Fernando Falceto

Modified Ehrenfest Formalism for Efficient Large-Scale ab initio Molecular Dynamics.

We present in detail the recently derived ab initio molecular dynamics (AIMD) formalism [Alonso et al. Phys. Rev. Lett. 2008, 101, 096403], which due to its numerical properties, is ideal for simulating the dynamics of systems containing thousands of atoms. A major drawback of traditional AIMD methods is the necessity to enforce the orthogonalization of the wave functions, which can become the bottleneck for very large systems. Alternatively, one can handle the electron-ion dynamics within the Ehrenfest scheme where no explicit orthogonalization is necessary, however the time step is too small for practical applications. Here we preserve the desirable properties of Ehrenfest in a new scheme that allows for a considerable increase of the time step while keeping the system close to the Born-Oppenheimer surface. We show that the automatically enforced orthogonalization is of fundamental importance for large systems because not only it improves the scaling of the approach with the system size but it also allows for an additional very efficient parallelization level. In this work, we provide the formal details of the new method, describe its implementation, and present some applications to some test systems. Comparisons with the widely used Car-Parrinello molecular dynamics method are made, showing that the new approach is advantageous above a certain number of atoms in the system. The method is not tied to a particular wave function representation, making it suitable for inclusion in any AIMD software package.

Consistency of the regularization of gauge theories by high covariant derivatives

We show that regularization of gauge theories by higher covariant derivatives and gauge-invariant Pauli-Villars regulators is a consistent method if the Pauli-Villars vector fields are considered in a covariant {alpha} gauge with {alpha}{ne}0 and a given auxiliary preregularization is introduced in order to uniquely define the regularization. The limit {alpha}{r_arrow}0 in the regulating Pauli-Villars fields is pathological and the original Slavnov proposal in the covariant Landau gauge is not correct because of the appearance of massless modes in the regulators which do not decouple when the ultraviolet regulator is removed. In such a case the method does not correspond to the regularization of a pure gauge theory but that of a gauge theory in interaction with massless ghost fields. However, a minor modification of the Slavnov method provides a consistent regularization even for such a case. The regularization that we introduce also solves the problem of overlapping divergences in a way similar to geometric regularization and yields the standard values of the {beta} and {gamma} functions of the renormalization group equations. {copyright} {ital 1996 The American Physical Society.}

Poisson reduction and branes in Poisson-Sigma models

We analyse the problem of boundary conditions for the Poisson–Sigma model and extend previous results showing that non-coisotropic branes are allowed. We discuss the canonical reduction of a Poisson structure to a submanifold, leading to a Poisson algebra that generalizes Dirac’s construction. The phase space of the model on the strip is related to the (generalized) Dirac bracket on the branes through a dual pair structure.

Nodes, monopoles and confinement in (2+1)-dimensional gauge theories

Abstract In the presence of Chern-Simons interactions the wave functionals of physical states in 2 + 1-dimensional gauge theories vanish at a number of nodal points. We show that those nodes are located at some classical configurations which carry a non-trivial magnetic charge. In abelian gauge theories this fact explains why magnetic monopoles are suppressed by Chern-Simons interactions. In non-abelian theories it suggests a relevant role for nodal gauge field configurations in the confinement mechanism of Yang-Mills theories. We show that the vacuum nodes correspond to the chiral gauge orbits of reducible gauge fields with non-trivial magnetic monopole components.

Excited state entanglement in homogeneous fermionic chains

We study the Renyi entanglement entropy of an interval in a periodic fermionic chain for a general eigenstate of a free, translational invariant Hamiltonian. In order to analytically compute the entropy we use two technical tools. The first is used to logarithmically reduce the complexity of the problem and the second to compute the Renyi entropy of the chosen subsystem. We introduce new strategies to perform the computations, derive new expressions for the entropy of these general states and show the perfect agreement of the analytical computations and the numerical outcome. Finally we discuss the physical interpretation of our results and generalize them to compute the entanglement entropy for a fragment of a fermionic ladder.

Chern-Simons states and topologically massive gauge theories

Abstract In an abelian topologically massive gauge theory, any eigenstate of the Hamiltonian can be decomposed into a factor describing massive propagating gauge bosons and a Chern-Simons wave function describing a set of nonpropagating “topological” excitations. The energy depends only on the propagating modes, and energy eigenstates thus occur with a degeneracy that can be parametrized by the Hilbert space of the pure Chern-Simons theory. We show that for a nonabelian topologically massive gauge theory, this degeneracy is lifted: although the Gauss law constraint can be solved with a similar factorization, the Hamiltonian couples the propagating and nonpropagating (topological) modes.

Topological Poisson sigma models on Poisson-Lie groups

We solve the topological Poisson Sigma model for a Poisson-Lie group G and its dual G*. We show that the gauge symmetry for each model is given by its dual group that acts by dressing transformations on the target. The resolution of both models in the open geometry reveals that there exists a map from the reduced phase space of each model (P and P*) to the main symplectic leaf of the Heisenberg double (D0) such that the symplectic forms on P, P* are obtained as the pull-back by those maps of the symplectic structure on D0. This uncovers a duality between P and P* under the exchange of bulk degrees of freedom of one model with boundary degrees of freedom of the other one. We finally solve the Poisson Sigma model for the Poisson structure on G given by a pair of r-matrices that generalizes the Poisson-Lie case. The hamiltonian analysis of the theory requires the introduction of a deformation of the Heisenberg double.

Boundary G/G theory and topological Poisson-Lie sigma model

We study a boundary version of the gauged WZW model with a Poisson–Lie group G as the target. The Poisson–Lie structure of G is used to define the Wess–Zumino term of the action on surfaces with boundary. We clarify the relation of the model to the topological Poisson sigma model with the dual Poisson–Lie group G* as the target and show that the phase space of the theory on a strip is essentially the Heisenberg double of G introduced by Semenov–Tian–Shansky.

Geometric regularization of gauge theories

A new regularization of gauge theories is introduced in a continuum space-time. The regularization is based on a geometric interpretation of the Yang-Mills functional integral in the covariant formalism. Besides a regularization of the classical action by higher covariant derivatives we introduce a regularization of the functional volume element by means of a strong riemannian metric in the space of gauge orbits M and two families of trace class operators defined in the tangent spaces of M. The conditions for the cancellation of ultraviolet divergences are shown to be independent of the gauge condition. This method opens the possibility of a non-perturbative covariant approach to gauge theories in a continuum space-time.

Reduction of Lie–Jordan Banach algebras and quantum states

In this paper, it is shown that the concept of dynamical correspondence for Jordan Banach algebras is equivalent to a Lie structure compatible with the Jordan one. Then a theory of reduction of Lie–Jordan Banach algebras in the presence of quantum constraints is presented and compared to the standard reduction of C*-algebras of observables of a quantum system. The space of states of the reduced Lie–Jordan Banach algebra is characterized in terms of Dirac states on the physical algebra of observables and its GNS representations described in terms of states on the unreduced algebra.