Enforced Gaplessness from States with Exponentially Decaying Correlations

Understand

It is well known that an exponentially localized Hamiltonian must be gapless if its ground state has algebraic correlations.

• We show that even certain exponentially decaying correlations can imply gaplessness.
• This is exemplified by the deformed toric code $\propto \exp(\beta \sum_{\ell} Z_{\ell}) |\mathsf{TC}\rangle$, where $|\mathsf{TC}\rangle$ is a fixed-point toric code wavefunction.
• Although it has a confined regime for $\beta > \beta_c$, recent work has drawn attention to its perimeter law loop correlations.