CMSA Quantum Matter in Mathematics and Physics: Quantum Algorithms to Recognize Phases of Matter and Exactly Solvable 2D Models with Anomalous Entanglement Entropy

In this talk, I will report my two recent results at the intersection of quantum information and strongly interacting phases of matters.

In the first half of the talk, we describe exact quantum algorithms that recognize a class of 1D gapped phases, namely symmetry protected topological phases or spontaneous symmetry breaking phases protected by abelian internal symmetry. The key idea is to observe the conceptual similarity between renormalization group (RG) flow and error correction, and to implement the latter as unitary circuits emulating the RG flow. Our algorithm guarantees faithful recognition of a target phase with a small number of input quantum state samples.

In the second half, we present a class of 2D Hamiltonians, where the exact ground state wavefunctions can be exactly evaluated and shown to exhibit anomalous entanglement properties. One class of our models exhibit area-law scaling entanglement entropy, but this is mostly due to non-local correlation: one finds that the topological entanglement entropy also scales with the size of subsystem choices. By making simple modifications, we can also devise 2D models with volume-law scaling bipartite entanglement entropy. Our results can be understood as a generation of the 1D Motzkin model to 2D systems.

Based on:
Work done with Ethan Lake and Shankar Balasubramanian
https://arxiv.org/abs/2211.09803
https://arxiv.org/abs/2305.07028

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