arXiv subjects

Anders W. Sandvik

Publications and source records attributed to Anders W. Sandvik.

At least 127 records · Page 7Linked to original sources

arXiv2007

Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions

Using ground-state projector quantum Monte Carlo simulations in the valence bond basis, it is demonstrated that non-frustrating four-spin interactions can destroy the Neel order of the two-dimensional S=1/2 Heisenberg antiferromagnet and drive it into a valence-bond solid (VBS) phase. Results for spin and dimer correlations are consistent with a single continuous transition, and all data exhibit finite-size scaling with a single set of exponents; z=1, nu=0.78 +/- 0.03, and eta=0.26 +/- 0.03. The unusually large eta and an emergent U(1) symmetry, detected using VBS order parameter histograms, provide strong evidence for a deconfined quantum critical point.

cond-mat.str-el↗

arXiv2007

Emergence of U(1) symmetry in the 3D XY model with Zq anisotropy

We study the three-dimensional XY model with a Z_q anisotropic term. At temperatures T < Tc this dangerously irrelevant perturbation is relevant only above a length scale Lambda, which diverges as a power of the correlation length; Lambda ~ xi^a_q. Below Lambda the order parameter is U(1) symmetric. We derive the full scaling function controlling the emergence of U(1) symmetry and use Monte Carlo results to extract the exponent a_q for q=4,...,8. We find that a_q = a_4 (q/4)^2, with a_4 only marginally larger than 1. We discuss these results in the context of U(1) symmetry at "deconfined" quantum critical points separating antiferromagnetic and valence-bond-solid states in quantum spin systems.

cond-mat.str-el↗

arXiv2007

Impurity induced spin texture in quantum critical 2D antiferromagnets

We describe the uniform and staggered magnetization distributions around a vacancy in a quantum critical two-dimensional S=1/2 antiferromagnet. The distributions are delocalized across the entire sample with a universal functional form arising from an uncompensated Berry phase. The numerical results, obtained using quantum Monte Carlo simulations of the Heisenberg model on bilayer lattices with up to approximately 10^5 spins, are in good agreement with the proposed scaling structure. We determine the exponent eta'=0.40 +/- 0.02, which governs both the staggered and uniform magnetic structure away from the impurity and also controls the impurity spin dynamics.

cond-mat.str-el↗

arXiv2006

Valence bond solid phases in a cubic antiferromagnet

We report on a valence bond projector Monte Carlo simulation of the cubic lattice quantum Heisenberg model with additional higher-order exchange interactions in each unit cell. The model supports two different valence bond solid ground states. In one of these states, the dimer pattern is a three-dimensional analogue of the columnar pattern familiar from two dimensions. In the other, the dimers are regularly arranged along the four main diagonals in 1/8 of the unit cells. The phases are separated from one other and from a Neel phase by strongly first order boundaries. Our results strengthen the case for exotic transitions in two dimensions, where no discontinuities have been detected at the Heisenberg Neel-VBS transition driven by four-spin plaquet interactions.

cond-mat.str-el↗

arXiv2006

Low-energy dynamics of the two-dimensional S=1/2 Heisenberg antiferromagnet on percolating clusters

We investigate the quantum dynamics of site diluted S=1/2 Heisenberg antiferromagnetic clusters at the percolation threshold. We use Lanczos diagonalization to calculate the lowest excitation gap Delta and, to reach larger sizes, study an upper bound for Delta obtained from sum rules involving the staggered structure factor and susceptibility, which we evaluate by quantum Monte Carlo simulations. Scaling the gap distribution with the cluster length L, Delta sim 1/L^z, we obtain a dynamic exponent z approximate 2D_f, where D_f=91/48 is the fractal dimensionality of the percolating cluster. This is in contrast to previous expectations of z=D_f. We argue that the low-energy excitations are due to weakly coupled effective moments formed due to local imbalance in sublattice occupation.

cond-mat.str-el↗

arXiv2005

High-precision finite-size scaling analysis of the quantum-critical point of S=1/2 Heisenberg antiferromagnetic bilayers

We use quantum Monte Carlo (stochastic series expansion) and finite-size scaling to study the quantum critical points of two S=1/2 Heisenberg antiferromagnets in two dimensions: a bilayer and a Kondo-lattice-like system (incomplete bilayer), each with intra- and inter-plane couplings J and J_perp. We discuss the ground-state finite-size scaling properties of three different quantities--the Binder moment ratio, the spin stiffness, and the long-wavelength magnetic susceptibility--which we use to extract the critical value of the coupling ratio g=J_perp/J. The individual estimates of g_c are consistent provided that subleading finite-size corrections are properly taken into account. In the case of the complete bilayer, the Binder ratio leads to the most precise estimate of the critical coupling, although the subleading finite-size corrections to the stiffness are considerably smaller. For the incomplete bilayer, the subleading corrections to the stiffness are extremely small, and this quantity then gives the best estimate of the critical point. Contrary to predictions, we do not find a universal prefactor of the 1/L spin stiffness scaling at the critical point, whereas the Binder ratio is consistent with a universal value. Our results for the critical coupling ratios are g_c=2.52181(3) (full bilayer) and g_c=1.38882(2) (incomplete bilayer), which represent improvements of two orders of magnitude relative to the previous best estimates. For the correlation length exponent we obtain nu = 0.7106(9), consistent with the expected 3D Heisenberg universality class.

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arXiv2005

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.

cond-mat.str-el↗

arXiv2005

Site dilution of quantum spins in the honeycomb lattice

We discuss the effect of site dilution on both the magnetization and the density of states of quantum spins in the honeycomb lattice, described by the antiferromagnetic Heisenberg spin-S model. For this purpose a real-space Bogoliubov-Valatin transformation is used. In this work we show that for the S>1/2 the system can be analyzed in terms of linear spin wave theory. For spin S=1/2, however, the linear spin wave approximation breaks down. In this case, we have studied the effect of dilution on the staggered magnetization using the Stochastic Series Expansion Monte Carlo method. Two main results are to be stressed from the Monte Carlo method: (i) a better value for the staggered magnetization of the undiluted system, m=0.2677(6); (ii) a finite value of the staggered magnetization of the percolating cluster at the classical percolation threshold, showing that there is no quantum critical transition driven by dilution in the Heisenberg model. In the solution of the problem using linear the spin wave method we pay special attention to the presence of zero energy modes. Using a combination of linear spin wave analysis and the recursion method we were able to obtain the thermodynamic limit behavior of the density of states for both the square and the honeycomb lattices. We have used both the staggered magnetization and the density of states to analyze neutron scattering experiments and Neel temperature measurements on quasi-two- -dimensional honeycomb systems. Our results are in quantitative agreement with experimental results on Mn_pZn_{1-p}PS_3 and on the Ba(Ni_pMg_{1-p})_2V_2O_8.

cond-mat.str-el↗

arXiv2005

Deconfinement and criticality in extended two-dimensional dimer models

A square-lattice hard-core dimer model with links extending beyond nearest-neighbors is studied using a directed-loop Monte Carlo method. An arbitrarily small fraction of next-nearest-neighbor dimers is found to cause deconfinement, whereas a critical state with $r^{-2}$ distance dependence of the dimer-dimer correlations persists in the presence of longer dimers preserving the bipartite graph structure. However, the critical confinement exponent governing the correlation of two test monomers is non-universal. Implications for resonating-valence-bond states are discussed.

cond-mat.str-el↗

arXiv2005

Data collapse in the critical region using finite-size scaling with subleading corrections

We propose a treatment of the subleading corrections to finite-size scaling that preserves the notion of data collapse. This approach is used to extend and improve the usual Binder cumulant analysis. As a demonstration, we present results for the two- and three-dimensional classical Ising models and the two-dimensional, double-layer quantum antiferromagnet.

cond-mat.stat-mech↗

arXiv2004

Stochastic series expansion algorithm for the S=1/2 XY model with four-site ring exchange

We describe a stochastic series expansion (SSE) quantum Monte Carlo method for a two-dimensional S=1/2 XY-model (or, equivalently, hard-core bosons at half-filling) which in addition to the standard pair interaction J includes a four-particle term K that flips spins on a square plaquette. The model has three ordered ground state phases; for K/J<8 it has long-range xy spin order (superfluid bosons), for K/J>15 it has staggered spin order in the z direction (charge-density-wave), and between these phases it is in a state with columnar order in the bond and plaquette energy densities. We discuss an implementation of directed-loop updates for the SSE simulations of this model and also introduce a "multi-branch" cluster update which significantly reduces the autocorrelation times for large K/J. In addition to the pure J-K model, which in the z basis has only off-diagonal terms, we also discuss modifications of the algorithm needed when various diagonal interactions are included.

cond-mat.stat-mech↗

arXiv2004

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.

cond-mat.str-el↗

arXiv2004

Impurity effects at finite temperature in the two-dimensional S=1/2 Heisenberg antiferromagnet

We discuss effects of various impurities on the magnetic susceptibility and the specific heat of the quantum S=1/2 Heisenberg antiferromagnet on a two-dimensional square lattice. For impurities with spin S_i > 0 (here S_i=1/2 in the case of a vacancy or an added spin, and S_i=1 for a spin coupled ferromagnetically to its neighbors), our quantum Monte Carlo simulations confirm a classical-like Curie susceptibility contribution S_i^2/4T, which originates from an alignment of the impurity spin with the local Néel order. In addition, we find a logarithmically divergent contribution, which we attribute to fluctuations transverse to the local Néel vector. We also study frustrated and nonfrustrated bond impurities with S_i=0. For a simple intuitive picture of the impurity problem, we discuss an effective few-spin model that can distinguish between the different impurities and reproduces the leading-order simulation data over a wide temperature range.

cond-mat.str-el↗

arXiv2003

Crossover effects in the random exchange spin-1/2 antiferromagnetic chain

The random antiferromagnetic spin-1/2 XX and XXZ chain is studied numerically for varying strength of the disorder, using exact diagonalization and stochastic series expansion methods. The spin-spin correlation function as well as the stiffness display a clear crossover from the pure behavior (no disorder) to the infinite randomness fixed point or random singlet behavior predicted by the the real space renormalization group. The crossover length scale is shown to diverge as $ξ\sim{\mathcal D}^{-γ}$, where ${\mathcal D}$ is the variance of the random bonds. Our estimates for the exponent $γ$ agrees well within the error bars with the one for the localization length exponent emerging within an analytical bosonization calculation. Exact diagonalization and stochastic series expansion results for the string correlation function are also presented.

cond-mat.str-el↗

arXiv2003

Susceptibility of the 2D S=1/2 Heisenberg antiferromagnet with an impurity

We use a quantum Monte Carlo method (stochastic series expansion) to study the effects of a magnetic or nonmagnetic impurity on the magnetic susceptibility of the two-dimensional Heisenberg antiferromagnet. At low temperatures, we find a log-divergent contribution to the transverse susceptibility. We also introduce an effective few-spin model that can quantitatively capture the differences between magnetic and nonmagnetic impurities at high and intermediate temperatures.

cond-mat.str-el↗

arXiv2003

The directed-loop algorithm

The directed-loop scheme is a framework for generalized loop-type updates in quantum Monte Carlo, applicable both to world-line and stochastic series expansion methods. Here, the directed-loop equations, the solution of which gives the probabilities of the various loop-building steps, are discussed in the context of the anisotropic $S=1/2$ Heisenberg model in a uniform magnetic field. This example shows how the directed-loop concept emerges as a natural generalization of the conventional loop algorithm, where the loops are selfavoiding, to cases where selfintersection must be allowed in order to satisfy detailed balance.

cond-mat.str-el↗

arXiv2003

Specific heat of quasi-2D antiferromagnetic Heisenberg models with varying inter-planar couplings

We have used the stochastic series expansion (SSE) quantum Monte Carlo (QMC) method to study the three-dimensional (3D) antiferromagnetic Heisenberg model on cubic lattices with in-plane coupling J and varying inter-plane coupling J_perp < J. The specific heat curves exhibit a 3D ordering peak as well as a broad maximum arising from short-range 2D order. For J_perp << J, there is a clear separation of the two peaks. In the simulations, the contributions to the total specific heat from the ordering across and within the layers can be separated, and this enables us to study in detail the 3D peak around T_c (which otherwise typically is dominated by statistical noise). We find that the peak height decreases with decreasing J_perp, becoming nearly linear below J_perp = 0.2J. The relevance of these results to the lack of observed specific heat anomaly at the ordering transition of some quasi-2D antiferromagnets is discussed.

cond-mat.str-el↗

arXiv2003

Stochastic series expansion method for quantum Ising models with arbitrary interactions

A quantum Monte Carlo algorithm for the transverse Ising model with arbitrary short- or long-range interactions is presented. The algorithm is based on sampling the diagonal matrix elements of the power series expansion of the density matrix (stochastic series expansion), and avoids the interaction summations necessary in conventional methods. In the case of long-range interactions, the scaling of the computation time with the system size N is therefore reduced from N^2 to Nln(N). The method is tested on a one-dimensional ferromagnet in a transverse field, with interactions decaying as 1/r^2.

cond-mat.stat-mech↗