Fourier transform of fermionic systems and the spectral tensor network

Leveraging the decomposability of the fast Fourier transform, I propose a new class of tensor network that is efficiently contractible and able to represent many-body systems with local entanglement that is greater than the area law. Translationally invariant systems of free fermions in arbitrary dimensions as well as 1D systems solved by the Jordan-Wigner transformation are shown to be exactly represented in this class. Further, it is proposed that these tensor networks be used as generic structures to variationally describe more complicated systems, such as interacting fermions. This class shares some similarities with Evenbly & Vidal's branching MERA, but with some important differences and greatly reduced computational demands.Comment: Accepted in Phys. Rev. Lett. 9 pages, 13 figures. This version is reorganized to be more pedagogical and includes a new derivation of the FFT decomposition, as well as extra details on the contraction scheme in the Appendi

Multimode analysis of non-classical correlations in double well Bose-Einstein condensates

The observation of non-classical correlations arising in interacting two to size weakly coupled Bose-Einstein condensates was recently reported by Esteve et al. [Nature 455, 1216 (2008)]. In order to observe fluctuations below the standard quantum limit, they utilized adiabatic passage to reduce the thermal noise to below that of thermal equilibrium at the minimum realizable temperature. We present a theoretical analysis that takes into account the spatial degrees of freedom of the system, allowing us to calculate the expected correlations at finite temperature in the system, and to verify the hypothesis of adiabatic passage by comparing the dynamics to the idealized model.Comment: 12 pages, 7 figure

Do alternative measures of government result in alternative explanations for government size?

This note extends the work of Borcherding, Ferris and Garzoni (2003) on government size by considering how traditional tests respond to alternative definitions of government size. An error correction format is used to show that a) qualitatively all measures of size perform well, b) government consumption (plus transfers) works best when explaining short run (long run) changes and c) public choice and Kau/Rubin variables often perform differently with respect to the short and long run.

Variational Monte Carlo with the Multi-Scale Entanglement Renormalization Ansatz

Monte Carlo sampling techniques have been proposed as a strategy to reduce the computational cost of contractions in tensor network approaches to solving many-body systems. Here we put forward a variational Monte Carlo approach for the multi-scale entanglement renormalization ansatz (MERA), which is a unitary tensor network. Two major adjustments are required compared to previous proposals with non-unitary tensor networks. First, instead of sampling over configurations of the original lattice, made of L sites, we sample over configurations of an effective lattice, which is made of just log(L) sites. Second, the optimization of unitary tensors must account for their unitary character while being robust to statistical noise, which we accomplish with a modified steepest descent method within the set of unitary tensors. We demonstrate the performance of the variational Monte Carlo MERA approach in the relatively simple context of a finite quantum spin chain at criticality, and discuss future, more challenging applications, including two dimensional systems.Comment: 11 pages, 12 figures, a variety of minor clarifications and correction