arXiv subjects

M. Stewart Siu

Publications and source records attributed to M. Stewart Siu.

6 recordsLinked to original sources

arXiv2008

Bootstrap Approximations in Contractor Renormalization

We propose a bootstrap method for approximating the long-range terms in the Contractor Renormalization (CORE) method. The idea is tested on the 2-D Heisenberg antiferromagnet and the frustrated J_2-J_1 model. We obtain renormalization group flows that directly reveal the Neel phase of the unfrustrated HAF and the existence of a phase transition in the J_2-J_1 model for weak frustration. However, we find that this bootstrap method is dependent on blocking and truncation schemes. For this reason, we discuss these dependencies and unresolved issues that researchers who use this approach must consider.

cond-mat.str-el↗

arXiv2007

Adiabatic Rotation, Quantum Search and Preparation of Superposition States

We introduce the idea of using adiabatic rotation to generate superpositions of a large class of quantum states. For quantum computing this is an interesting alternative to the well-studied "straight line" adiabatic evolution. In ways that complement recent results, we show how to efficiently prepare three types of states: Kitaev's toric code state, the cluster state of the measurement-based computation model and the history state used in the adiabatic simulation of quantum circuit. We also show that the method, when adapted for quantum search, provides quadratic speedup as other optimal methods do with the advantages that the problem Hamiltonian is time-independent and that the energy gap above the ground state is strictly nondecreasing with time. Likewise the method can be used for optimization as an alternative to the usual adiabatic algorithm.

quant-ph↗

arXiv2007

Exploring Contractor Renormalization: Tests on the 2-D Heisenberg Antiferromagnet and Some New Perspectives

Contractor Renormalization (CORE) is a numerical renormalization method for Hamiltonian systems that has found applications in particle and condensed matter physics. There have been few studies, however, on further understanding of what exactly it does and its convergence properties. The current work has two main objectives. First, we wish to investigate the convergence of the cluster expansion for a two-dimensional Heisenberg Antiferromagnet(HAF). This is important because the linked cluster expansion used to evaluate this formula non-perturbatively is not controlled by a small parameter. Here we present a study of three different blocking schemes which reveals some surprises and in particular, leads us to suggest a scheme for defining successive terms in the cluster expansion. Our second goal is to present some new perspectives on CORE in light of recent developments to make it accessible to more researchers, including those in Quantum Information Science. We make some comparison to entanglement-based approaches and discuss how it may be possible to improve or generalize the method.

cond-mat.str-el↗

arXiv2005

From quantum circuits to adiabatic algorithms

This paper explores several aspects of the adiabatic quantum computation model. We first show a way that directly maps any arbitrary circuit in the standard quantum computing model to an adiabatic algorithm of the same depth. Specifically, we look for a smooth time-dependent Hamiltonian whose unique ground state slowly changes from the initial state of the circuit to its final state. Since this construction requires in general an n-local Hamiltonian, we will study whether approximation is possible using previous results on ground state entanglement and perturbation theory. Finally we will point out how the adiabatic model can be relaxed in various ways to allow for 2-local partially adiabatic algorithms as well as 2-local holonomic quantum algorithms.

quant-ph↗

arXiv2003

Resonance-continuum interference in the di-photon Higgs signal at the LHC

A low mass Standard Model Higgs boson should be visible at the Large Hadron Collider through its production via gluon-gluon fusion and its decay to two photons. We compute the interference of this resonant process, gg -> H -> gamma gamma, with the continuum QCD background, gg -> gamma gamma induced by quark loops. Helicity selection rules suppress the effect, which is dominantly due to the imaginary part of the two-loop gg -> gamma gamma scattering amplitude. The interference is destructive, but only of order 5% in the Standard Model, which is still below the 10-20% present accuracy of the total cross section prediction. We comment on the potential size of such effects in other Higgs models.

hep-ph↗

arXiv1999

Solidification pipes: from solder pots to igneous rocks

When a substance that shrinks in volume as it solidifies (for example, lead) is melted in a container and then cooled, a deep hole is often found in the center after resolidification. We use a simple model to describe the shape of the pipe and compare it with experimental results.

physics.ed-ph↗