Authors:

Grayson Welch

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About Paper:

Entanglement entropy is a measure of how correlated one part of a quantum system is with another, possibly providing clues on why macroscopic phenomena are emergent from quantum mechanics. In fermionic systems, M-body entanglement entropy measures these correlations between M particles and the remainder of the system. All N- fermion systems have a theoretical upper bound to the entropy defined by a maximally mixed M-body density matrix. We developed software to simulate the Hubbard and t-V models and to track changes in M-body entanglement entropy under time evolution. To observe these changes, we evolved single slater determinant states, which have initially zero entropy, until entropic saturation was reached. In the case of the Hubbard model, the total spin of the initial slater determinant provides a refined upper bound which is less than the absolute upper bound. The arrangement of particles and strength of their interaction energies further contributes to the rate of change of entanglement entropy. The number of neighboring fermions in the t-V model are hypothesized to exhibit similar behavior during evolution of single slater states. There is strong evidence that conserved quantities within a system, such as spin, refine the upper bound of M-body entanglement. Keywords: Entanglement; Hamiltonian; Time Evolution; Quantum Mechanics; Software

Source:

Purdue University / 2025

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Co-authors:

Grayson Welch