Logarithmic Corrections to Scaling in the XY2XY_2--Model

We study the distribution of partition function zeroes for the $XY$--model in two dimensions. In particular we find the scaling behaviour of the end of the distribution of zeroes in the complex external magnetic field plane in the thermodynamic limit (the Yang--Lee edge) and the form for the density of these zeroes. Assuming that finite--size scaling holds, we show that there have to exist logarithmic corrections to the leading scaling behaviour of thermodynamic quantities in this model. These logarithmic corrections are also manifest in the finite--size scaling formulae and we identify them numerically. The method presented here can be used to check the compatibility of scaling behaviour of odd and even thermodynamic functions in other models too.Comment: 3 pages, latex, 2 figure

Search for the Nondimerized Quantum Nematic Phase in the Spin-1 Chain

Chubukov's proposal concerning the possibility of a nondimerized quantum nematic phase in the ground-state phase diagram of the bilinear-biquadratic spin-1 chain is studied numerically. Our results do not support the existence of this phase, but they rather indicate a direct transition from the ferromagnetic into the dimerized phase.Comment: REVTEX, 14 pages +8 PostScript figure

Logarithmic Corrections to Scaling in the Two Dimensional XYXY--Model

By expressing thermodynamic functions in terms of the edge and density of Lee--Yang zeroes, we relate the scaling behaviour of the specific heat to that of the zero field magnetic susceptibility in the thermodynamic limit of the $XY$--model in two dimensions. Assuming that finite--size scaling holds, we show that the conventional Kosterlitz--Thouless scaling predictions for these thermodynamic functions are not mutually compatable unless they are modified by multiplicative logarithmic corrections. We identify these logarithmic corrections analytically in the case of the specific heat and numerically in the case of the susceptibility. The techniques presented here are general and can be used to check the compatibility of scaling behaviour of odd and even thermodynamic functions in other models too.Comment: 11 pages, latex, 4 figure

Charge-density waves in one-dimensional Hubbard superlattices

We study the formation of charge density waves (CDW's) in one-dimensional Hubbard superlattices, modeled by a repeated pattern of repulsive (U>0) and free (U=0) sites. By means of Lanczos diagonalizations for the ground state, we calculate the charge structure factor. Our results show that while the superlattice structure affects the modulation of the charge density waves, the periodicity can still be predicted through an effective density. We also show that, for a fixed repulsive layer thickness, the periodicity of the CDW is an oscillatory function of the free layer thickness.Comment: 4 pages, 4 figure

Charge-density waves in the Hubbard chain: evidence for 4k_F instability

Charge density waves in the Hubbard chain are studied by means of finite-temperature Quantum Monte Carlo simulations and Lanczos diagonalizations for the ground state. We present results both for the charge susceptibilities and for the charge structure factor at densities \rho=1/6 and 1/3; for \rho=1/2 (quarter filled) we only present results for the charge structure factor. The data are consistent with a 4k_F instability dominating over the 2k_F one, at least for sufficiently large values of the Coulomb repulsion, U. This can only be reconciled with the Luttinger liquid analyses if the amplitude of the 2k_F contribution vanishes above some U^*(\rho).Comment: RevTeX, 4 two-column pages with 7 colour figures embedded in tex

Numerical study of the frustrated ferromagnetic spin-1/2 chain

The ground state phase diagram of the frustrated ferromagnetic spin-1/2 chain is investigated using the exact diagonalization technique. It is shown that there is a jump in the spontaneous magnetization and the ground state of the system undergos to a phase transition from a ferromagnetic phase to a phase with dimer ordering between next-nearest-neighbor spins. Near the quantum transition point, the critical behavior of the ground state energy is analyzed numerically. Using a practical finite-size scaling approach, the critical exponent of the ground state energy is computed. Our numerical results are in good agreement with the results obtained by other theoretical approaches.Comment: 6 pages, 5 figure

Crossover behavior of the J1-J2 model in a staggered magnetic field

The ground states of the $S=\frac12$ Heisenberg chain with the nearest-neighbor and the next-nearest-neighbor antiferromagnetic couplings are numerically investigated in a staggered magnetic field. While the staggered magnetic field may induce the N\'eel-type excitation gap, and it is characterized by the Gaussian fixed point in the spin-fluid region, the crossover to the behavior controlled by the Ising fixed point is expected to be observed for the spontaneously dimerized state at finite field. Treating a low-lying excitation gap by the phenomenological renormalization-group method, we numerically determine the massless flow connecting the Gaussian and Ising fixed points. Further, to check the criticalities, we perform the finite-size-scaling analysis of the excitation gap.Comment: 4 pages, 3 figure

Quantum-fluctuation-induced collisions and subsequent excitation gap of an elastic string between walls

An elastic string embedded between rigid walls is simulated by means of the density-matrix renormalization group. The string collides against the walls owing to the quantum-mechanical zero-point fluctuations. Such ``quantum entropic'' interaction has come under thorough theoretical investigation in the context of the stripe phase observed experimentally in doped cuprates. We found that the excitation gap opens in the form of exponential singularity DeltaE ~ exp(-Ad^sigma) (d: wall spacing) with the exponent sigma =0.6(3), which is substantially smaller than the meanfield value sigma=2. That is, the excitation gap is much larger than that anticipated from meanfield, suggesting that the string is subjected to robust pinning potential due to the quantum collisions. This feature supports Zaanen's ``order out of disorder'' mechanism which would be responsible to the stabilization of the stripe phase

Magnetization plateau in the spin ladder with the four-spin exchange

The magnetization process of the $S$=1/2 antiferromagnetic spin ladder with the four-spin cyclic exchange interaction at T=0 is studied by the exact diagonalization of finite clusters and size scaling analyses. It is found that a magnetization plateau appears at half the saturation value if the ratio of the four- and two-spin exchange coupling constants $J_4$ is larger than the critical value $J_{4c}=0.05\pm$0.04. The phase transition with respect to $J_4$ at $J_{4c}$ is revealed to be the Kosterlitz-Thouless-type.Comment: 4 pages, Revtex, with 5 eps figure

Phase diagram of S=1 XXZ chain with next-nearest neighbor interaction

The one dimensional S=1 XXZ model with next-nearest-neighbor interaction $\alpha$ and Ising-type anisotropy $\Delta$ is studied by using a numerical diagonalization technique. We discuss the ground state phase diagram of this model numerically by the twisted-boundary-condition level spectroscopy method and the phenomenological renormalization group method, and analytically by the spin wave theory. We determine the phase boundaries among the XY phase, the Haldane phase, the ferromagnetic phase and the N\'{e}el phase, and then we confirm the universality class. Moreover, we map this model onto the non-linear $\sigma$ model and analyze the phase diagram in the $\alpha$ $\ll$ -1 and $\Delta$ $\sim$ 1 region by using the renormalization group method.Comment: 18 pages, 10 figure