Dynamical Correlations after a Quantum Quench

In many integrable models static (equal time) correlation functions of local observables after a quantum quench relax to stationary values, which are described by a generalized Gibbs ensemble (GGE). Here we establish that the same holds true for dynamic (non equal time) correlation functions. More generally we show that in the absence of long-range interactions in the final Hamiltonian, the dynamics is determined by the same ensemble that describes static correlations. When the latter is a GGE the basic form of the fluctuation dissipation theorem holds, although the absorption and emission spectra are not simply related as in the thermal case. For quenches in the transverse field Ising chain (TFIC) we derive explicit expressions for the time evolution of dynamic order parameter correlators after a quench.Comment: 6 pages, 3 figure

Modular invariance in the gapped XYZ spin 1/2 chain

We show that the elliptic parametrization of the coupling constants of the quantum XYZ spin chain can be analytically extended outside of their natural domain, to cover the whole phase diagram of the model, which is composed of 12 adjacent regions, related to one another by a spin rotation. This extension is based on the modular properties of the elliptic functions and we show how rotations in parameter space correspond to the double covering PGL(2,Z)of the modular group, implying that the partition function of the XYZ chain is invariant under this group in parameter space, in the same way as a Conformal Field Theory partition function is invariant under the modular group acting in real space. The encoding of the symmetries of the model into the modular properties of the partition function could shed light on the general structure of integrable models.Comment: 17 pages, 4 figures, 1 table. Accepted published versio

Finite-Size Effects in Graphene Nanostructures

Finite-Size Effects in Graphene Nanostructure

A Novel Intermolecular Potential to Describe the Interaction Between the Azide Anion and Carbon Nanotubes

47 P.International audienceIn this contribution we propose a novel and accurate intermolecular potential that can be used for the simulation of the azide anion confined inside carbon nanotubes of arbitrary size. The peculiarity of our approach is to include an explicit term, modeling the induction attractive contributions from the negatively charged azide ion, that can be generalized to other ions confined in carbon nanotubes of different size and length. Through a series of accurate DLPNO-CCSD(T) calculations, we show that this potential reproduces the ab initio interaction energy to within a few kcal/mol. The potential is implemented in a molecular dynamics program, with which we carried out illustrative simulations to demonstrate the effectiveness of our approach. At last, the guidelines provided by this investigation can be applied to build up force fields for many neutral/ionic molecular species confined within carbon nanotubes; a crucial requirement to carry out molecular dynamics simulations under a variety of conditions

Full configuration interaction calculation of singlet excited states of Be3

The full configuration interaction (FCI) study of the singlets vertical spectrum of the neutral beryllium trimer has been performed using atomic natural orbitals [3s2p1d] basis set. The FCI triangular equilibrium structure of the ground state has been used to calculate the FCI vertical excitation energies up to 4.8 eV. The FCI vertical ionization potential for the same geometry and basis set amounts to 7.6292 eV. The FCI dipole and quadrupole transition moments from the ground state are reported as well. The FCI electric quadrupole moment of the X 3A1′ ground state has been also calculated with the same basis set (Θzz = −2.6461 a.u., Θxx = Θyy = −1/2Θzz). Twelve of the 19 calculated excited singlets are doubly excited states. Most of the states have large multiconfigurational character. These results provide benchmark values for electronic correlation multireference methods. (4e×6MO)CAS-SDCI values for the same energies and properties are also [email protected]

Essential singularity in the Renyi entanglement entropy of the one-dimensional XYZ spin-1/2 chain

We study the Renyi entropy of the one-dimensional XYZ spin-1/2 chain in the entirety of its phase diagram. The model has several quantum critical lines corresponding to rotated XXZ chains in their paramagnetic phase, and four tri-critical points where these phases join. Two of these points are described by a conformal field theory and close to them the entropy scales as the logarithm of its mass gap. The other two points are not conformal and the entropy has a peculiar singular behavior in their neighbors, characteristic of an essential singularity. At these non-conformal points the model undergoes a discontinuous transition, with a level crossing in the ground state and a quadratic excitation spectrum. We propose the entropy as an efficient tool to determine the discontinuous or continuous nature of a phase transition also in more complicated models.Comment: 5 pages, 2 figure

Distributed Gaussian orbitals for molecular calculations: application to simple systems

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