comment: 7 pages, 10 figure

Fidelity and Quantum phase transition for the Heisenberg chain with the next-nearest-neighbor interaction

In this paper, we investigate the fidelity for the Heisenberg chain with the next-nearest-neighbor interaction (or the $J_1-J_2$ model) and analyze its connections with quantum phase transition. We compute the fidelity between the ground states and find that the phase transition point of the $J_1-J_2$ model can not be well characterized by the ground state fidelity for finite-size systems. Instead, we introduce and calculate the fidelity between the first excited states. Our results show that the quantum transition can be well characterized by the fidelity of the first excited state even for a small-size system.Comment: 4 pages, 5 figures, version published in Phys. Rev.

A density matrix renormalisation group algorithm for quantum lattice systems with a large number of states per site

A variant of White's density matrix renormalisation group scheme which is designed to compute low-lying energies of one-dimensional quantum lattice models with a large number of degrees of freedom per site is described. The method is tested on two exactly solvable models---the spin-1/2 antiferromagnetic Heisenberg chain and a dimerised XY spin chain. To illustrate the potential of the method, it is applied to a model of spins interacting with quantum phonons. It is shown that the method accurately resolves a number of energy gaps on periodic rings which are sufficiently large to afford an accurate investigation of critical properties via the use of finite-size scaling theory.Comment: RevTeX, 8 pages, 2 figure

Search of low-dimensional magnetics on the basis of structural data: spin-1/2 antiferromagnetic zigzag chain compounds In2VO5, beta-Sr(VOAsO4)2,(NH4,K)2VOF4 and alpha-ZnV3O8

A new technique for searching low-dimensional compounds on the basis of structural data is presented. The sign and strength of all magnetic couplings at distances up to 12 A in five predicted new antiferromagnetic zigzag spin-1/2 chain compounds In2VO5, beta-Sr(VOAsO4)2, (NH4)2VOF4, K2VOF4 and alpha-ZnV3O8 were calculated. It was stated that in the compound In2VO5 zigzag spin chains are frustrated, since the ratio (J2/J1) of competing antiferromagnetic (AF) nearest- (J1) and AF next-to-nearest-neighbour (J2) couplings is equal to 1.68 that exceeds the Majumdar-Ghosh point by 1/2. In other compounds the zigzag spin chains are AF magnetically ordered single chains as value of ratios J2/J1 is close to zero. The interchain couplings were analyzed in detail.Comment: 14 pages, 6 figure, 1 table, minor change

Small-Angle X-ray and neutron scattering from diamond single crystals

Results of Small-Angle Scattering study of diamonds with various types of point and extended defects and different degrees of annealing are presented. It is shown that thermal annealing and/or mechanical deformation cause formation of nanosized planar and threedimensional defects giving rise to Small-Angle Scattering. The defects are often facetted by crystallographic planes 111, 100, 110, 311, 211 common for diamond. The scattering defects likely consist of clusters of intrinsic and impurity-related defects; boundaries of mechanical twins also contribute to the SAS signal. There is no clear correlation between concentration of nitrogen impurity and intensity of the scattering.Comment: 6 pages, 5 figures; presented at SANS-YuMO User Meeting 2011, Dubna, Russi

Orientation of rapid thermally annealed lead zirconate titanate thin films on (111) Pt substrates

The nucleation, growth, and orientation of lead zirconate titanate thin films prepared from organometallic precursor solutions by spin coating on (111) oriented platinum substrates and crystallized by rapid thermal annealing was investigated. The effects of pyrolysis temperature, post-pyrolysis thermal treatments, and excess lead addition are reported. The use of post-pyrolysis oxygen anneals at temperatures in the regime of 350-450 °C was found to strongly affect the kinetics of subsequent amorphous-pyrochlore-perovskite crystallization by rapid thermal annealing. The use of such post-pyrolysis anneals allowed films of reproducible microstructure and textures [both (100) and (111)] to be prepared by rapid thermal annealing. It is proposed that such anneals and pyrolysis temperature affect the oxygen concentration/average Pb valence in the amorphous films prior to annealing. Such changes in the Pb valence state then affect the stability of the transient pyrochlore phase and thus the kinetics of perovskite crystallizatio

Interchain interactions and magnetic properties of Li2CuO2

An effective Hamiltonian is constructed for an insulating cuprate with edge-sharing chains Li2CuO2.The Hamiltonian contains the nearest and next-nearest neighboring intrachain and zigzag-type interchain interactions.The values of the interactions are obtained from the analysis of the magnetic susceptibility, and this system is found to be described as coupled frustrated chains.We calculate the dynamical spin correlation function S(q,\omega) by using the exact diagonalization method, and show that the spectra of S(q,\omega) are characterized by the zigzag-type interchain interactions. The results of the recent inelastic neutron scattering experiment are discussed in the light of the calculated spectra.Comment: 4 pages, 3 figures, RevTe