Entanglement entropy in quantum spin chains with broken reflection symmetry

Journal Article · Wed Sep 15 00:00:00 EDT 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.82.032334· OSTI ID:21448672

Kadar, Zoltan; Zimboras, Zoltan ^[1]

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1. Institute for Scientific Interchange Foundation, Villa Gualino, Viale Settimio Severo 75, I-10131 Torino (Italy)

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 are calculated analytically for general gauge-invariant models, which have, until now, been done only for the reflection-symmetric sector. Analytical results are also derived for certain nongauge-invariant models (e.g., for the Ising model with Dzyaloshinskii-Moriya interaction). We also study numerically finite chains of length N with a nonreflection-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 noncritical 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.

• OSTI ID: 21448672
• Journal Information: Physical Review. A, Vol. 82, Issue 3; Other Information: DOI: 10.1103/PhysRevA.82.032334; (c) 2010 The American Physical Society; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ASYMPTOTIC SOLUTIONS
ENTROPY
FERMIONS
GAUGE INVARIANCE
HAMILTONIANS
ISING MODEL
QUANTUM ENTANGLEMENT
REFLECTION
SPIN
SYMMETRY
SYMMETRY BREAKING
ANGULAR MOMENTUM
CRYSTAL MODELS
INVARIANCE PRINCIPLES
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATHEMATICAL SOLUTIONS
PARTICLE PROPERTIES
PHYSICAL PROPERTIES
QUANTUM OPERATORS
THERMODYNAMIC PROPERTIES