Lieb-Schultz-Mattis anomalies and web of dualities induced by gauging in quantum spin chains

Lieb-Schultz-Mattis (LSM) theorems impose non-perturbative constraints on the zero temperature phase diagrams of quantum lattice Hamiltonians. LSM theorems have recently been interpreted as the lattice counterparts to mixed ’t Hooft anomalies in quantum field theories that arise from a combination of crystalline and global internal symmetry groups. In this talk, we provide a systematic diagnostic for LSM anomalies in one spatial dimension. We show that gauging subgroups of the global internal symmetry group of a quantum lattice model obeying an LSM anomaly delivers a dual quantum lattice Hamiltonian such that its internal and crystalline symmetries mix non-trivially through a group extension, a direct consequence of the LSM anomaly. We exemplify this procedure for a quantum spin-1/2 chain obeying an LSM anomaly resulting from combining a global internal Z₂ × Z₂ symmetry with translation or reflection symmetry. We establish a triality of models by gauging a Z₂ ⊂ Z₂ × Z₂ symmetry in two ways, one of which amounts to performing a Kramers-Wannier duality, while the other implements a Jordan-Wigner duality. We discuss the mapping of the phase diagram of the quantum spin-1/2 XYZ chains under such a triality. We show that the deconfined quantum critical transitions between Neel and dimer orders are mapped to either topological or conventional Landau-Ginzburg transitions.