Symmetries, Gauging, and Nonunitary Dynamics in Quantum Many-Body Systems

This dissertation explores the role of symmetries in the kinematics and dynamics of quantum many-body systems, through two thematically distinct but conceptually related parts.

The first part focuses on the gauging of discrete symmetries, which gives rise to novel phases and critical points, exact self-dualities, and generalized bosonization in one and higher dimensions. In particular, it uncovers new gapless symmetry-protected topological phases and generalized deconfined quantum critical points by gauging a Z2 subgroup of a continuous U(1) symmetry. It also revisits a family of models related to the XX chain from the perspective of Z2 gauging, revealing exact self-dualities that flow in the infrared to the T-duality of the compact boson conformal field theory, interchanging the momentum and winding U(1) charges. Additionally, it develops a general framework for bosonization and Kramers–Wannier dualities in arbitrary dimensions by gauging the Z2 fermion parity of Majorana systems. These results contribute to a deeper understanding of how symmetry, topology, and duality intertwine in quantum systems.

The second part turns to integrability and dynamics in nonunitary quantum circuits, motivated by recent developments in open and measured quantum dynamics and non-Hermitian physics. It presents many classes of nonunitary quantum circuits that remain integrable and exhibit rich dynamical behavior, and studies the phase structure and time evolution of a nonunitary Floquet transverse-field Ising model. These investigations reveal how nonunitarity can lead to novel dynamical regimes and phase transitions beyond the scope of conventional Hermitian quantum mechanics.

Together, these two parts offer complementary perspectives on how symmetries and their generalizations shape the structure and dynamics of both unitary and nonunitary quantum many-body systems.