On Quantum Entanglement in Topological Phases on a Torus
arXiv:1603.01777 · doi:10.1103/PhysRevB.94.075126
Abstract
In this paper we study the effect of non-trivial spatial topology on quantum entanglement by examining the degenerate ground states of a topologically ordered system on torus. Using the string-net (fixed-point) wave-function, we propose a general formula of the reduced density matrix when the system is partitioned into two cylinders. The cylindrical topology of the subsystems makes a significant difference in regard to entanglement: a global quantum number for the many-body states comes into play, together with a decomposition matrix which describes how topological charges of the ground states decompose into boundary degrees of freedom. We obtain a general formula for entanglement entropy and generalize the concept of minimally entangled states to minimally entangled sectors. Concrete examples are demonstrated with data from both finite groups and modular tensor categories (i.e., Fibonacci, Ising, etc.), supported by numerical verification.
v2. more references added; v3: submitted version
References in corpus (12)
- Non-Abelian Anyons and Topological Quantum Computation
- Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
- Identifying Topological Order by Entanglement Entropy
- Condensate induced transitions between topologically ordered phases
- Bipartite entanglement and entropic boundary law in lattice spin systems
- Ground state entanglement and geometric entropy in the Kitaev's model
- Topological boundary conditions in abelian Chern-Simons theory
- Entanglement renormalization and topological order
- Boson Condensation in Topologically Ordered Quantum Liquids
- Ground State Degeneracy of Topological Phases on Open Surfaces
- Charged Topological Entanglement Entropy
- Tensor-product representations for string-net condensed states