Huan-Qiang Zhou et al 2008 J. Phys. A: Math. Theor. 41 492002 doi:10.1088/1751-8113/41/49/492002
Huan-Qiang Zhou, Jian-Hui Zhao and Bo Li
Show affiliationsWe analyze the fidelity per lattice site for two different ground states of the one-dimensional quantum Ising model in a transverse field near the critical point. It is found that, in the thermodynamic limit, the fidelity per lattice site is singular, and the derivative of its logarithmic function with respect to the transverse field strength is logarithmically divergent at the critical point. The scaling behavior is confirmed numerically by performing a finite-size scaling analysis for systems of different sizes, consistent with the conformal invariance at the critical point. This allows us to extract the correlation length critical exponent, which turns out to be universal in the sense that the correlation length critical exponent does not depend on either the anisotropic parameter or the transverse field strength.
05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
05.70.Jk Critical point phenomena
05.30.-d Quantum statistical mechanics
82B30 Statistical thermodynamics (See also 80-XX)
82B10 Quantum equilibrium statistical mechanics (general)
82B80 Numerical methods (Monte Carlo, series resummation, etc.) (See also 65-XX, 81T80)
82B26 Phase transitions (general)
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
Quantum gases, liquids and solids
Issue 49 (12 December 2008)
Received 17 September 2008
Published 29 October 2008
Huan-Qiang Zhou et al 2008 J. Phys. A: Math. Theor. 41 492002
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