Matrix product states and variational methods applied to critical quantum field theory

We study the second-order quantum phase-transition of massive real scalar field theory with a quartic interaction ($\phi^4$ theory) in (1+1) dimensions on an infinite spatial lattice using matrix product states (MPS). We introduce and apply a naive variational conjugate gradient method, based on the time-dependent variational principle (TDVP) for imaginary time, to obtain approximate ground states, using a related ansatz for excitations to calculate the particle and soliton masses and to obtain the spectral density. We also estimate the central charge using finite-entanglement scaling. Our value for the critical parameter agrees well with recent Monte Carlo results, improving on an earlier study which used the related DMRG method, verifying that these techniques are well-suited to studying critical field systems. We also obtain critical exponents that agree, as expected, with those of the transverse Ising model. Additionally, we treat the special case of uniform product states (mean field theory) separately, showing that they may be used to investigate non-critical quantum field theories under certain conditions.Comment: 24 pages, 21 figures, with a minor improvement to the QFT sectio

Variational Matrix Product Ansatz for Nonuniform Dynamics in the Thermodynamic Limit

We describe how to implement the time-dependent variational principle for matrix product states in the thermodynamic limit for nonuniform lattice systems. This is achieved by confining the nonuniformity to a (dynamically growable) finite region with fixed boundary conditions. The suppression of unphysical quasiparticle reflections from the boundary of the nonuniform region is also discussed. Using this algorithm we study the dynamics of localized excitations in infinite systems, which we illustrate in the case of the spin-1 anti-ferromagnetic Heisenberg model and the $\phi^4$ model.Comment: 8 pages, 5 figures, tensor network diagrams. Code available at http://amilsted.github.io/evoMPS

Quantum Yang-Mills theory: An overview of a program

We present an overview of a program to understand the low-energy physics of quantum Yang-Mills theory from a quantum-information perspective. Our setting is that of the Hamiltonian formulation of pure Yang-Mills theory in the temporal gauge on the lattice. Firstly, inspired by recent constructions for Z/2Z lattice gauge theory, in particular, Kitaev’s toric code, we describe the gauge-invariant sector of Hilbert space by introducing a primitive quantum gate: the quantum parallel transporter. We then develop a non-Abelian generalization of Laplace interpolation to present an ansatz for the ground state of pure Yang-Mills theory which interpolates between the weak- and strong-coupling renormalization group fixed points. The resulting state acquires the structure of a tensor network, namely, a multiscale entanglement renormalization ansatz, and allows for the efficient computation of local observables and Wilson loops. Various refinements of the tensor network are discussed leading to several generalizations. Finally, the continuum limit of our ansatz as the lattice regulator is removed is then described. This paper is intended as an abstract for an ongoing program: there are still many open problems

Statistical translation invariance protects a topological insulator from interactions

We investigate the effect of interactions on the stability of a disordered, two-dimensional topological insulator realized as an array of nanowires or chains of magnetic atoms on a superconducting substrate. The Majorana zero-energy modes present at the ends of the wires overlap, forming a dispersive edge mode with thermal conductance determined by the central charge $c$ of the low-energy effective field theory of the edge. We show numerically that, in the presence of disorder, the $c=1/2$ Majorana edge mode remains delocalized up to extremely strong attractive interactions, while repulsive interactions drive a transition to a $c=3/2$ edge phase localized by disorder. The absence of localization for strong attractive interactions is explained by a self-duality symmetry of the statistical ensemble of disorder configurations and of the edge interactions, originating from translation invariance on the length scale of the underlying mesoscopic array.Comment: 5+2 pages, 8 figure

Quantum phases of a chain of strongly interacting anyons

We study a strongly interacting chain of anyons with fusion rules determined by SO(5)2. The phase portrait is identified with a combination of numerical and analytical techniques. Several critical phases with different central charges and their corresponding transitions identified.Comment: 5 pages, 4 figure

Neutron activation analysis traces copper artifacts to geographical point of origin

Impurities remaining in the metallic copper are identified and quantified by spectrographic and neutron activation analysis. Determination of the type of ore used for the copper artifact places the geographic point of origin of the artifact

Testosterone Effects On Renal Norepinephrine Content and Release in Rats With Different Y Chromosomes

The Y chromosome in spontaneously hypertensive rats (SHR) and stroke-prone rats has been shown to contain a locus that contributes to the hypertensive effect; both the sympathetic nervous system and testosterone may be involved. The objective of this study was to look at the effects of testosterone on renal norepinephrine (NE) release and content in the isolated perfused kidney in different Y chromosome backgrounds. The study involved male SHR, Wistar-Kyoto rats (WKY), and 2 consomic strains with different Y chromosomes (n=5 to 8 per group). Adult animals were castrated, and implants containing testosterone propionate were placed at the base of the neck. Blood testosterone levels were measured by radioimmunoassay 2 weeks after castration. The left kidney was isolated and perfused with oxygenated Krebs solution at a constant flow and temperature with KCl and electrical stimulation of the renal nerves. Perfusate was collected and analyzed for NE by high-performance liquid chromatography. Lactate dehydrogenase analyses were performed as a marker for potential tissue damage. Renal perfusate and renal tissue NE levels were significantly elevated by testosterone. The average NE increase with a single testosterone implant was 13.2 ng/mL, and for a double testosterone implant it was 29.8 ng/mL. The Y chromosome from the SHR produced a significant increase in renal NE release compared with the WKY Y chromosome. Significance was shown between all groups: 1 versus 2 implants, P=0.0067; 1 versus sham implants, P=0.015; 2 versus sham implants,

CALCULATIONS OF YIELDS OF PRODUCTS IN HIGH-FLUX NEUTRON IRRADIATIONS OF HEAVY ELEMENT SAMPLES

Calculations have been made of the build-up of higher nuclides in samples of various heavy-element starting materials, at neutron fluxes ranging from 4 x 10/sup 13/ to 1 x 10/sup 16/ n/ cm/sup 2//sec, including the flux expected from the HFIR reactor at Oak Ridge (namely, 5 x 10/sup 15/ n/cm/sup 2// sec). Attempts have been made to estimate yields of the heavier fermium isotopes and of Md/sup 259/ by means of the nuclear properties predicted from systematics. The results indicate that it may be possible to detect Md/sup 259/ in the products of californium irradiated in HFIR, and that a further two-fold increase in flux would increase the yields of the heaviest nuclides considerably. (auth