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

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

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

Transport properties of one-dimensional interacting fermions in aperiodic potentials

Motivated by the existence of metal-insulator transition in one-dimensional non-interacting fermions in quasiperiodic and pseudorandom potentials, we studied interacting spinless fermion models using exact many-body Lanczos diagonalization techniques. Our main focus was to understand the effect of the fermion-fermion interaction on the transport properties of aperiodic systems. We calculated the ground state energy and the Kohn charge stiffness Dc. Our numerical results indicate that there exists a region in the interaction strength parameter space where the system may behave differently from the metallic and insulating phases. This intermediate phase may be characterized by a power law scaling of the charge stiffness constant in contrast to the localized phase where Dc scales exponentially with the size of the system.Comment: 11 pages LaTex document with 5 eps figures. Uses revtex style file

Field-induced Ordering in Critical Antiferromagnets

Transfer-matrix scaling methods have been used to study critical properties of field-induced phase transitions of two distinct two-dimensional antiferromagnets with discrete-symmetry order parameters: triangular-lattice Ising systems (TIAF) and the square-lattice three-state Potts model (SPAF-3). Our main findings are summarised as follows. For TIAF, we have shown that the critical line leaves the zero-temperature, zero -field fixed point at a finite angle. Our best estimate of the slope at the origin is $(dT_c/dH)_{T=H=0} = 4.74 \pm 0.15$. For SPAF-3 we provided evidence that the zero-field correlation length diverges as $\xi(T \to 0, H=0) \simeq \exp (a/T^{x})$, with $x=1.08 \pm 0.13$, through analysis of the critical curve at $H \neq 0$ plus crossover arguments. For SPAF-3 we have also ascertained that the conformal anomaly and decay-of-correlations exponent behave as: (a) H=0: $c=1, \eta=1/3$; (b) $H \neq 0: c=1/2, \eta=1/4$.Comment: RevTex, 7 pages, 4 eps figures, to be published in Phys. Rev.

Universal Short-Time Dynamics in the Kosterlitz-Thouless Phase

We study the short-time dynamics of systems that develop ``quasi long-range order'' after a quench to the Kosterlitz-Thouless phase. With the working hypothesis that the ``universal short-time behavior'', previously found in Ising-like systems, also occurs in the Kosterlitz-Thouless phase, we explore the scaling behavior of thermodynamic variables during the relaxational process following the quench. As a concrete example, we investigate the two-dimensional $6$-state clock model by Monte Carlo simulation. The exponents governing the magnetization, the second moment, and the autocorrelation function are calculated. From them, by means of scaling relations, estimates for the equilibrium exponents $z$ and $\eta$ are derived. In particular, our estimates for the temperature-dependent anomalous dimension $\eta$ that governs the static correlation function are consistent with existing analytical and numerical results and, thus, confirm our working hypothesis.Comment: 16 pages, 9 postscript figures, REVTEX 3.0, submitted to Phys. Rev.

Bond-charge Interaction in the extended Hubbard chain

We study the effects of bond-charge interaction (or correlated hopping) on the properties of the extended ({\it i.e.,} with both on-site ($U$) and nearest-neighbor ($V$) repulsions) Hubbard model in one dimension at half-filling. Energy gaps and correlation functions are calculated by Lanczos diagonalization on finite systems. We find that, irrespective of the sign of the bond-charge interaction, $X$, the charge--density-wave (CDW) state is more robust than the spin--density-wave (SDW) state. A small bond-charge interaction term is enough to make the differences between the CDW and SDW correlation functions much less dramatic than when $X=0$. For $X=t$ and fixed $V<2t$ ($t$ is the uncorrelated hopping integral), there is an intermediate phase between a charge ordered phase and a phase corresponding to singly-occupied sites, the nature of which we clarify: it is characterized by a succession of critical points, each of which corresponding to a different density of doubly-occupied sites. We also find an unusual slowly decaying staggered spin-density correlation function, which is suggestive of some degree of ordering. No enhancement of pairing correlations was found for any $X$ in the range examined.Comment: 10 pages, 7 PostScript figures, RevTeX 3; to appear in Phys Rev

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

A layering model for superconductivity in the borocarbides

We propose a superlattice model to describe superconductivity in layered materials, such as the borocarbide families with the chemical formul\ae\ $RT_2$B$_2$C and $RT$BC, with $R$ being (essentially) a rare earth, and $T$ a transition metal. We assume a single band in which electrons feel a local attractive interaction (negative Hubbard-$U$) on sites representing the $T$B layers, while U=0 on sites representing the $R$C layers; the multi-band structure is taken into account minimally through a band offset $\epsilon$. The one-dimensional model is studied numerically through the calculation of the charge gap, the Drude weight, and of the pairing correlation function. A comparison with the available information on the nature of the electronic ground state (metallic or superconducting) indicates that the model provides a systematic parametrization of the whole borocarbide family.Comment: 4 figure