Entanglement entropy of aperiodic quantum spin chains

Abstract

We study the entanglement entropy of blocks of contiguous spins in non-periodic (quasi-periodic or more generally aperiodic) critical Heisenberg, XX and quantum Ising spin chains, e.g. in Fibonacci chains. For marginal and relevant aperiodic modulations, the entanglement entropy is found to be a logarithmic function of the block size with log-periodic oscillations. The effective central charge, c_eff, defined through the constant in front of the logarithm may depend on the ratio of couplings and can even exceed the corresponding value in the homogeneous system. In the strong modulation limit, the ground state is constructed by a renormalization group method and the limiting value of c_eff is exactly calculated. Keeping the ratio of the block size and the system size constant, the entanglement entropy exhibits a scaling property, however, the corresponding scaling function may be nonanalytic.

6 pages, 2 figures

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• Increasing of entanglement entropy from pure to random quantum critical chains
• Low-energy properties of aperiodic quantum spin chains
• New Universality Class in the S=1/2 Fibonacci Heisenberg Chains
• Real Space Renormalization Group Study of the S=1/2 XXZ Chains with Fibonacci Exchange Modulation

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• 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