Exact Solution of Noncommutative Field Theory in Background Magnetic Fields

We obtain the exact non-perturbative solution of a scalar field theory defined on a space with noncommuting position and momentum coordinates. The model describes non-locally interacting charged particles in a background magnetic field. It is an exactly solvable quantum field theory which has non-trivial interactions only when it is defined with a finite ultraviolet cutoff. We propose that small perturbations of this theory can produce solvable models with renormalizable interactions.Comment: 9 Pages AMSTeX; Typos correcte

Entanglement Entropy and Quantum Field Theory

We carry out a systematic study of entanglement entropy in relativistic quantum field theory. This is defined as the von Neumann entropy S_A=-Tr rho_A log rho_A corresponding to the reduced density matrix rho_A of a subsystem A. For the case of a 1+1-dimensional critical system, whose continuum limit is a conformal field theory with central charge c, we re-derive the result S_A\sim(c/3) log(l) of Holzhey et al. when A is a finite interval of length l in an infinite system, and extend it to many other cases: finite systems,finite temperatures, and when A consists of an arbitrary number of disjoint intervals. For such a system away from its critical point, when the correlation length \xi is large but finite, we show that S_A\sim{\cal A}(c/6)\log\xi, where \cal A is the number of boundary points of A. These results are verified for a free massive field theory, which is also used to confirm a scaling ansatz for the case of finite-size off-critical systems, and for integrable lattice models, such as the Ising and XXZ models, which are solvable by corner transfer matrix methods. Finally the free-field results are extended to higher dimensions, and used to motivate a scaling form for the singular part of the entanglement entropy near a quantum phase transition.Comment: 33 pages, 2 figures. Our results for more than one interval are in general incorrect. A note had been added discussing thi

Machine learning as an improved estimator for magnetization curve and spin gap

The magnetization process is a very important probe to study magnetic materials, particularly in search of spin-liquid states in quantum spin systems. Regrettably, however, progress of the theoretical analysis has been unsatisfactory, mostly because it is hard to obtain sufficient numerical data to support the theory. Here we propose a machine-learning algorithm that produces the magnetization curve and the spin gap well out of poor numerical data. The plateau magnetization, its critical field and the critical exponent are estimated accurately. One of the hyperparameters identifies by its score whether the spin gap in the thermodynamic limit is zero or finite. After checking the validity for exactly solvable one-dimensional models we apply our algorithm to the kagome antiferromagnet. The magnetization curve that we obtain from the exact-diagonalization data with 36 spins is consistent with the DMRG results with 132 spins. We estimate the spin gap in the thermodynamic limit at a very small but finite value.Comment: 10pages, 4figures. Revised and the algorithm improve

Tachyons on Dp-branes from Abelian Higgs sphalerons

We consider the Abelian Higgs model in a (p+2)-dimensional space time with topology M^{p+1} x S^1 as a field theoretical toy model for tachyon condensation on Dp-branes. The theory has periodic sphaleron solutions with the normal mode equations resembling Lame-type equations. These equations are quasi-exactly solvable (QES) for specific choices of the Higgs- to gauge boson mass ratio and hence a finite number of algebraic normal modes can be computed explicitely. We calculate the tachyon potential for two different values of the Higgs- to gauge boson mass ratio and show that in comparison to previously studied pure scalar field models an exact cancellation between the negative energy contribution at the minimum of the tachyon potential and the brane tension is possible for the simplest truncation in the expansion about the field around the sphaleron. This gives further evidence for the correctness of Sen's conjecture.Comment: 14 Latex pages including 3 eps-figure

Deformations of infrared-conformal theories in two dimensions

We study two exactly solvable two-dimensional conformal models, the critical Ising model and the Sommerfield model, on the lattice. We show that finite-size effects are important and depend on the aspect ratio of the lattice. In particular, we demonstrate how to obtain the correct massless behavior from an infinite tower of finite-size-induced masses and show that it is necessary to first take the cylindrical geometry limit in order to get correct results. In the Sommerfield model we also introduce a mass deformation to measure the mass anomalous dimension, $\gamma_m$. We find that the explicit scale breaking of the lattice setup induces corrections which must be taken into account in order to reproduce $\gamma_m$ at the infrared fixed point. These results can be used to improve the methodology in the search for the conformal window in QCD-like theories with many flavors.Comment: 7 pages, 2 figures. Talk presented at the 32nd International Symposium on Lattice Field Theory (Lattice 2014), 23-28 June, 2014, Columbia University, New York, N