Quasiperiodic Hubbard chains

Low energy properties of half-filled Fibonacci Hubbard models are studied by weak coupling renormalization group and density matrix renormalization group method. In the case of diagonal modulation, weak Coulomb repulsion is irrelevant and the system behaves as a free Fibonacci chain, while for strong Coulomb repulsion, the charge sector is a Mott insulator and the spin sector behaves as a uniform Heisenberg antiferromagnetic chain. The off-diagonal modulation always drives the charge sector to a Mott insulator and the spin sector to a Fibonacci antiferromagnetic Heisenberg chain.Comment: 4 pages, 4 figures; Final version to appear in Phys. Rev. Let

Magnetization plateaus in antiferromagnetic-(ferromagnetic)_{n} polymerized S=1/2 XXZ chains

The plateau-non-plateau transition in the antiferromagnetic-(ferromagnetic)$_{n}$ polymerized $S=1/2$ XXZ chains under the magnetic field is investigated. The universality class of this transition belongs to the Brezinskii-Kosterlitz-Thouless (BKT) type. The critical points are determined by level spectroscopy analysis of the numerical diagonalization data for $4 \leq p \leq 13$ where $p(\equiv n+1)$ is the size of a unit cell. It is found that the critical strength of ferromagnetic coupling decreases with $p$ for small $p$ but increases for larger enough $p$. It is also found that the plateau for large $p$ is wide enough for moderate values of exchange coupling so that it should be easily observed experimentally. This is in contrast to the plateaus for $p = 3$ chains which are narrow for a wide range of exchange coupling even away from the critical point

Critical Properties of the transition between the Haldane phase and the large-D phase of the spin-1/2 ferromagnetic-antiferromagnetic Heisenberg chain with on-site anisotropy"

We analytically study the ground-state quantum phase transition between the Haldane phase and the large-$D$ (LD) phase of the $S=1/2$ ferromagnetic-antiferromagnetic alternating Heisenberg chain with on-site anisotropy. We transform this model into a generalized version of the alternating antiferromagnetic Heisenberg model with anisotropy. In the transformed model, the competition between the transverse and longitudinal bond alternations yields the Haldane-LD transition. Using the bosonization method, we show that the critical exponents vary continuously on the Haldane-LD boundary. Our scaling relations between critical exponents very well explains the numerical results by Hida.Comment: text 12 pages (Plain TeX), LaTeX sourse files of a table and a figure on reques

The antiferromagnetic order in an F-AF random alternating quantum spin chain : (CH_3)_2 CHNH_3 Cu(Cl_x Br_{1-x})_3

A possibility of the uniform antiferromagnetic order is pointed out in an S=1/2 ferromagnetic (F) - antiferromagnetic (AF) random alternating Heisenberg quantum spin chain compound: (CH_3)_2 CHNH_3 Cu(Cl_x Br_{1-x})_3. The system possesses the bond alternation of strong random bonds that take +/- 2J and weak uniform AF bonds of -J. In the pure concentration limits, the model reduces to the AF-AF alternation chain at x=0 and to the F-AF alternation chain at x=1. The nonequilibrium relaxation of large-scale quantum Monte Carlo simulations exhibits critical behaviors of the uniform AF order in the intermediate concentration region, which explains the experimental observation of the magnetic phase transition. The present results suggest that the uniform AF order may survive even in the presence of the randomly located ferromagnetic bonds.Comment: 4 pages, 3 figure

Boson Fock representations of stochastic processes

A, classification theory of quantum stationary processes similar to the corresponding theory for classical stationary processes is presented, Our main result is the classificatio

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

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

Behavior of a frustrated quantum spin chain with bond dimerization

We clarified behavior of the excitation gap in a frustrated S=1/2 quantum spin chain with bond dimerization by using the numerical diagonalization of finite systems and a variational approach. The model interpolates between the independent dimer model and the S=1 spin chain by changing a strength of the dimerization. The energy gap is minimum at the fully-frustrated point, where a localized kink and a freely mobile anti-kink govern the low-lying excitations. Away from the point, a kink and an antikink form a bound state by an effective triangular potential between them. The consequential gap enhancement and the localization length of the bound state is obtained exactly in the continuous limit. The gap enhancement obeys a power law with exponent 2/3. The method and the obtained results are common to other frustrated double spin-chain systems, such as the one-dimensional J_1 - J_2 model, or the frustrated ladder model.Comment: 11 pages, REVTeX, 8 figures in eps-fil

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

Ferrimagnetism of the Heisenberg Models on the Quasi-One-Dimensional Kagome Strip Lattices

We study the ground-state properties of the S=1/2 Heisenberg models on the quasi-onedimensional kagome strip lattices by the exact diagonalization and density matrix renormalization group methods. The models with two different strip widths share the same lattice structure in their inner part with the spatially anisotropic two-dimensional kagome lattice. When there is no magnetic frustration, the well-known Lieb-Mattis ferrimagnetic state is realized in both models. When the strength of magnetic frustration is increased, on the other hand, the Lieb-Mattis-type ferrimagnetism is collapsed. We find that there exists a non-Lieb-Mattis ferrimagnetic state between the Lieb-Mattis ferrimagnetic state and the nonmagnetic ground state. The local magnetization clearly shows an incommensurate modulation with long-distance periodicity in the non-Lieb-Mattis ferrimagnetic state. The intermediate non-Lieb-Mattis ferrimagnetic state occurs irrespective of strip width, which suggests that the intermediate phase of the two-dimensional kagome lattice is also the non-Lieb-Mattis-type ferrimagnetism.Comment: 9pages, 11figures, accepted for publication in J. Phys. Soc. Jp