Local response of topological order to an external perturbation

Abstract

We study the behavior of the Rényi entropies for the toric code subject to a variety of different perturbations, by means of 2D density matrix renormalization group and analytical methods. We find that Rényi entropies of different index α display derivatives with opposite sign, as opposed to typical symmetry breaking states, and can be detected on a very small subsystem regardless of the correlation length. This phenomenon is due to the presence in the phase of a point with flat entanglement spectrum, zero correlation length, and area law for the entanglement entropy. We argue that this kind of splitting is common to all the phases with a certain group theoretic structure, including quantum double models, cluster states, and other quantum spin liquids. The fact that the size of the subsystem does not need to scale with the correlation length makes it possible for this effect to be accessed experimentally.

updated to published version

References in corpus (13)

• Non-Abelian Anyons and Topological Quantum Computation
• Bipartite entanglement and entropic boundary law in lattice spin systems
• Ground state entanglement and geometric entropy in the Kitaev's model
• Measuring entanglement entropy of a generic many-body system with a quantum switch
• Characterizing topological order by studying the ground states of an infinite cylinder
• Applying matrix product operators to model systems with long-range interactions
• A quantum topological phase transition at the microscopic level
• Entanglement, fidelity and topological entropy in a quantum phase transition to topological order
• Catalytic Conversion Probabilities for Bipartite Pure States
• Necessary and Sufficient Conditions for the Trumping Relation
• Topological phases and topological entropy of two-dimensional systems with finite correlation length
• Fate of the cluster state on the square lattice in a magnetic field
• Quantum entanglement in states generated by bilocal group algebras

Cited by in corpus (17)

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• Local characterization of 1d topologically ordered states
• Local convertibility and the quantum simulation of edge states in many-body systems
• Characterizing Genuine Multisite Entanglement in Isotropic Spin Lattices
• Entanglement convertibility by sweeping through the quantum phases of the alternating bonds $XXZ$ chain
• On the robustness of topological quantum codes: Ising perturbation
• The Kitaev-Ising model, Transition between topological and ferromagnetic order
• Local convertibility of the ground state of the perturbed Toric code
• Non universality of entanglement convertibility
• Thermalization of Topological Entropy after a Quantum Quench
• Quantum phase transition in the $Z_3$ Kitaev-Potts model
• Long- and short-range interaction footprints in entanglement entropies of two-particle Wigner molecules in 2D quantum traps
• Detecting dimensional crossover and finite Hilbert space through entanglement entropies
• Stability of topological purity under random local unitaries
• Free fermion representation of the topological surface code
• Tighter monogamy relations for the Tsallis-q and Rényi-$\alpha$ entanglement in multiqubit systems