Numerical Studies of the two-leg Hubbard ladder

The Hubbard model on a two-leg ladder structure has been studied by a combination of series expansions at T=0 and the density-matrix renormalization group. We report results for the ground state energy $E_0$ and spin-gap $\Delta_s$ at half-filling, as well as dispersion curves for one and two-hole excitations. For small $U$ both $E_0$ and $\Delta_s$ show a dramatic drop near $t/t_{\perp}\sim 0.5$, which becomes more gradual for larger $U$. This represents a crossover from a "band insulator" phase to a strongly correlated spin liquid. The lowest-lying two-hole state rapidly becomes strongly bound as $t/t_{\perp}$ increases, indicating the possibility that phase separation may occur. The various features are collected in a "phase diagram" for the model.Comment: 10 figures, revte

Order and disorder in the triangular-lattice t-J-V model at 2/3 electron density

Motivated by the recent discovery of superconductivity in Na$_x$CoO$_2\cdot y$H$_2$O, we use series expansion methods and cluster mean-field theory to study spontaneous charge order, Neel order, ferromagnetic order, dimer order and phase-separation in the triangular-lattice t-J-V model at 2/3 electron density. We find that for t<0, the charge ordered state, with electrons preferentially occupying a honeycomb lattice, is very robust. Quite surprisingly, hopping to the third sublattice can even enhance Neel order. At large negative t and small V, the Nagaoka ferromagnetic state is obtained. For large positive t, charge and Neel order vanish below a critical V, giving rise to an itinerant antiferromagnetically correlated state.Comment: 4 pages, 5 figure

Spectral weight contributions of many-particle bound states and continuum

Cluster expansion methods are developed for calculating the spectral weight contributions of multiparticle excitations - continuum and bound states - to high orders. A complete 11th order calculation is carried out for the alternating Heisenberg chain. For $\lambda=0.27$, relevant to the material $Cu(NO_3)_2.2.5D_2O$, we present detailed spectral weights for the two-triplet continuum and all bound states. We also examine variation of the relative weights of one and two-particle states with bond alternation from the dimerized to the uniform chain limit.Comment: 4 pages, 5 figures, revte

Anomalous Excitation Spectra of Frustrated Quantum Antiferromagnets

We use series expansions to study the excitation spectra of spin-1/2 antiferromagnets on anisotropic triangular lattices. For the isotropic triangular lattice model (TLM) the high-energy spectra show several anomalous features that differ strongly from linear spin-wave theory (LSWT). Even in the Neel phase, the deviations from LSWT increase sharply with frustration, leading to roton-like minima at special wavevectors. We argue that these results can be interpreted naturally in a spinon language, and provide an explanation for the previously observed anomalous finite-temperature properties of the TLM. In the coupled-chains limit, quantum renormalizations strongly enhance the one-dimensionality of the spectra, in agreement with experiments on Cs_2CuCl_4.Comment: 4 pages, 5 figures. New Fig. 3 with higher-order series data, paper shortened, references updated, one added (Ref. 28), minor changes otherwise. Published versio

Persistent superfluid phase in a three-dimensional quantum XY model with ring exchange

We present quantum Monte Carlo simulation results on a quantum S=1/2 XY model with ring exchange (the J-K model) on a three-dimensional simple cubic lattice. We first characterize the ground state properties of the pure XY model, obtaining estimations for the energy, spin stiffness and spin susceptibility at T=0 in the superfluid phase. With the ring exchange, we then present simulation data on small lattices which suggests that the superfluid phase persists to very large values of the ring exchange K, without signatures of a phase transition. We comment on the consequences of this result for the search for various exotic phases in three dimensions.Comment: 4 pages, 4 figure

Further Series Studies of the Spin-1/2 Heisenberg Antiferromagnet at T=0: Magnon Dispersion and Structure Factors

We have extended our previous series studies of quantum antiferromagnets at zero temperature by computing the one-magnon dispersion curves and various structure factors for the linear chain, square and simple cubic lattices. Many of these results are new; others are a substantial extension of previous work. These results are directly comparable with neutron scattering experiments and we make such comparisons where possible.Comment: 15 pages, 12 figures, revised versio

Competing Spin-Gap Phases in a Frustrated Quantum Spin System in Two Dimensions

We investigate quantum phase transitions among the spin-gap phases and the magnetically ordered phases in a two-dimensional frustrated antiferromagnetic spin system, which interpolates several important models such as the orthogonal-dimer model as well as the model on the 1/5-depleted square lattice. By computing the ground state energy, the staggered susceptibility and the spin gap by means of the series expansion method, we determine the ground-state phase diagram and discuss the role of geometrical frustration. In particular, it is found that a RVB-type spin-gap phase proposed recently for the orthogonal-dimer system is adiabatically connected to the plaquette phase known for the 1/5-depleted square-lattice model.Comment: 6 pages, to appear in JPSJ 70 (2001

Excitation spectra of the spin-1/2 triangular-lattice Heisenberg antiferromagnet

We use series expansion methods to calculate the dispersion relation of the one-magnon excitations for the spin-1/2 triangular-lattice nearest-neighbor Heisenberg antiferromagnet above a three-sublattice ordered ground state. Several striking features are observed compared to the classical (large-S) spin-wave spectra. Whereas at low energies the dispersion is only weakly renormalized by quantum fluctuations, significant anomalies are observed at high energies. In particular, we find roton-like minima at special wave-vectors and strong downward renormalization in large parts of the Brillouin zone, leading to very flat or dispersionless modes. We present detailed comparison of our calculated excitation energies in the Brillouin zone with the spin-wave dispersion to order 1/S calculated recently by Starykh, Chubukov, and Abanov [cond-mat/0608002]. We find many common features but also some quantitative and qualitative differences. We show that at temperatures as low as 0.1J the thermally excited rotons make a significant contribution to the entropy. Consequently, unlike for the square lattice model, a non-linear sigma model description of the finite-temperature properties is only applicable at extremely low temperatures.Comment: 14 pages, 11 figure