Scaling of entanglement entropy in a quantum phase transition in the transverse Ising model induced by a quench

Journal Article · Fri Jan 15 04:00:00 EST 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.81.012311· OSTI ID:21388697

Majumdar, Priyadarshi; Bandyopadhyay, Pratul ^[1]

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1. Jyotinagar Bidyasree Niketan H. S. School, 41 Jyotinagar, Kolkata 700 108 (India)

It is known that at the critical point of a zero-temperature quantum phase transition in a one-dimensional spin system the entanglement entropy of a block of L spins with the rest of the system scales logarithmically with L with a prefactor determined by the central charge of the relevant conformal field theory. When we introduce critical slowing down incorporating the Kibble-Zurek mechanism of defect formation induced by a quench, the implicit nonadiabatic transition disturbs the scaling behavior. We have shown that in this case the entanglement entropy also obeys a scaling law such that it increases logarithmically with L but the prefactor depends on the quench time. This puts a constraint on the block size L so that we cannot arbitrarily choose it. Thus, the entanglement entropy obeys the scaling law only in a restrictive sense due to the formation of defects.

• OSTI ID: 21388697
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 1 Vol. 81; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANGULAR MOMENTUM
CONFORMAL INVARIANCE
CRYSTAL MODELS
ENTROPY
FIELD THEORIES
INVARIANCE PRINCIPLES
ISING MODEL
MATHEMATICAL MODELS
ONE-DIMENSIONAL CALCULATIONS
PARTICLE PROPERTIES
PHASE TRANSFORMATIONS
PHYSICAL PROPERTIES
QUANTUM ENTANGLEMENT
QUANTUM FIELD THEORY
SCALING LAWS
SLOWING-DOWN
SPIN
THERMODYNAMIC PROPERTIES