Abstract.
Condensed matter physics traditionally focuses on systems with binary local degrees of freedom, just as quantum computing focuses on operations on qubits. Yet, when the local Hilbert space dimension is enlarged even just from two to three, unexpected qualitatively different phenomena are usually in store. In this talk I will first briefly survey a few models with colour degrees of freedom as examples of relaxed frustration that results in (partially) solvability in spin chains and self-similar higher dimensional lattices. The rest of the talk focuses on 2D loop models where introducing colour reduces solvability. Quantum loop models are well studied objects in the context of lattice gauge theories and quantum error correction codes. They usually carry long range entanglement that is captured by the topological entanglement entropy. I consider new generalisations of the toric code model to bicolour loop models and show that the long range entanglement can be reflected in three different ways: a topologically invariant constant, a sub-leading logarithmic correction to the area law, or a modified bond dimension for the area-law term. The Hamiltonian is not exactly solvable for the whole spectrum, but admits a tower of area-law exact excited states corresponding to the frustration free superposition of loop configurations with arbitrary pairs of localised vertex defects. The continuity of colour along loops imposes kinetic constraints on the model and results in Hilbert space fragmentation, unless plaquette operators involving two neighbouring faces are introduced to the Hamiltonian.
References:
[1] Z Zhang, arXiv:2306.05464
[2] Z Zhang, Annals of Physics 457, 169395
[3] Z Zhang, G Mussardo, Physical Review B 106 (13), 134420
(Unless this is a blackboard talk, the slides will be available here)