503 research outputs found
Optimization of quantum Monte Carlo wave functions by energy minimization
We study three wave function optimization methods based on energy
minimization in a variational Monte Carlo framework: the Newton, linear and
perturbative methods. In the Newton method, the parameter variations are
calculated from the energy gradient and Hessian, using a reduced variance
statistical estimator for the latter. In the linear method, the parameter
variations are found by diagonalizing a non-symmetric estimator of the
Hamiltonian matrix in the space spanned by the wave function and its
derivatives with respect to the parameters, making use of a strong
zero-variance principle. In the less computationally expensive perturbative
method, the parameter variations are calculated by approximately solving the
generalized eigenvalue equation of the linear method by a nonorthogonal
perturbation theory. These general methods are illustrated here by the
optimization of wave functions consisting of a Jastrow factor multiplied by an
expansion in configuration state functions (CSFs) for the C molecule,
including both valence and core electrons in the calculation. The Newton and
linear methods are very efficient for the optimization of the Jastrow, CSF and
orbital parameters. The perturbative method is a good alternative for the
optimization of just the CSF and orbital parameters. Although the optimization
is performed at the variational Monte Carlo level, we observe for the C
molecule studied here, and for other systems we have studied, that as more
parameters in the trial wave functions are optimized, the diffusion Monte Carlo
total energy improves monotonically, implying that the nodal hypersurface also
improves monotonically.Comment: 18 pages, 8 figures, final versio
Phase Transitions with Discrete Symmetry Breaking in Antiferromagnetic Heisenberg Models on a Triangular Lattice
We study phase transition behavior of the Heisenberg model on a distorted
triangular lattice with competing interactions. The ground-state phase diagram
indicates that underlying symmetry can be changed by tuning parameters. We
focus on two cases in which a phase transition with discrete symmetry breaking
occurs. The first is that the order parameter space is SO(3). In
this case, a first-order phase transition, with threefold symmetry breaking,
occurs. The second has the order parameter space SO(3). In this
case, a second-order phase transition occurs with twofold symmetry breaking. To
investigate finite-temperature properties of these phase transitions from a
microscopic viewpoint, we introduce a method to make the connection between
continuous frustrated spin systems and the Potts model with invisible states.Comment: 5 pages, 2 figure
Low-energy properties of two-dimensional quantum triangular antiferromagnets: Non-perturbative renormalization group approach
We explore low temperature properties of quantum triangular Heisenberg
antiferromagnets in two dimension in the vicinity of the quantum phase
transition at zero temperature. Using the effective field theory described by
the matrix Ginzburg-Landau-Wilson model and the
non-perturbative renormalization group method, we clarify how quantum and
thermal fluctuations affect long-wavelength behaviors in the parameter region
where the systems exhibit a fluctuation-driven first order transition to a
long-range ordered state. We show that at finite temperatures the crossover
from a quantum theory to a renormalized two-dimensional classical
nonlinear sigma model region appears, and in this crossover region, massless
fluctuation modes with linear dispersion a la spin waves govern low-energy
physics. Our results are in good agreement with the recent experimental
observations for the two-dimensional triangular Heisenberg spin system,
NiGaS.Comment: 14 pages,7 figures, version accepted for publication in Physical
Review
Kondo lattice on the edge of a two-dimensional topological insulator
We revisit the problem of a single quantum impurity on the edge of a
two-dimensional time-reversal invariant topological insulator and show that the
zero temperature phase diagram contains a large local moment region for
antiferromagnetic Kondo coupling which was missed by previous poor man's
scaling treatments. The combination of an exact solution at the so-called
decoupling point and a renormalization group analysis \`a la
Anderson-Yuval-Hamann allows us to access the regime of strong
electron-electron interactions on the edge and strong Kondo coupling. We apply
similar methods to the problem of a regular one-dimensional array of quantum
impurities interacting with the edge liquid. When the edge electrons are at
half-filling with respect to the impurity lattice, the system remains gapless
unless the Luttinger parameter of the edge is less than 1/2, in which case
two-particle backscattering effects drive the system to a gapped phase with
long-range Ising antiferromagnetic order. This is in marked contrast with the
gapped disordered ground state of the ordinary half-filled one-dimensional
Kondo lattice.Comment: 18 pages, 3 figures; fixed typos, updated reference
Full counting statistics of spin transfer through the Kondo dot
We calculate the spin current distribution function for a Kondo dot in two
different regimes. In the exactly solvable Toulouse limit the linear response,
zero temperature statistics of the spin transfer is trinomial, such that all
the odd moments vanish and the even moments follow a binomial distribution. On
the contrary, the corresponding spin-resolved distribution turns out to be
binomial. The combined spin and charge statistics is also determined. In
particular, we find that in the case of a finite magnetic field or an
asymmetric junction the spin and charge measurements become statistically
dependent. Furthermore, we analyzed the spin counting statistics of a generic
Kondo dot at and around the strong-coupling fixed point (the unitary limit).
Comparing these results with the Toulouse limit calculation we determine which
features of the latter are generic and which ones are artifacts of the spin
symmetry breaking.Comment: 9 pages, 3 eps figure
The Universlity Class of Monopole Condensation in Non-Compact, Quenched Lattice QED
Finite size scaling studies of monopole condensation in noncompact quenched
lattice indicate an authentic second order phase transition lying in the
universality class of four dimensional percolation. Since the upper critical
dimension of percolation is six, the measured critical indices are far from
mean-field values. We propose a simple set of ratios as the exact critical
indices for this transition. The implication of these results for critical
points in Abelian gauge theories are discussed.Comment: ILL-(TH)-92-6, CERN-TH.6515/92, 10 pages, no figures available as PS
fil
Full optimization of Jastrow-Slater wave functions with application to the first-row atoms and homonuclear diatomic molecules
We pursue the development and application of the recently-introduced linear
optimization method for determining the optimal linear and nonlinear parameters
of Jastrow-Slater wave functions in a variational Monte Carlo framework. In
this approach, the optimal parameters are found iteratively by diagonalizing
the Hamiltonian matrix in the space spanned by the wave function and its
first-order derivatives, making use of a strong zero-variance principle. We
extend the method to optimize the exponents of the basis functions,
simultaneously with all the other parameters, namely the Jastrow, configuration
state function and orbital parameters. We show that the linear optimization
method can be thought of as a so-called augmented Hessian approach, which helps
explain the robustness of the method and permits us to extend it to minimize a
linear combination of the energy and the energy variance. We apply the linear
optimization method to obtain the complete ground-state potential energy curve
of the C_2 molecule up to the dissociation limit, and discuss size consistency
and broken spin-symmetry issues in quantum Monte Carlo calculations. We perform
calculations of the first-row atoms and homonuclear diatomic molecules with
fully optimized Jastrow-Slater wave functions, and we demonstrate that
molecular well depths can be obtained with near chemical accuracy quite
systematically at the diffusion Monte Carlo level for these systems.Comment: 15 pages, 3 figures, to appear in Journal of Chemical Physic
The sawtooth chain: From Heisenberg spins to Hubbard electrons
We report on recent studies of the spin-half Heisenberg and the Hubbard model
on the sawtooth chain. For both models we construct a class of exact
eigenstates which are localized due to the frustrating geometry of the lattice
for a certain relation of the exchange (hopping) integrals. Although these
eigenstates differ in details for the two models because of the different
statistics, they share some characteristic features. The localized eigenstates
are highly degenerate and become ground states in high magnetic fields
(Heisenberg model) or at certain electron fillings (Hubbard model),
respectively. They may dominate the low-temperature thermodynamics and lead to
an extra low-temperature maximum in the specific heat. The ground-state
degeneracy can be calculated exactly by a mapping of the manifold of localized
ground states onto a classical hard-dimer problem, and explicit expressions for
thermodynamic quantities can be derived which are valid at low temperatures
near the saturation field for the Heisenberg model or around a certain value of
the chemical potential for the Hubbard model, respectively.Comment: 16 pages, 6 figure, the paper is based on an invited talk on the XXXI
International Workshop on Condensed Matter Theories, Bangkok, Dec 2007;
notation of x-axis in Fig.6 corrected, references update
Charge Order in the Falicov-Kimball Model
We examine the spinless one-dimensional Falicov-Kimball model (FKM) below
half-filling, addressing both the binary alloy and valence transition
interpretations of the model. Using a non-perturbative technique, we derive an
effective Hamiltonian for the occupation of the localized orbitals, providing a
comprehensive description of charge order in the FKM. In particular, we uncover
the contradictory ordering roles of the forward-scattering and backscattering
itinerant electrons: the latter are responsible for the crystalline phases,
while the former produces the phase separation. We find an Ising model
describes the transition between the phase separated state and the crystalline
phases; for weak-coupling we present the critical line equation, finding
excellent agreement with numerical results. We consider several extensions of
the FKM that preserve the classical nature of the localized states. We also
investigate a parallel between the FKM and the Kondo lattice model, suggesting
a close relationship based upon the similar orthogonality catastrophe physics
of the associated single-impurity models.Comment: 39 pages, 6 figure
Cosmology in a String-Dominated Universe
The string-dominated universe locally resembles an open universe, and fits
dynamical measures of power spectra, cluster abundances, redshift distortions,
lensing constraints, luminosity and angular diameter distance relations and
microwave background observations. We show examples of networks which might
give rise to recent string-domination without requiring any fine-tuned
parameters. We discuss how future observations can distinguish this model from
other cosmologies.Comment: 17 pages including 4 figures, of which one is in colo
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