When symmetry does the unexpected
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pace-sdpace-phd-physics-2026-thesis.pdf
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4.37 MB
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Author(s)
Pace, Salvatore D.
Advisor(s)
Wen, Xiao-Gang
Date Issued
May 2026
Publisher
Massachusetts Institute of Technology
Abstract
Symmetry is foundational in theoretical physics. In this thesis, we show how recent advances in symmetry have reinforced its power to classify, characterize, and constrain quantum systems non-perturbatively. We study symmetries, ranging from spatial symmetries to generalized symmetries, in both quantum field theory and quantum lattice systems. In particular, this thesis develops five sets of results. First, we show that ordinary ordered phases generically host emergent generalized symmetries in the infrared, associated with homotopy defects of the order-parameter space. We use these emergent generalized symmetries to characterize and classify defect-suppressed disorder transitions to phases with topological order and emergent gauge structures.
Second, we turn to lattice anomalies and show how the chiral anomaly of a massless Dirac fermion in two spacetime dimensions can be realized on the lattice. In particular, we identify lattice realizations of the vector and axial symmetries and demonstrate how their anomaly is matched by the non-abelian Onsager algebra in the staggered fermion Hamiltonian.
Third, we give a microscopic lattice understanding of T-duality in quantum spin chains using non-invertible symmetry. This non-invertible symmetry, together with lattice momentum and winding symmetries, also enforces gaplessness, hence providing a novel way to realize perturbative anomalies in quantum spin-chain models. Fourth, we show that in local lattice models of spinless fermions, fermion-number conservation combined with a non-onsite Majorana translation symmetry enforces a Fermi surface. This symmetry-enforced Fermi surface is a strong form of symmetry-enforced gaplessness. Finally, we introduce a framework of stratified symmetries and stratified anomalies to understand and discover new Lieb–Schultz–Mattis constraints. We apply this framework to modulated symmetries and find an explicit criterion for when local anomaly data imply obstructions to a trivial gapped phase. Together, these results demonstrate the broad applicability and power of symmetry and its generalizations, both for organizing quantum phases and for deriving robust non-perturbative constraints.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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