Emergent Magnetic Monopole Charges in a Two Qubit System

Speaker: Tiago Souza

When: October 27, 2014 (Mon), 11:30AM to 12:30PM (add to my calendar)
Location: SCI 328

This event is part of the Preliminary Oral Exam.

Examining Committee:

Anatoli Polkovnikov, Claudio Chamon, Shyam Erramilli and Ami Katz

Abstract: We introduce a simple Hamiltonian describing the interaction of two coupled qubits (modeled by two spins) with external magnetic elds. Borrowing ideas from topology, we calculate the Berry connection and curvature, as well as the Chern number, and a natural mapping shows that the latter is equivalent to the magnetic eld produced by monopole charges in real space. We suggest a method for measuring the magnetic monopole charge density (i. e., the ground state degeneracies in a coupled XY quantum system) and detail its motion as external parameters are varied. Using symmetry arguments, we derive the result that the Berry connec- tion ~A is proportional to the expectation value of z tot in the ground state, thereby allowing for measurements to be obtained for all the quantities related to the Berry curvature, ~F = r ~ A, by simply measuring hz toti.

Using Maxwell's equations with the addition of magnetic monopoles, we obtain the eective charge density and the current density as a function of the parameters changed. We show how particular choices for param- eters give rise to peculiar kinds of motion of the monopole charges, how one can go from magnetic monopole charges to continuous charge distributions like rings and surfaces by properly changing the system's symmetries through its parameters, and probe the interesting but as of yet unexplored consequences on r ~F as said changes are made.

Tiago