Quantum Critical Spin-2 Chain with Emergent SU(3) Symmetry

We study the quantum critical phase of an SU(2) symmetric spin-2 chain obtained from spin-2 bosons in a one-dimensional lattice. We obtain the scaling of the finite-size energies and entanglement entropy by exact diagonalization and density-matrix renormalization group methods. From the numerical results of the energy spectra, central charge, and scaling dimension we identify the conformal field theory describing the whole critical phase to be the $\mathrm{SU}(3{)}_1$ Wess-Zumino-Witten model. We find that, while the Hamiltonian is only SU(2) invariant, in this critical phase there is an emergent SU(3) symmetry in the thermodynamic limit.

Figure 1

Rescaled energy spectrum obtained from exact diagonalization with $L=15$ and $\overrightarrow{\epsilon }=(0,-1,0)$.

Figure 2

(a) Finite-size scaling of the ground state energy $E_g(L)$. (b) Finite-size scaling of the spin-wave velocity $v(L)$. (c) Finite-size scaling of the scaling dimension $x(L)$, which is obtained from excited state energies by applying the sum rule as described in the text.

Figure 3

$c(L,m)$ as a function of the DMRG truncation number $m$ of SU(2) states for various systems sizes $L$ with $\overrightarrow{\epsilon }=(0,-1,0)$. The $m=2800$ states are equivalent to at least about 25000 standard DMRG states.