The entanglement negativity in random spin chains

Abstract

We investigate the logarithmic negativity in strongly-disordered spin chains in the random-singlet phase. We focus on the spin-1/2 random Heisenberg chain and the random XX chain. We find that for two arbitrary intervals the disorder-averaged negativity and the mutual information are proportional to the number of singlets shared between the two intervals. Using the strong-disorder renormalization group (SDRG), we prove that the negativity of two adjacent intervals grows logarithmically with the intervals length. In particular, the scaling behavior is the same as in conformal field theory, but with a different prefactor. For two disjoint intervals the negativity is given by a universal simple function of the cross ratio, reflecting scale invariance. As a function of the distance of the two intervals, the negativity decays algebraically in contrast with the exponential behavior in clean models. We confirm our predictions using a numerical implementation of the SDRG method. Finally, we also implement DMRG simulations for the negativity in open spin chains. The chains accessible in the presence of strong disorder are not sufficiently long to provide a reliable confirmation of the SDRG results.

16 pages, 11 figures

References in corpus (27)

• The density-matrix renormalization group in the age of matrix product states
• Entanglement negativity in quantum field theory
• Entanglement spectrum in one-dimensional systems
• Entanglement entropy of two disjoint intervals in conformal field theory II
• Mutual Information and Boson Radius in c=1 Critical Systems in One Dimension
• Finite temperature entanglement negativity in conformal field theory
• Scaling of Entanglement Entropy in the Random Singlet Phase
• Entanglement negativity in the harmonic chain out of equilibrium
• Entanglement negativity after a global quantum quench
• On the partial transpose of fermionic Gaussian states
• Scaling of entanglement between separated blocks in spin chains at criticality
• Comments on Entanglement Negativity in Holographic Field Theories
• Entanglement negativity and entropy in non-equilibrium conformal field theory
• Conformal Blocks and Negativity at Large Central Charge
• Entanglement entropy and negativity of disjoint intervals in CFT: Some numerical extrapolations
• Entanglement spectrum of random-singlet quantum critical points
• Entanglement entropy at infinite randomness fixed points in higher dimensions
• Entanglement Entropy in the Two-Dimensional Random Transverse Field Ising Model
• An order parameter for impurity systems at quantum criticality
• Entanglement entropy of aperiodic quantum spin chains
• Correlation amplitude and entanglement entropy in random spin chains
• Increasing of entanglement entropy from pure to random quantum critical chains
• Finite-size scaling of the entanglement entropy of the quantum Ising chain with homogeneous, periodically modulated and random couplings
• Entanglement entropy of the random spin-1 Heisenberg chain
• Protecting clean critical points by local disorder correlations
• Increasing entanglement through engineered disorder in the random Ising chain
• Entanglement in low-energy states of the random-hopping model

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