Emergent quantum criticality from fractionalizing one-dimensional SO(5) symmetric valence-bond solid states

Abstract

A common feature of topological phases of matter is the fractionalization of the quantum number in their low-energy excitations. Such information is encoded in their ground state wave functions, but emerges in the bipartite entanglement spectra. The symmetric extensive bipartition is an effective novel method to create deconfined fractionalized edge particles in the reduced subsystem, which lead to quantum critical behavior associated with the transition from the topological phase to its adjacent trivial phase. Here we report the interesting results revealed by applying this method to the one-dimensional SO(5) symmetric valence-bond solid state being a spin-2 symmetry protected topological phase. From the finite-size entanglement spectrum, we find the lowest level to be an SO(5) singlet with a logarithmic entanglement entropy. Surprisingly, the first excited level is also an SO(5) singlet and the spectral gap scales with the subsystem size as ${L}_{A}^{\ensuremath{-}\ensuremath{\nu}}$ with $\ensuremath{\nu}\ensuremath{\simeq}1.978$. In the thermodynamic limit, a novel quantum criticality emerges with SO(5) spinons and their four-body singlet bound states as elementary excitations, hence ruling out the possibility of being described by a conformal field theory. Moreover, the entanglement Hamiltonian can be determined as an SO(5) symmetric nearest neighbor spin-3/2 quadruple-quadruple interaction with a negative coupling. Our work thus demonstrates the power of this new method in the study of quantum criticality encoded in the topological ground states.