Quantum phase transitions out of a Z2 x Z2 topological phase

We investigate the low-energy spectral properties and robustness of the topological phase of color code, which is a quantum spin model for the aim of fault-tolerant quantum computation, in the presence of a uniform magnetic field or Ising interactions, using high-order series expansion and exact diagonalization. In a uniform magnetic field, we find 1st-order phase transitions in all field directions. In contrast, our results for the Ising interactions unveil that for strong enough Ising couplings, the Z2 x Z2 topological phase of color code breaks down to symmetry broken phases by 1st- or 2nd-order phase transitions.