Bulk-Measurement-Induced Boundary Phase Transition in Toric Code and Gauge-Higgs Model
Abstract: Study of boundary phase transition in toric code under cylinder geometry via bulk projective measurement is reported. As the frequency of local measurement for bulk qubits is increased, spin-glass type long-range order on the boundaries emerges indicating spontaneous-symmetry breaking (SSB) of $Z_2$ symmetry. From the lattice-gauge-theory viewpoint, this SSB is a signal of a transition to Higgs phase with symmetry protected topological order. We numerically elucidate the properties of this phase transition in detail, especially its criticality, and give a physical picture using non-local gauge-invariant symmetry operators. Phase transition in the bulk is also studied and its relationship to the boundary transition is discussed.
- R. Raussendorf and H. J. Briegel, Phys. Rev. Lett. 86 5188 (2001).
- D. Gottesman, arXiv:9807006 (1997).
- A. Sorge, Pyfssa 0.7.6 (2015).
- O. Melchert, arXiv:0910.5403 (2009).
- We note that pcsubscript𝑝𝑐p_{c}italic_p start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT corresponds to the scaling function x=0𝑥0x=0italic_x = 0 in Fig. 2(b). The point x=0𝑥0x=0italic_x = 0 in the scaling function is off-peak. This implies that the ordered phase (SSB phase) emerges after strict suppression of the fluctuations of the spins on the boundary in the thermodynamic limit. This is some peculiar feature of the present system, which comes from the fact that effective couplings between boundary spins are induced by the bulk measurements and they do not exist at the onset.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.
