Whether it is valid to mapping Z2 gauge field into 1D transverse Ising chains

[jywu20]

The gauge choice $\sigma^z_\text{horizontal bonds} = 1$ does not commute with the string tension term $-h \sum_i \sigma^x_i$. Does this gauge fixing step used in 1812.05621 really work for a generic Z_2 gauge theory???

[jywu20]

After some discussion we conclude the short answer is "no". When h=0, however, the picture of "a bundle of separate spin chains" is useful because it demonstrates the absence of thermal phase transition.

[jywu20]

Things yet to do is to edit note.tex.