arXiv subjects

Alexander Hahn

Publications and source records attributed to Alexander Hahn.

22 records · Page 2Linked to original sources

arXiv2020

Generalized string-nets for unitary fusion categories without tetrahedral symmetry

The Levin-Wen model of string-net condensation explains how topological phases emerge from the microscopic degrees of freedom of a physical system. However, the original construction is not applicable to all unitary fusion category since some additional symmetries for the $F$-symbols are imposed. In particular, the so-called tetrahedral symmetry is not fulfilled by many interesting unitary fusion categories. In this paper, we present a generalized construction of the Levin-Wen model for arbitrary multiplicity-free unitary fusion categories that works without requiring these additional symmetries. We explicitly calculate the matrix elements of the Hamiltonian and, furthermore, show that it has the same properties as the original one.

quant-ph↗

arXiv2019

Gauging Defects in Quantum Spin Systems

The goal of this work is to build a dynamical theory of defects for quantum spin systems. A kinematic theory for an indefinite number of defects is first introduced exploiting distinguishable Fock space. Dynamics are then incorporated by allowing the defects to become mobile via a microscopic Hamiltonian. This construction is extended to topologically ordered systems by restricting to the ground state eigenspace of Hamiltonians generalizing the golden chain. We illustrate the construction with the example of a spin chain with $\mathbf{Vec}(\mathbb{Z}/2\mathbb{Z})$ fusion rules, employing generalized tube algebra techniques to model the defects in the chain. The resulting dynamical defect model is equivalent to the critical transverse Ising model.

quant-ph↗

arXiv2018

From categories to anyons: a travelogue

In this paper we provide an overview of category theory, focussing on applications in physics. The route we follow is motivated by the final goal of understanding anyons and topological QFTs using category theory. This entails introducing modular tensor categories and fusion rings. Rather than providing an in-depth mathematical development we concentrate instead on presenting the "highlights for a physicist".

quant-ph↗

arXiv2015

Silicon Photomultiplier Research and Development Studies for the Large Size Telescope of the Cherenkov Telescope Array

The Cherenkov Telescope Array (CTA) is the the next generation facility of imaging atmospheric Cherenkov telescopes; two sites will cover both hemispheres. CTA will reach unprecedented sensitivity, energy and angular resolution in very-high-energy gamma-ray astronomy. Each CTA array will include four Large Size Telescopes (LSTs), designed to cover the low-energy range of the CTA sensitivity ($\sim$20 GeV to 200 GeV). In the baseline LST design, the focal-plane camera will be instrumented with 265 photodetector clusters; each will include seven photomultiplier tubes (PMTs), with an entrance window of 1.5 inches in diameter. The PMT design is based on mature and reliable technology. Recently, silicon photomultipliers (SiPMs) are emerging as a competitor. Currently, SiPMs have advantages (e.g. lower operating voltage and tolerance to high illumination levels) and disadvantages (e.g. higher capacitance and cross talk rates), but this technology is still young and rapidly evolving. SiPM technology has a strong potential to become superior to the PMT one in terms of photon detection efficiency and price per square mm of detector area. While the advantage of SiPMs has been proven for high-density, small size cameras, it is yet to be demonstrated for large area cameras such as the one of the LST. We are working to develop a SiPM-based module for the LST camera, in view of a possible camera upgrade. We will describe the solutions we are exploring in order to balance a competitive performance with a minimal impact on the overall LST camera design.

astro-ph.IM↗