Entanglement entropy fluctuations in quantum Ising chains

Journal Article · Fri Oct 15 04:00:00 EDT 2010 · Journal of Experimental and Theoretical Physics

DOI:https://doi.org/10.1134/S1063776110100018· OSTI ID:21443378

The behavior of Ising chains with the spin-spin interaction value {lambda} in a transverse magnetic field of constant intensity (h = 1) is considered. For a chain of infinite length, exact analytical formulas are obtained for the second central moment (dispersion) of the entropy operator S = -ln{rho} with reduced density matrix {rho}, which corresponds to a semi-infinite part of the model chain occurring in the ground state. In the vicinity of a critical point {lambda}{sub c} = 1, the entanglement entropy fluctuation {Delta}S (defined as the square root of dispersion) diverges as {Delta}S {approx} [ln(1/ vertical bar 1 - {lambda} vertical bar )]{sup 1/2}. For the known behavior of the entanglement entropy S, this divergence results in that the relative fluctuation {delta}S = {Delta}S/S vanishes at the critical point, that is, a state with almost nonfluctuating entanglement is attained.

• OSTI ID: 21443378
• Journal Information: Journal of Experimental and Theoretical Physics, Journal Name: Journal of Experimental and Theoretical Physics Journal Issue: 4 Vol. 111; ISSN 1063-7761
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
COUPLING
CRYSTAL MODELS
DENSITY MATRIX
ENERGY LEVELS
ENTROPY
FLUCTUATIONS
GROUND STATES
INTERMEDIATE COUPLING
ISING MODEL
J-J COUPLING
MAGNETIC FIELDS
MATHEMATICAL MODELS
MATRICES
PHYSICAL PROPERTIES
QUANTUM ENTANGLEMENT
THERMODYNAMIC PROPERTIES
VARIATIONS