Asia Wyatt

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Faculty Mentor: Peter W. Shor

Direct Supervisor: Ramis Movassagh

Home University: Spelman College

Major: Mathematics

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Biography

I am a senior mathematics major at Spelman College in Atlanta, GA. Through humble beginnings in the town of Covington, GA, I have gained a passion not only for the mathematical sciences, but also the education system and economics. That being said, my research interests include the aforementioned topics with a primary focus on the mathematics behind the economics of education. More so than number crunching, I enjoy dancing, singing, and writing poetry.

Abstract

Entanglement Entropy and Quasicrystal Structured Ground State of Quantum Spin Chains

Expanding on the concepts in the paper “Criticality without frustration for quantum spin-1 chains,” it is possible to construct a Hamiltonian whose ground state exhibits one dimensional quasicrystal structure. We label the spin states using 7 symbols. The interactions given by the Hamiltonian ‘implement’ 18 rules affecting the spin states. Once the zero energy ground state, or null space, of this Hamiltonian is understood through the superposition of spin chains, we will try to quantify the entanglement entropy from the combinatorial structure of the ground state. There seems to be an intimate connection between these correlations and the Fibonacci sequence of numbers. The work is quantum information theoretical and combinatorial in nature.