Finite-size scaling of the entanglement entropy of the quantum Ising chain with homogeneous, periodically modulated and random couplings

Abstract

Using free-fermionic techniques we study the entanglement entropy of a block of contiguous spins in a large finite quantum Ising chain in a transverse field, with couplings of different types: homogeneous, periodically modulated and random. We carry out a systematic study of finite-size effects at the quantum critical point, and evaluate subleading corrections both for open and for periodic boundary conditions. For a block corresponding to a half of a finite chain, the position of the maximum of the entropy as a function of the control parameter (e.g. the transverse field) can define the effective critical point in the finite sample. On the basis of homogeneous chains, we demonstrate that the scaling behavior of the entropy near the quantum phase transition is in agreement with the universality hypothesis, and calculate the shift of the effective critical point, which has different scaling behaviors for open and for periodic boundary conditions.

17 pages, 5 figures, v2: references added+updated

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Cited by in corpus (22)

• Entanglement equipartition in critical random spin chains
• Coherent and dissipative dynamics at quantum phase transitions
• Entanglement spectrum of random-singlet quantum critical points
• Global quantum correlations in finite-size spin chains
• Entanglement in spin chains with gradients
• Negativity Spectrum in the Random Singlet Phase
• Gapless symmetry-protected topological phase of quantum antiferromagnets on anisotropic triangular strip
• Probability distribution of the entanglement across a cut at an infinite-randomness fixed point
• Entanglement entropy of the long-range Dyson hierarchical model
• Study of the long-range transverse field Ising model with fermionic Gaussian states
• Mixed-order transition in the antiferromagnetic quantum Ising chain in a field
• Universal scaling of a classical impurity in the quantum Ising chain
• Entanglement in composite free-fermion systems
• Multi-fractality of the entanglement Hamiltonian eigen-modes
• Entanglement entropy of the $Q\ge 4$ quantum Potts chain
• Entanglement entropy and localization in disordered quantum chains
• Corrections to the singlet-length distribution and the entanglement entropy in random singlet phases
• Interacting Majorana modes at surfaces of noncentrosymmetric superconductors
• Multipartite Entanglement in the Random Ising Chain
• Scaling of finite size effect of $\alpha$-Rényi entropy in disjointed intervals under dilation
• Scaling of entanglement entropy at quantum critical points in random spin chains
• Boundary Criticality at the Nishimori Multicritical Point