An entropic invariant for 2D gapped quantum phases

Abstract

We introduce an entropic quantity for two-dimensional (2D) quantum spin systems to characterize gapped quantum phases modeled by local commuting projector code Hamiltonians. The definition is based on a recently introduced specific operator algebra defined on an annular region, which encodes the superselection sectors of the model. The quantity is calculable from local properties, and it is invariant under any constant-depth local quantum circuit, and thus an indicator of gapped quantum spin-liquids. We explicitly calculate the quantity for Kitaev's quantum double models, and show that the value is exactly same as the topological entanglement entropy of the models. Our method circumvents some of the problems around extracting the TEE, allowing us to prove invariance under constant-depth quantum circuits.

On the Stability of Charges in Infinite Quantum Spin Systems

“…This result was generalized to Hamiltonians with non-commuting terms by Michalakis and Zwolak [48]. Existing results regarding the stability properties of the anyon structure are however rather limited, but see [12,32,38,40]. Our methods are applicable to a wider class of models and retain more of the structure of the anyons.…”

Intermediate symmetric construction of transformation between anyon and Gentile statistics

“…Fractional statistics are applied in many hot fields of physics. For instance, topological quantum computation [16][17][18], quantum phase [19][20][21], quantum information [22,23], solving many-body interacting problem approximately using quantum field method [24][25][26][27], and quantum materials [28,29].…”