Density of defects and the scaling law of the entanglement entropy in quantum phase transition of one-dimensional spin systems induced by a quench

Journal Article · Tue Mar 15 04:00:00 EDT 2011 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.83.032312· OSTI ID:21537407

Basu, Banasri; Bandyopadhyay, Pratul; Majumdar, Priyadarshi ^[1]

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1. Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700 108 (India)

We have studied quantum phase transition induced by a quench in different one-dimensional spin systems. Our analysis is based on the dynamical mechanism which envisages nonadiabaticity in the vicinity of the critical point. This causes spin fluctuation which leads to the random fluctuation of the Berry phase factor acquired by a spin state when the ground state of the system evolves in a closed path. The two-point correlation of this phase factor is associated with the probability of the formation of defects. In this framework, we have estimated the density of defects produced in several one-dimensional spin chains. At the critical region, the entanglement entropy of a block of L spins with the rest of the system is also estimated which is found to increase logarithmically with L. The dependence on the quench time puts a constraint on the block size L. It is also pointed out that the Lipkin-Meshkov-Glick model in point-splitting regularized form appears as a combination of the XXX model and Ising model with magnetic field in the negative z axis. This unveils the underlying conformal symmetry at criticality which is lost in the sharp point limit. Our analysis shows that the density of defects as well as the scaling behavior of the entanglement entropy follows a universal behavior in all these systems.

• OSTI ID: 21537407
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 3 Vol. 83; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
ANGULAR MOMENTUM
CONFORMAL INVARIANCE
CORRELATIONS
CRYSTAL MODELS
DIMENSIONLESS NUMBERS
ENTROPY
FLUCTUATIONS
INVARIANCE PRINCIPLES
ISING MODEL
MAGNETIC FIELDS
MATHEMATICAL MODELS
ONE-DIMENSIONAL CALCULATIONS
PARTICLE PROPERTIES
PHASE TRANSFORMATIONS
PHYSICAL PROPERTIES
POWER FACTOR
PROBABILITY
QUANTUM ENTANGLEMENT
RANDOMNESS
SCALING LAWS
SPIN
THERMODYNAMIC PROPERTIES
VARIATIONS