Density Matrix Renormalization Group Study of the Haldane Phase in Random One-Dimensional Antiferromagnets

It is conjectured that the Haldane phase of the S=1 antiferromagnetic Heisenberg chain and the $S=1/2$ ferromagnetic-antiferromagnetic alternating Heisenberg chain is stable against any strength of randomness, because of imposed breakdown of translational symmetry. This conjecture is confirmed by the density matrix renormalization group calculation of the string order parameter and the energy gap distribution.Comment: 4 Pages, 7 figures; Considerable revisions are made in abstract and main text. Final accepted versio

Field Induced Multiple Reentrant Quantum Phase Transitions in Randomly Dimerized Antiferromagnetic S=1/2 Heisenberg Chains

The multiple reentrant quantum phase transitions in the $S=1/2$ antiferromagnetic Heisenberg chains with random bond alternation in the magnetic field are investigated by the density matrix renormalization group method combined with the interchain mean field approximation. It is assumed that the odd-th bond is antiferromagnetic with strength $J$ and even-th bond can take the values {\JS} and {\JW} ({\JS} > J > {\JW} > 0) randomly with probability $p$ and $1-p$, respectively. The pure version ($p=0$ and $p=1$) of this model has a spin gap but exhibits a field induced antiferromagnetism in the presence of interchain coupling if Zeeman energy due to the magnetic field exceeds the spin gap. For $0 < p < 1$, the antiferromagnetism is induced by randomness at small field region where the ground state is disordered due to the spin gap in the pure case. At the same time, this model exhibits randomness induced plateaus at several values of magnetization. The antiferromagnetism is destroyed on the plateaus. As a consequence, we find a series of reentrant quantum phase transitions between the transverse antiferromagnetic phases and disordered plateau phases with the increase of the magnetic field for moderate strength of interchain coupling. Above the main plateaus, the magnetization curve consists of a series of small plateaus and the jumps between them, It is also found that the antiferromagnetism is induced by infinitesimal interchain coupling at the jumps between the small plateaus. We conclude that this antiferromagnetism is supported by the mixing of low lying excited states by the staggered interchain mean field even though the spin correlation function is short ranged in the ground state of each chain.Comment: 5 pages, 8 figure

Interacting Boson Theory of the Magnetization Process of the Spin-1/2 Ferromagnetic-Antiferromagnetic Alternating Heisenberg Chain

The low temperature magnetization process of the ferromagnetic-antiferromagnetic Heisenberg chain is studied using the interacting boson approximation. In the low field regime and near the saturation field, the spin wave excitations are approximated by the $\delta$ function boson gas for which the Bethe ansatz solution is available. The finite temperature properties are calculated by solving the integral equation numerically. The comparison is made with Monte Carlo calculation and the limit of the applicability of the present approximation is discussed.Comment: 4 pages, 7 figure

Random Hamiltonian in thermal equilibrium

A framework for the investigation of disordered quantum systems in thermal equilibrium is proposed. The approach is based on a dynamical model--which consists of a combination of a double-bracket gradient flow and a uniform Brownian fluctuation--that `equilibrates' the Hamiltonian into a canonical distribution. The resulting equilibrium state is used to calculate quenched and annealed averages of quantum observables.Comment: 8 pages, 4 figures. To appear in DICE 2008 conference proceeding

Density Matrix Renormalization Group Study of the S=1/2 Anisotropic Antiferromagnetic Heisenberg Chains with Quasiperiodic Exchange Modulation

The low energy behavior of the S=1/2 antiferromagnetic XY-like XXZ chains with precious mean quasiperiodic exchange modulation is studied by the density matrix renormalization group method. It is found that the energy gap of the chain with length N scales as $\exp (-cN^{\omega})$ with nonuniversal exponent $\omega$ if the Ising component of the exhange coupling is antiferromagnetic. This behavior is expected to be the characteristic feature of the quantum spin chains with relevant aperiodicity. This is in contrast to the XY chain for which the precious mean exchange modulation is marginal and the gap scales as $N^{-z}$. On the contrary, it is also verified that the energy gap scales as $N^{-1}$ if the Ising component of the exhange coupling is ferromagnetic. Our results are not only consistent with the recent bosonization analysis of Vidal, Mouhanna and Giamarchi but also clarify the nature of the strong coupling regime which is inaccesssible by the bosonization approach.Comment: 8 pages, 15 figures, 1 table; Proceedings of the workshop 'Frontiers in Magnetism', Kyoto, Oct. 199

A modal model for diffraction gratings

A description of an algorithm for a rather general modal grating calculation is presented. Arbitrary profiles, depth, and permittivity are allowed. Gratings built up from sub-gratings are allowed, as are coatings on the sidewalls of lines, and arbitrary complex structure. Conical angles and good conductors are supported

Quasi-periodic spin chains in a magnetic field

We study the interplay between a (quasi) periodic coupling array and an external magnetic field in a spin-1/2 XXZ chain. A new class of magnetization plateaux are obtained by means of Abelian bosonization methods which give rise to a sufficient quantization condition. The investigation of magnetic phase diagrams via exact diagonalization of finite clusters finds a complete agreement with the continuum treatment in a variety of situations.Comment: 4 pages RevTeX, 5 PostScript figures included. Final version to appear in PR

Interplay between quasi-periodicity and disorder in quantum spin chains in a magnetic field

We study the interplay between disorder and a quasi periodic coupling array in an external magnetic field in a spin-1/2 XXZ chain. A simple real space decimation argument is used to estimate the magnetization values where plateaux show up. The latter are in good agreement with exact diagonalization results on fairly long XX chains. Spontaneous susceptibility properties are also studied, finding a logarithmic behaviour similar to the homogeneously disordered case.Comment: 5 RevTeX pages, 5 Postscript figures include

Effects of Single-site Anisotropy on Mixed Diamond Chains with Spins 1 and 1/2

Effects of single-site anisotropy on mixed diamond chains with spins 1 and 1/2 are investigated in the ground states and at finite temperatures. There are phases where the ground state is a spin cluster solid, i.e., an array of uncorrelated spin-1 clusters separated by singlet dimers. The ground state is nonmagnetic for the easy-plane anisotropy, while it is paramagnetic for the easy-axis anisotropy. Also, there are the N\'eel, Haldane, and large-$D$ phases, where the ground state is a single spin cluster of infinite size and the system is equivalent to the spin-1 Heisenberg chain with alternating anisotropy. The longitudinal and transverse susceptibilities and entropy are calculated at finite temperatures in the spin-cluster-solid phases. Their low-temperature behaviors are sensitive to anisotropy.Comment: 8 pages, 4 figure