Exact relationship between the entanglement entropies of XY and quantum Ising chains

Abstract

We consider two prototypical quantum models, the spin-1/2 XY chain and the quantum Ising chain and study their entanglement entropy, S(l,L), of blocks of l spins in homogeneous or inhomogeneous systems of length L. By using two different approaches, free-fermion techniques and perturbational expansion, an exact relationship between the entropies is revealed. Using this relation we translate known results between the two models and obtain, among others, the additive constant of the entropy of the critical homogeneous quantum Ising chain and the effective central charge of the random XY chain.

6 pages

References in corpus (9)

• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Evolution of entanglement after a local quench
• Entanglement scaling in critical two-dimensional fermionic and bosonic systems
• Scaling of Entanglement Entropy in the Random Singlet Phase
• Entanglement entropy at infinite randomness fixed points in higher dimensions
• Entanglement entropy of aperiodic quantum spin chains
• Entanglement in the XX spin chain with an energy current
• Comb entanglement in quantum spin chains
• Finite-size scaling of pseudo-critical point distributions in the random transverse-field Ising chain

Cited by in corpus (28)

• Entanglement entropy of two disjoint blocks in XY chains
• Unusual Corrections to Scaling in Entanglement Entropy
• Universal parity effects in the entanglement entropy of XX chains with open boundary conditions
• On the partial transpose of fermionic Gaussian states
• Universal corrections to scaling for block entanglement in spin-1/2 XX chains
• Coherent and dissipative dynamics at quantum phase transitions
• Entanglement spectrum of random-singlet quantum critical points
• Solution of the fermionic entanglement problem with interface defects
• Entanglement in a periodic quench
• Entanglement spectrum degeneracy and Cardy formula in 1+1 dimensional conformal field theories
• Global quantum correlations in finite-size spin chains
• Universal front propagation in the quantum Ising chain with domain-wall initial states
• Entanglement Hamiltonians: from field theory, to lattice models and experiments
• Non-equilibrium quantum impurity problems via matrix-product states in the temporal domain
• Universal behavior of a bipartite fidelity at quantum criticality
• Finite-size scaling of the entanglement entropy of the quantum Ising chain with homogeneous, periodically modulated and random couplings
• Entanglement Hamiltonians for non-critical quantum chains
• Corrections to scaling for block entanglement in massive spin-chains
• Entanglement in composite free-fermion systems
• Entanglement in non-critical inhomogeneous quantum chains
• Entanglement entropy of the $Q\ge 4$ quantum Potts chain
• Corrections to the singlet-length distribution and the entanglement entropy in random singlet phases
• Entanglement entropy of random partitioning
• Quantum Renyi relative entropies on a spin chain with interface defects
• Multipartite Entanglement in the Random Ising Chain
• Entanglement across extended random defects in the XX spin chain
• Quantized and maximum entanglement from sublattice symmetry
• Comparing quantum complexity and quantum fidelity