No abstract

We investigate thermal properties of the X-Cube model and its Z p "clocktype" (pX-Cube) extension. In the latter, the elementary spin-1/2 operators of the X-Cube model are replaced by elements of the Weyl algebra. We study different boundary condition realizations of these models and analyze their finite temperature dynamics and thermodynamics. We find that (i) no finite temperature phase transitions occur in these systems. In tandem, employing bond-algebraic dualities, we show that for Glauber type solvable baths, (ii) thermal fluctuations might not enable system size dependent time autocorrelations at all positive temperatures (i.e., they are thermally fragile). Qualitatively, our results demonstrate that similar to Kitaev's toric code model, the X-Cube model (and its p-state clock-type descendants) may be mapped to simple classical Ising (p-state clock) chains in which neither phase transitions nor anomalously slow glassy dynamics might appear.

Stabilizer code quantum Hamiltonians have been introduced with the intention of physically realizing a quantum memory because of their resilience to decoherence. In order to analyze their finite temperature thermodynamics, we show how to generically solve their partition function using duality techniques. By unveiling each model's universality class and effective dimension, insights may be gained on their finite temperature dynamics and robustness. Our technique is demonstrated in particular on the 4D Toric Code and Haah's Code -we find that the former falls into the 4D Ising universality class, whereas Haah's Code exhibits dimensional reduction and falls into the 1D Ising universality class.

No abstract