Entanglement entropy in quantum spin chains with broken parity number symmetry

Abstract

Consider a generic quantum spin chain that can be mapped to free quadratic fermions via Jordan-Wigner (JW) transformation. In the presence of arbitrary boundary magnetic fields, this Hamiltonian is no longer a quadratic Hamiltonian after JW transformation. Using ancillary sites and enlarging the Hamiltonian we first introduce a bigger quadratic Hamiltonian. Then we diagonalize this enlarged Hamiltonian in its most generic form and show that all the states are degenerate because of the presence of a zero mode. The eigenstates of the original spin chain with boundary magnetic fields can be derived after appropriate projection. We study in-depth the properties of the eigenstates of the enlarged Hamiltonian. In particular, we find: 1) the eigenstates in configuration bases, 2) calculate all the correlation functions, 3) find the reduced density matrices, 4) calculate the entanglement entropy. We show that the generic eigenstate of the enlarged Hamiltonian (including the eigenstates of the original spin chain) breaks the parity number symmetry and consequently one needs to take care of some technicalities regarding the calculation of the reduced density matrix and entanglement entropy. Interestingly we show that the entanglement structure of these eigenstates is quite universal and independent of the Hamiltonian. We support our results by applying them to a couple of examples.

57 pages. 5 figures; typos corrected

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• Entanglement of low-energy excitations in Conformal Field Theory
• Entanglement in fermionic systems
• Quantum phase transitions and quantum fidelity in free fermion graphs
• Universal parity effects in the entanglement entropy of XX chains with open boundary conditions
• Antiperiodic spin-1/2 XXZ quantum chains by separation of variables: Complete spectrum and form factors
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Cited by in corpus (3)

• Non-equilibrium entanglement asymmetry for discrete groups: the example of the XY spin chain
• Generalization of Balian-Brezin decomposition for exponentials with linear fermionic part
• Rényi entropies for one-dimensional quantum systems with mixed boundary conditions