Date of Award
12-1-2025
Document Type
Dissertation
Degree Name
Ph.D. in Physics
First Advisor
Kevin Beach
Second Advisor
Alakabha Datta
Third Advisor
Luca Bombelli
School
University of Mississippi
Relational Format
dissertation/thesis
Abstract
In this dissertation, we present work on the entanglement properties of the Fredkin spin chain, a spin one-half chain with local three-body interactions. We focus on the development and use of Monte Carlo techniques to measure the entanglement entropy for bipartitions of the Fredkin spin chain.
In the first chapter, we formally develop an extension to existing Monte Carlo techniques to allow for the calculation of higher-order Rényi entanglement entropies using the replica trick. The method clarifies how multiple systems can be simulated in parallel to calculate the Rényi entanglement entropy at any order.
In the next chapter, we apply analytical and Monte Carlo techniques to a one-parameter family of related t-deformed Fredkin spin chains to study the finite-size scaling properties of the entanglement entropy in the vicinity of a quantum critical point. We note the first characterization of the universal exponent ν which describes how the correlation length diverges as the system approaches criticality.
Recommended Citation
Moore, Joshua Tyler, "Numerical Studies of Entanglement Entropy in the Fredkin Spin Chain" (2025). Electronic Theses and Dissertations. 3524.
https://egrove.olemiss.edu/etd/3524