Ground states of a frustrated quantum spin chain with long-range interactions

The ground state of a spin-1/2 Heisenberg chain with both frustration and long-range interactions is studied using Lanczos exact diagonalization. The evolution of the well known dimerization transition of the system with short-range frustrated interactions (the J1-J2 chain) is investigated in the presence of additional unfrustrated interactions decaying with distance as 1/r^a. It is shown that the continuous (infinite-order) dimerization transition develops into a first-order transition between a long-range ordered antiferromagnetic state and a state with coexisting dimerization and critical spin correlations at wave-number k=\pi/2. The relevance of the model to real systems is discussed.Comment: 4 pages, 5 figures, final published versio

Ground state projection of quantum spin systems in the valence bond basis

A Monte Carlo method for quantum spin systems is formulated in the basis of valence bond (singlet pair) states. The non-orthogonality of this basis allows for an efficient importance-sampled projection of the ground state out of an arbitrary state. The method provides access to resonating valence-bond physics, enables a direct improved estimator for the singlet-triplet gap, and extends the class of models that can be studied without negative-sign problems. As a demonstration, the valence bond distribution in the ground state of the 2D Heisenberg antiferromagnet is calculated. Generalizations of the method to fermion systems are also discussed.Comment: 4+ pages, accepted for publication in Phys. Rev. Let

Master equation approach to computing RVB bond amplitudes

We describe a "master equation" analysis for the bond amplitudes h(r) of an RVB wavefunction. Starting from any initial guess, h(r) evolves (in a manner dictated by the spin hamiltonian under consideration) toward a steady-state distribution representing an approximation to the true ground state. Unknown transition coefficients in the master equation are treated as variational parameters. We illustrate the method by applying it to the J1-J2 antiferromagnetic Heisenberg model. Without frustration (J2=0), the amplitudes are radially symmetric and fall off as 1/r^3 in the bond length. As the frustration increases, there are precursor signs of columnar or plaquette VBS order: the bonds preferentially align along the axes of the square lattice and weight accrues in the nearest-neighbour bond amplitudes. The Marshall sign rule holds over a large range of couplings, J2/J1 < 0.418. It fails when the r=(2,1) bond amplitude first goes negative, a point also marked by a cusp in the ground state energy. A nonrigourous extrapolation of the staggered magnetic moment (through this point of nonanalyticity) shows it vanishing continuously at a critical value J2/J1 = 0.447. This may be preempted by a first-order transition to a state of broken translational symmetry.Comment: 8 pages, 7 figure

Critical temperature and the transition from quantum to classical order parameter fluctuations in the three-dimensional Heisenberg antiferromagnet

We present results of extensive quantum Monte Carlo simulations of the three-dimensional (3D) S=1/2 Heisenberg antiferromagnet. Finite-size scaling of the spin stiffness and the sublattice magnetization gives the critical temperature Tc/J = 0.946 +/- 0.001. The critical behavior is consistent with the classical 3D Heisenberg universality class, as expected. We discuss the general nature of the transition from quantum mechanical to classical (thermal) order parameter fluctuations at a continuous Tc > 0 phase transition.Comment: 5 pages, Revtex, 4 PostScript figures include

Impurity-induced frustration in correlated oxides

Using the example of Zn-doped La2CuO4, we demonstrate that a spinless impurity doped into a non-frustrated antiferromagnet can induce substantial frustrating interactions among the spins surrounding it. This counterintuitive result is the key to resolving discrepancies between experimental data and earlier theories. Analytic and quantum Monte Carlo studies of the impurity-induced frustration are in a close accord with each other and experiments. The mechanism proposed here should be common to other correlated oxides as well.Comment: 4 pages, updated figures, accepted versio

Magnetic ordering in a doped frustrated spin-Peierls system

Based on a model of a quasi-one dimensional spin-Peierls system doped with non-magnetic impurities, an effective two-dimensional Hamiltonian of randomly distributed S=1/2 spins interacting via long-range pair-wise interaction is studied using a stochastic series expansion quantum Monte Carlo method. The susceptibility shows Curie-like behavior at the lowest temperatures reached although the staggered magnetisation is found to be finite for $T\to 0$. The doping dependance of the corresponding three-dimensional Neel temperature is also computed.Comment: Published version, 4 pages, 5 figure

Properties of Resonating-Valence-Bond Spin Liquids and Critical Dimer Models

We use Monte Carlo simulations to study properties of Anderson's resonating-valence-bond (RVB) spin-liquid state on the square lattice (i.e., the equal superposition of all pairing of spins into nearest-neighbor singlet pairs) and compare with the classical dimer model (CDM). The latter system also corresponds to the ground state of the Rokhsar-Kivelson quantum dimer model at its critical point. We find that although spin-spin correlations decay exponentially in the RVB, four-spin valence-bond-solid (VBS) correlations are critical, qualitatively like the well-known dimer-dimer correlations of the CDM, but decaying more slowly (as $1/r^a$ with $a \approx 1.20$, compared with $a=2$ for the CDM). We also compute the distribution of monomer (defect) pair separations, which decay by a larger exponent in the RVB than in the CDM. We further study both models in their different winding number sectors and evaluate the relative weights of different sectors. Like the CDM, all the observed RVB behaviors can be understood in the framework of a mapping to a "height" model characterized by a gradient-squared stiffness constant $K$. Four independent measurements consistently show a value $K_{RVB} \approx 1.6 K_{CDM}$, with the same kinds of numerical evaluations of $K_{CDM}$ give results in agreement with the rigorously known value $K_{CDM}=\pi/16$. The background of a nonzero winding number gradient $W/L$ introduces spatial anisotropies and an increase in the effective K, both of which can be understood as a consequence of anharmonic terms in the height-model free energy, which are of relevance to the recently proposed scenario of "Cantor deconfinement" in extended quantum dimer models. We also study ensembles in which fourth-neighbor (bipartite) bonds are allowed, at a density controlled by a tunable fugacity, resulting (as expected) in a smooth reduction of K.Comment: 26 pages, 21 figures. v3: final versio

Two-Dimensional Quantum XY Model with Ring Exchange and External Field

We present the zero-temperature phase diagram of a square lattice quantum spin 1/2 XY model with four-site ring exchange in a uniform external magnetic field. Using quantum Monte Carlo techniques, we identify various quantum phase transitions between the XY-order, striped or valence bond solid, staggered Neel antiferromagnet and fully polarized ground states of the model. We find no evidence for a quantum spin liquid phase.Comment: 4 pages, 4 figure

Double-layer Heisenberg antiferromagnet at finite temperature: Brueckner Theory and Quantum Monte Carlo simulations

The double-layer Heisenberg antiferromagnet with intra- and inter-layer couplings $J$ and $J_\perp$ exhibits a zero temperature quantum phase transition between a quantum disordered dimer phase for $g>g_c$ and a Neel phase with long range antiferromagnetic order for $g<g_c$, where $g=J_\perp/J$ and $g_c \approx 2.5$. We consider the behavior of the system at finite temperature for $g \ge g_c$ using two different and complementary approaches; an analytical Brueckner approximation and numerically exact quantum Monte Carlo simulations. We calculate the temperature dependent spin excitation spectrum (including the triplet gap), dynamic and static structure factors, the specific heat, and the uniform magnetic susceptibility. The agreement between the analytical and numerical approaches is excellent. For $T \to 0$ and $g \to g_c$, our analytical results for the specific heat and the magnetic susceptibility coincide with those previously obtained within the nonlinear $\sigma$ model approach for $N\to \infty$. Our quantum Monte Carlo simulations extend to significantly lower temperatures than previously, allowing us to obtain accurate results for the asymptotic quantum critical behavior. We also obtain an improved estimate for the critical coupling: $g_c = 2.525 \pm 0.002$.Comment: 23 pages, 12 figure

Effects of intrabilayer coupling on the magnetic properties of YBa2_2Cu3_3O6_6

A two-layer Heisenberg antiferromagnet is studied as a model of the bilayer cuprate YBa$_2$Cu$_3$O$_6$. Quantum Monte Carlo results are presented for the temperature dependence of the spin correlation length, the static structure factor, the magnetic susceptibility, and the $^{63}$Cu NMR spin-echo decay rate $1/T_{2G}$. As expected, when the ratio $J_2/J_1$ of the intrabilayer and in-plane coupling strengths is small, increasing $J_2$ pushes the system deeper inside the renormalized classical regime. Even for $J_2/J_1$ as small as $0.1$ the correlations are considerably enhanced at temperatures as high as $T/J_1 \approx 0.4-0.5$. This has a significant effect on $1/T_{2G}$, and it is suggested that measurements of this quantity at high temperatures can reveal the strength of the intrabilayer coupling in YBa$_2$Cu$_3$O$_6$.Comment: 10 pages (Revtex) + 5 uuencoded ps figures. To appear in Phys. Rev. B, Rapid Com