2024/06/08 by Su, Hang, Yao, Yuan, Furusaki, Akira
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech) #Strongly Correlated Electrons (cond-mat.str-el)
paper · doi:10.48550/arxiv.2406.05407
We show that the ground-state expectation value of twisting operator is a topological order parameter for U(1)- and ℤN-symmetric symmetry-protected topological (SPT) phases in one-dimensional "spin" systems -- it is quantized in the thermodynamic limit and can be used to identify different SPT phases and to diagnose phase transitions among them. We prove that this (non-local) order parameter must take values in N-th roots of unity, and its value can be changed by a generalized lattice translation acting as an N-ality transformation connecting distinct phases. This result also implies the Lieb-Schultz-Mattis ingappability for SU(N) spins if we further impose a general translation symmetry. Furthermore, our exact result for the order parameter of SPT phases can predict a large number of LSM ingappabilities by the general lattice translation. We also apply the N-ality property to provide an efficient way to construct possible multi-critical phase transitions starting from a single Hamiltonian with a unique gapped ground state.