Combination of Spatial and Spin Functions; Calculation of the Matrix Elements of Operators

Ruben Pauncz

Norm M. Tubman, David ChangMo Yang

Several algorithms have been proposed to calculate the spatial entanglement spectrum from high order R\'enyi entropies and maximum entropy techniques. We present an alternative approach for computing the entanglement spectrum with quantum Monte Carlo for both continuum and lattice Hamiltonians. This method provides direct access to the matrix elements of the spatially reduced density matrix and we determine an estimator that can be used in variational Monte Carlo as well as other Monte Carlo methods. The algorithm is based on using a generalization of the swap operator, which can be extended to calculate a general class of density matrices that can include combinations of spin, space, particle, and even momentum degrees of freedom. We demonstrate the method by applying it to the ${\mathrm{H}}_{2}$ and ${\mathrm{N}}_{2}$ molecules and describe how the spatial entanglement spectrum encodes a covalent bond that includes all the many body correlations.

Vladimir S. Filinov, P. Thomas, Imre Varga +4 more

The quantum dynamics of an ensemble of interacting electrons in an array of random scatterers is treated using a numerical approach for the calculation of average values of quantum operators and time correlation functions in the Wigner representation. The Fourier transform of the product of matrix elements of the dynamic propagators obeys an integral Wigner-Liouville-type equation. Initial conditions for this equation are given by the Fourier transform of the Wiener path-integral representation of the matrix elements of the propagators at the chosen initial times. This approach combines both molecular dynamics and Monte Carlo methods and computes numerical traces and spectra of the relevant dynamical quantities such as momentum-momentum correlation functions and spatial dispersions. Considering, as an application, a system with fixed scatterers, the results clearly demonstrate that the many-particle interaction between the electrons leads to an enhancement of the conductivity and spatial dispersion compared to the noninteracting case.

F Berencz

Ruben Pauncz

G. Kulkarni, N. A. Slavnov

We consider an $$XYZ$$ spin chain within the framework of the generalized algebraic Bethe ansatz. We calculate the actions of monodromy matrix elements on Bethe vectors as linear combinations of new Bethe vectors. We also compute the multiple action of the gauge-transformed monodromy matrix elements on the pre-Bethe vector and express the results in terms of the partition function of the $$8$$ -vertex model.