Entanglement entropy in quantum spin chains with broken reflection symmetry

Abstract

We investigate the entanglement entropy of a block of L sites in quasifree translation-invariant spin chains concentrating on the effect of reflection symmetry breaking. The majorana two-point functions corresponding to the Jordan-Wigner transformed fermionic modes are determined in the most general case; from these it follows that reflection symmetry in the ground state can only be broken if the model is quantum critical. The large L asymptotics of the entropy is calculated analytically for general gauge-invariant models, which has, until now, been done only for the reflection symmetric sector. Analytical results are also derived for certain non-gauge-invariant models, e.g., for the Ising model with Dzyaloshinskii-Moriya interaction. We also study numerically finite chains of length N with a non-reflection-symmetric Hamiltonian and report that the reflection symmetry of the entropy of the first L spins is violated but the reflection-symmetric Calabrese-Cardy formula is recovered asymptotically. Furthermore, for non-critical reflection-symmetry-breaking Hamiltonians, we find an anomaly in the behavior of the "saturation entropy" as we approach the critical line. The paper also provides a concise but extensive review of the block entropy asymptotics in translation invariant quasifree spin chains with an analysis of the nearest neighbor case and the enumeration of the yet unsolved parts of the quasifree landscape.

12 pages and 4 figures

References in corpus (14)

• Reduced density matrices and entanglement entropy in free lattice models
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Parity effects in the scaling of block entanglement in gapless spin chains
• Phase Diagram and Entanglement of Ising Model With Dzyaloshinskii-Moriya Interaction
• Unusual Corrections to Scaling in Entanglement Entropy
• Valence bond solids for SU(n) spin chains: exact models, spinon confinement, and the Haldane gap
• Exact relationship between the entanglement entropies of XY and quantum Ising chains
• Entanglement in the XX spin chain with an energy current
• Exact entanglement entropy of the XYZ model and its sine-Gordon limit
• Entanglement entropy in quantum spin chains with finite range interaction
• Dynamic probes of quantum spin chains with the Dzyaloshinskii-Moriya interaction
• Finite-size scaling of the entanglement entropy of the quantum Ising chain with homogeneous, periodically modulated and random couplings
• Time Asymptotics and Entanglement Generation of Clifford Quantum Cellular Automata
• Spontaneous Parity Violation in a Quantum Spin Chain

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