Entanglement entropy of the random spin-1 Heisenberg chain

Abstract

Random spin chains at quantum critical points exhibit an entanglement entropy between a segment of length L and the rest of the chain that scales as log_2 L with a universal coefficient. Since for pure quantum critical spin chains this coefficient is fixed by the central charge of the associated conformal field theory, the universal coefficient in the random case can be understood as an effective central charge. In this paper we calculate the entanglement entropy and effective central charge of the spin-1 random Heisenberg model in its random-singlet phase and also at the critical point at which the Haldane phase breaks down. The latter is the first entanglement calculation for an infinite-randomness fixed point that is not in the random-singlet universality class. Our results are consistent with a c-theorem for flow between infinite-randomness fixed points. The formalism we use can be generally applied to calculation of quantities that depend on the RG history in s>=1 random Heisenberg chains.

arXiv commentSubmitted to PRB; references added

References in corpus (25)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Entanglement Entropy and Quantum Field Theory
• Entanglement in quantum critical phenomena
• Aspects of Holographic Entanglement Entropy
• Entropy and Area
• Geometric and Renormalized Entropy in Conformal Field Theory
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Violation of the entropic area law for Fermions
• Strong disorder RG approach of random systems
• Entanglement entropy of random quantum critical points in one dimension
• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• Griffiths effects and quantum critical points in dirty superconductors without spin-rotation invariance: One-dimensional examples
• Random Walkers in 1-D Random Environments: Exact Renormalization Group Analysis
• Scaling of Entanglement Entropy in the Random Singlet Phase
• An Impurity Driven Phase Transition in the Antiferromagnetic Spin-1 Chain
• Infinite-Randomness Fixed Points for Chains of Non-Abelian Quasiparticles
• Entanglement entropy of aperiodic quantum spin chains
• Low-energy fixed points of random Heisenberg models
• The Thermodynamics of Quantum Systems and Generalizations of Zamolodchikov's C-theorem
• Phases of random antiferromagnetic spin-1 chains
• Spin Reduction Transition in Spin-3/2 Random Heisenberg Chains
• Permutation-Symmetric Multicritical Points in Random Antiferromagnetic Spin Chains
• Phase diagram of the random Heisenberg antiferromagnetic spin-1 chain
• Random Spin-1 Quantum Chains
• Griffiths Effects in Random Heisenberg Antiferromagnetic S=1 Chains

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• Strong Disorder RG approach - a short review of recent developments
• Criticality and entanglement in random quantum systems
• Entanglement entropy dynamics of disordered quantum spin chains
• Entanglement spectrum of random-singlet quantum critical points
• Entanglement entropy at infinite randomness fixed points in higher dimensions
• Infinite-Randomness Fixed Points for Chains of Non-Abelian Quasiparticles
• Entanglement Entropy in the Two-Dimensional Random Transverse Field Ising Model
• Entanglement entropy with localized and extended interface defects
• Bi-partite entanglement entropy in massive two-dimensional quantum field theory
• Correlation amplitude and entanglement entropy in random spin chains
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• Scaling of Entanglement Entropy at 2D quantum Lifshitz fixed points and topological fluids
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• Exact valence bond entanglement entropy and probability distribution in the XXX spin chain and the Potts model
• Nonadditive entropy for random quantum spin-S chains
• Infinite Randomness Phases and Entanglement Entropy of the Disordered Golden Chain
• Entanglement properties of correlated random spin chains and similarities with conformal invariant systems
• Negativity Spectrum in the Random Singlet Phase
• Self-assembling tensor networks and holography in disordered spin chains
• Entanglement renormalization for disordered systems
• Magnetization dynamics in clean and disordered spin-1 XXZ chains
• Random elastic networks : strong disorder renormalization approach
• Entanglement area law violation from field-curvature coupling
• Dynamics of decoherence of an entangled pair of qubits locally connected to a one-dimensional disordered spin chain
• Adaptive Density Matrix Renormalization Group for Disordered Systems
• Exact Results for the Bipartite Entanglement Entropy of the AKLT spin-1 chain
• Concurrence in Disordered Systems
• Entanglement entropy of the $Q\ge 4$ quantum Potts chain
• Entanglement entropy and localization in disordered quantum chains
• Effect of double local quenches on Loschmidt echo and entanglement entropy of a one-dimensional quantum system
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• Dynamical properties of the Haldane chain with bond disorder
• Scaling of entanglement entropy at quantum critical points in random spin chains
• Entanglement entropy of a three-spin interacting spin chain with a time-reversal breaking impurity at one boundary
• Comparative analysis of robust entanglement generation in engineered XX spin chains