Entanglement, fidelity and topological entropy in a quantum phase transition to topological order

Abstract

We present a numerical study of a quantum phase transition from a spin-polarized to a topologically ordered phase in a system of spin-1/2 particles on a torus. We demonstrate that this non-symmetry-breaking topological quantum phase transition (TOQPT) is of second order. The transition is analyzed via the ground state energy and fidelity, block entanglement, Wilson loops, and the recently proposed topological entropy. Only the topological entropy distinguishes the TOQPT from a standard QPT, and remarkably, does so already for small system sizes. Thus the topological entropy serves as a proper order parameter. We demonstrate that our conclusions are robust under the addition of random perturbations, not only in the topological phase, but also in the spin polarized phase and even at the critical point.

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References in corpus (8)

• Quantum critical scaling of the geometric tensors
• Quantum Phase Transitions and Bipartite Entanglement
• Bipartite entanglement and entropic boundary law in lattice spin systems
• Entanglement in a second order quantum phase transition
• Ground state entanglement and geometric entropy in the Kitaev's model
• Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension
• A quantum topological phase transition at the microscopic level
• Adiabatic Preparation of Topological Order

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