Quantum groups play a role of symmetries of integrable theories in two dimensions. They may be detected on the classical level as Poisson-Lie symmetries of the corresponding phase spaces. We discuss specifically the Wess-Zumino-Witten conformally invariant quantum field model combining two chiral parts which describe the left-and right-moving degrees of freedom. On one hand side, the quantum group plays the role of the symmetry of the chiral components of the theory. On the other hand, the model admits a lattice regularization (in the Minkowski space) in which the current algebra symmetry of the theory also becomes quantum, providing the simplest example of a quantum group symmetry coupling space-time and internal degrees of freedom. We develop a free field approach to the representation theory of the lattice sl(2)-based current algebra and show how to use it to rigorously construct an exact solution of the quantum SL(2) WZW model on lattice.

We present in detail the recently derived ab-initio molecular dynamics (AIMD) formalism [Phys. Rev. Lett. 101 096403 (2008)], 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. 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.

A new "on the fly" method to perform Born-Oppenheimer ab initio molecular dynamics (AIMD) is presented. Inspired by Ehrenfest dynamics in time-dependent density functional theory, the electronic orbitals are evolved by a Schrödinger-like equation, where the orbital time derivative is multiplied by a parameter. This parameter controls the time scale of the fictitious electronic motion and speeds up the calculations with respect to standard Ehrenfest dynamics. In contrast to other methods, wave function orthogonality needs not be imposed as it is automatically preserved, which is of paramount relevance for large scale AIMD simulations.PACS numbers: 71.15.Pd, 31.15.Ew Ab initio molecular dynamics (AIMD) on the ground state Born-Oppenheimer (gsBOMD) potential energy surface for the nuclei has become a standard tool for simulating the conformational behaviour of molecules, bioand nano-structures and condensed matter systems from first principles [1]. However, gsBOMD (in the DFT [2] picture) requires that the Kohn-Sham (KS) energy functional be minimized for each value of the nuclei positions. As this minimization can be very demanding, Car and Parrinello (CP) [3] proposed an elegant and efficient "on the fly" scheme in which the KS orbitals are propagated with a fictitious dynamics that mimics gsBOMD. The CP method has had a tremendous impact in many scientific areas [4,5]. Nevertheless, the numerical cost of AIMD hinders the application of the method to large scale simulations, such as those of interest in biochemistry or material science. Recently, new methods that allow larger systems and longer simulation times to be studied have been reported [6], but the cost associated with the wave function orthogonalization is still a potential bottleneck for both gsBOMD and CP.Time-dependent density functional theory (TDDFT) [7,8] has been for a long time recognized as an orthogonalization-free alternative for both ground state [9] and excited state AIMD. In its simplest implementation, Ehrenfest TDDFT, the ions are treated classically following electronic Hellmann-Feynman forces. For systems where the gap between the ground and the first excited state is large, Ehrenfest tends to gsBOMD and can mimic adiabatic dynamics [1]. However, the rapid movement of the electrons in TDDFT requires the use of a very small time step, which, in many occasions, renders its numerical application non-practical [10].In this letter, we borrow some of the ideas of CP and introduce a new TDDFT Ehrenfest dynamics that reduces the cost of AIMD simulations while keeping the accuracy of the results in tolerable levels, similar to CP. The whole scheme can be obtained from the following Lagrangian (atomic units are used throughout this paper):whereI M IṘI ·Ṙ I is the kinetic energy of the nuclei, M I their masses and E the KS energy. Note that the major modification with respect to TDDFT is the scaling of the electronic velocities by a parameter µ (TDDFT is recovered when µ = 1). We show in what follows that, in the µ → 0 limit, the trajectories ...

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 α-gauge with α = 0 and a given auxiliary preregularization is introduced in order to uniquely define the regularization. The limit α → 0 in the regulating Pauli-Villars fields is pathological and the original Slavnov proposal in 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 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 β and γ functions of the renormalization group equations.

We obtain a formula for the determinant of a block Toeplitz matrix associated with a quadratic fermionic chain with complex coupling. Such couplings break reflection symmetry and/or charge conjugation symmetry. We then apply this formula to compute the Rényi entropy of a partial observation to a subsystem consisting of contiguous sites in the limit of large size. (2008)]. A striking feature of our formula for the entanglement entropy is the appearance of a term scaling with the logarithm of the size. This logarithmic behavior originates from certain discontinuities in the symbol of the block Toeplitz matrix. Equipped with this formula we analyze the entanglement entropy of a Dzyaloshinski-Moriya spin chain and a Kitaev fermionic chain with long-range pairing.

Abstract. Quantum dynamics (i.e., the Schrödinger equation) and classical dynamics (i.e., Hamilton equations) can both be formulated in equal geometric terms: a Poisson bracket defined on a manifold. In this paper we first show that the hybrid quantum-classical dynamics prescribed by the Ehrenfest equations can also be formulated within this general framework, what has been used in the literature to construct propagation schemes for Ehrenfest dynamics. Then, the existence of a well defined Poisson bracket allows to arrive to a Liouville equation for a statistical ensemble of Ehrenfest systems. The study of a generic toy model shows that the evolution produced by Ehrenfest dynamics is ergodic and therefore the only constants of motion are functions of the Hamiltonian. The emergence of the canonical ensemble characterized by the Boltzmann distribution follows after an appropriate application of the principle of equal a priori probabilities to this case. Once we know the canonical distribution of a Ehrenfest system, it is straightforward to extend the formalism of Nosé (invented to do constant temperature Molecular Dynamics by a non-stochastic method) to our Ehrenfest formalism. This work also provides the basis for extending stochastic methods to Ehrenfest dynamics.

In this letter we study the conductance G through one-dimensional quantum wires with disorder configurations characterized by long-tailed distributions (Lévy-type disorder). We calculate analytically the conductance distribution which reveals a universal statistics: the distribution of conductances is fully determined by the exponent α of the power-law decay of the disorder distribution and the average ln G , i.e., all other details of the disorder configurations are irrelevant. For 0 < α < 1 we found that the fluctuations of ln G are not self-averaging and ln G scales with the length of the system as L α , in contrast to the predictions of the standard scaling-theory of localization where ln G is a self-averaging quantity and ln G scales linearly with L. Our theoretical results are verified by comparing with numerical simulations of one-dimensional disordered wires. p-5

We study the Rényi 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 one is used to reduce logarithmically the complexity of the problem and the second one to compute the Rényi 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 generalise them to compute the entanglement entropy for a fragment of a fermionic ladder.