Spin Physics in the age of Quantum Simulation: from Emergence to Chaos

The remarkable rise of quantum simulation as a viable strategy for studying many-body phenomena has introduced an entirely new dimension to research in quantum mechanics. These platforms offer unprecedented versatility and control over the interactions between their fundamental degrees of freedom. Thus, they present an opportunity for the first time to experimentally investigate arbitrary Hamiltonian systems, even those that might not occur naturally. The vast majority of these platforms employ a qubit architecture, that is, their fundamental degree of freedom is a single qubit that can mathematically be described by a spin algebra. Therefore, the most natural Hamiltonians to study using these architectures are spin Hamiltonians.

Spin is the intrinsic angular momentum associated with quantum particles that dictates their magnetic moments and quantum statistics. However, Hamiltonians involving other kinds of degrees of freedom may also be mathematically described by a spin algebra; the Hamiltonians used in quantum simulators being a prominent example. Spin Hamiltonians have been known to demonstrate an incredible variety of phases of matter, ranging all the way from the well-known magnetic phases such as ferromagnets and paramagnets to the recently discovered exotic quantum phases such as quantum spin liquids. They have been the subject of extensive theroretical and experimental studies for many decades and have revealed fundamental insights into the emergence of quantum phases and phase transitions.

Moreover, spin systems have also proved to be ideal settings for investigating the manifestations of chaos in quantum systems such as through the dynamical generation of entanglement. Given the significance of these two themes, emergence and chaos, for physics in the 21st century, the availability of quantum simulation architectures presents an almost miraculous opportunity for carrying out deeper explorations into the emergence of phases of matter and quantum chaos using spin systems as our guideline. This is precisely the goal of this dissertation.