Thermalization of Topological Entropy after a Quantum Quench
arXiv:1509.08613 · doi:10.1103/PhysRevB.94.125104
Abstract
In two spatial dimensions, topological order is robust for static deformations at zero temperature, while it is fragile at any finite temperature. How robust is topological order after a quantum quench? In this paper we show that topological order thermalizes under the unitary evolution after a quantum quench. If the quench preserves gauge symmetry, there is a residual topological entropy exactly like in the finite temperature case. We obtain this result by studying the time evolution of the topological 2-Rényi entropy in a fully analytical, exact way. These techniques can be then applied to systems with strong disorder to show whether a many-body localization phenomenon appears in topologically ordered systems.
new plot with finite time results added; typos fixed
References in corpus (38)
- Many-Body Physics with Ultracold Gases
- Non-Abelian Anyons and Topological Quantum Computation
- Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
- Thermalization and its mechanism for generic isolated quantum systems
- Many body localization and thermalization in quantum statistical mechanics
- Measuring entanglement entropy through the interference of quantum many-body twins
- Lieb-Robinson bounds and the generation of correlations and topological quantum order
- The Luttinger model following a sudden interaction switch-on
- Measuring entanglement growth in quench dynamics of bosons in an optical lattice
- Topological characterization of quantum phase transitions in a S=1/2 spin model
- Bipartite entanglement and entropic boundary law in lattice spin systems
- A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes
- Ground state entanglement and geometric entropy in the Kitaev's model
- Measuring entanglement entropy of a generic many-body system with a quantum switch
- Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension
- Propagation of Correlations in Quantum Lattice Systems
- Characterizing topological order by studying the ground states of an infinite cylinder
- Robustness of a perturbed topological phase
- General entanglement scaling laws from time evolution
- Autocorrelations and Thermal Fragility of Anyonic Loops in Topologically Quantum Ordered Systems
- Entanglement and topological entropy of the toric code at finite temperature
- Many-body mobility edge in a mean-field quantum spin glass
- Topological order in a 3D toric code at finite temperature
- Majorana Fermions, Exact Mappings between Classical and Topological Orders
- A quantum topological phase transition at the microscopic level
- Adiabatic Preparation of Topological Order
- Entanglement, fidelity and topological entropy in a quantum phase transition to topological order
- Diagnosing Deconfinement and Topological Order
- Dynamics at and near conformal quantum critical points
- Topological phases and topological entropy of two-dimensional systems with finite correlation length
- Robustness of a topological phase: Topological color code in parallel magnetic field
- Probing topological order with Rényi entropy
- The Non-Equilibrium Reliability of Quantum Memories
- Exact results on the quench dynamics of the entanglement entropy in the toric code
- Quantum entanglement in states generated by bilocal group algebras
- Focus on topological quantum computation
- The Kitaev-Ising model, Transition between topological and ferromagnetic order
- Identifying Quantum Topological Phases Through Statistical Correlation
Cited by in corpus (11)
- Anyonic self-induced disorder in a stabilizer code: quasi-many body localization in a translational invariant model
- Long-lived topological time-crystalline order on a quantum processor
- Multipartite entanglement of the topologically ordered state in a perturbed toric code
- Nonequilibrium symmetry-protected topological order: emergence of semilocal Gibbs ensembles
- Quantum Coherence in Ergodic and Many-Body Localized Systems
- Logarithmic light cone, slow entanglement growth, and quantum memory
- Quench of symmetry broken ground states
- Bounded light cone and robust topological order out of equilibrium
- Diagonal Entropy and Topological Phase Transitions in Extended Kitaev Chains
- Protecting topological order by dynamical localization
- Disorder-protected topological entropy after a quantum quench