Date of Completion


Thesis Type

College of Arts and Science Honors



First Advisor

Christopher Herdman

Second Advisor

Adrian Del Maestro


Entanglement, Lieb-Liniger Model, Bosons, Entropy, Exact Diagonalization, Ising Model, Second Quantization, Condensate


Experiments and simulations in confined liquid helium-4 (He-4) systems have shown quasi-one-dimensional behavior consistent with quantum phases of 1D bosons. In these experiments, confined He-4 becomes strongly correlated, and can be described by the linear quantum hydrodynamics known as Luttinger liquid theory, which also predicts a novel state of matter in 1D. Furthermore, 1D systems at near-zero temperature are highly entangled, and can offer insight into the use of entanglement as a resource for quantum information processing applications. In this research, I study 1D bosons with short-ranged interactions, described by the Lieb-Liniger model, by exactly diagonalizing the Hamiltonian to calculate physically important quantities, including the entanglement entropy that are inaccessible by any other means.