Concurrence in the two dimensional XXZ- and transverse field Ising-models

Numerical results for the concurrence and bounds on the localizable entanglement are obtained for the square lattice spin-1/2 XXZ-model and the transverse field Ising-model at low temperatures using quantum Monte Carlo.Comment: 9 pages, 4 figures, elsar

Dynamical structure factor of magnetic Bloch oscillations at finite temperatures

Domain-walls in one-dimensional Ising ferromagnets can undergo Bloch oscillations when subjected to a skew magnetic field. Such oscillations imply finite temperature non-dispersive low-frequency peaks in the dynamical structure factor which can be probed in neutron scattering. We study in detail the spectral weight of these peaks. Using an analytical approach based on an approximate treatment of a gas of spin-cluster excitations we give an explicit expression for the momentum- and temperature-dependence of the spectral weights. Generally the spectral weights increase with temperature and approaches the same order of magnitude as the spin-wave spectral weights at high temperatures. We compare the analytical expression to numerical exact diagonalizations and find that it can, without any adjustable parameters, account for the temperature and momentum-transfer dependence of the numerically obtained spectral weights in the parameter regime where the ratio of magnetic fields $h_x/h_z \ll 1$ and the temperature is $h_x < T <\sim J_z/2$. We also carry out numerical calculations pertinent to the material CoNb$_2$O$_6$, and find qualitatively similar results.Comment: 8 pages, 5 figure

Monte Carlo simulation of boson lattices

Boson lattices are theoretically well described by the Hubbard model. The basic model and its variants can be effectively simulated using Monte Carlo techniques. We describe two newly developed approaches, the Stochastic Series Expansion (SSE) with directed loop updates and continuous--time Diffusion Monte Carlo (CTDMC). SSE is a formulation of the finite temperature partition function as a stochastic sampling over product terms. Directed loops is a general framework to implement this stochastic sampling in a non--local fashion while maintaining detailed balance. CTDMC is well suited to finding exact ground--state properties, applicable to any lattice model not suffering from the sign problem; for a lattice model the evolution of the wave function can be performed in continuous time without any time discretization error. Both the directed loop algorithm and the CTDMC are important recent advances in development of computational methods. Here we present results for a Hubbard model for anti--ferromagnetic spin--1 bosons in one dimensions, and show evidence for a dimerized ground state in the lowest Mott lobe.Comment: 3 pages, 5 figur

Numerical evidence for unstable magnons at high fields in the Heisenberg antiferromagnet on the square lattice

We find evidence for decaying magnons at strong magnetic field in the square lattice spin-1/2 Heisenberg antiferromagnet. The results are obtained using Quantum Monte Carlo simulations combined with a Bayesian inference technique to obtain dynamics and are consistent with predictions from spin wave theory.Comment: 4 pages, 5 figure

Random walks near Rokhsar-Kivelson points

There is a class of quantum Hamiltonians known as Rokhsar-Kivelson(RK)-Hamiltonians for which static ground state properties can be obtained by evaluating thermal expectation values for classical models. The ground state of an RK-Hamiltonian is known explicitly, and its dynamical properties can be obtained by performing a classical Monte Carlo simulation. We discuss the details of a Diffusion Monte Carlo method that is a good tool for studying statics and dynamics of perturbed RK-Hamiltonians without time discretization errors. As a general result we point out that the relation between the quantum dynamics and classical Monte Carlo simulations for RK-Hamiltonians follows from the known fact that the imaginary-time evolution operator that describes optimal importance sampling, in which the exact ground state is used as guiding function, is Markovian. Thus quantum dynamics can be studied by a classical Monte Carlo simulation for any Hamiltonian that is free of the sign problem provided its ground state is known explicitly.Comment: 12 pages, 9 figures, RevTe

Nematic Bond Theory of Heisenberg Helimagnets

We study classical two-dimensional frustrated Heisenberg models with generically incommensurate groundstates. A new theory for the spin-nematic "order by disorder" transition is developed based on the self-consistent determination of the effective exchange coupling bonds. In our approach, fluctuations of the constraint field imposing conservation of the local magnetic moment drive nematicity at low temperatures. The critical temperature is found to be highly sensitive to the peak helimagnetic wavevector, and vanishes continuously when approaching rotation symmetric Lifshitz points. Transitions between symmetry distinct nematic orders may occur by tuning the exchange parameters, leading to lines of bicritical points.Comment: 4 pages, 4 figure

Interplay between Magnetic and Vestigial Nematic Orders in the Layered J1J_1-J2J_2 Classical Heisenberg Model

We study the layered $J_1$-$J_2$ classical Heisenberg model on the square lattice using a self-consistent bond theory. We derive the phase diagram for fixed $J_1$ as a function of temperature $T$, $J_2$ and interplane coupling $J_z$. Broad regions of (anti)ferromagnetic and stripe order are found, and are separated by a first-order transition near $J_2\approx 0.5$ (in units of $|J_1|$). Within the stripe phase the magnetic and vestigial nematic transitions occur simultaneously in first-order fashion for strong $J_z$. For weaker $J_z$ there is in addition, for $J_2^*<J_2 < J_2^{**}$, an intermediate regime of split transitions implying a finite temperature region with nematic order but no long-range stripe magnetic order. In this split regime, the order of the transitions depends sensitively on the deviation from $J_2^*$ and $J_2^{**}$, with split second-order transitions predominating for $J_2^* \ll J_2 \ll J_2^{**}$. We find that the value of $J_2^*$ depends weakly on the interplane coupling and is just slightly larger than $0.5$ for $|J_z| \lesssim 0.01$. In contrast the value of $J_2^{**}$ increases quickly from $J_2^*$ at $|J_z| \lesssim 0.01$ as the interplane coupling is further reduced. In addition, the magnetic correlation length is shown to directly depend on the nematic order parameter and thus exhibits a sharp increase (or jump) upon entering the nematic phase. Our results are broadly consistent with predictions based on itinerant electron models of the iron-based superconductors in the normal-state, and thus help substantiate a classical spin framework for providing a phenomenological description of their magnetic properties.Comment: 13 pages, 20 figure

Continuous-time Diffusion Monte Carlo and the Quantum Dimer Model

A continuous-time formulation of the Diffusion Monte Carlo method for lattice models is presented. In its simplest version, without the explicit use of trial wavefunctions for importance sampling, the method is an excellent tool for investigating quantum lattice models in parameter regions close to generalized Rokhsar-Kivelson points. This is illustrated by showing results for the quantum dimer model on both triangular and square lattices. The potential energy of two test monomers as a function of their separation is computed at zero temperature. The existence of deconfined monomers in the triangular lattice is confirmed. The method allows also the study of dynamic monomers. A finite fraction of dynamic monomers is found to destroy the confined phase on the square lattice when the hopping parameter increases beyond a finite critical value. The phase boundary between the monomer confined and deconfined phases is obtained.Comment: 4 pages, 4 figures, revtex; Added a figure showing the confinement/deconfinement phase boundary for the doped quantum dimer mode

Spin wave calculation of the field-dependent magnetization pattern around an impurity in Heisenberg antiferromagnets

We consider the magnetic-field dependent spatial magnetization pattern around a general impurity embedded in a Heisenberg antiferromagnet using both an analytical and a numerical spin wave approach. The results are compared to quantum Monte Carlo simulations. The decay of the magnetization pattern away from the impurity follows a universal form which reflects the properties of the pure antiferromagnetic Heisenberg model. Only the overall magnitude of the induced magnetization depends also on the size of the impurity spin and the impurity coupling.Comment: 11 pages, 11 figure