Order Parameter Statistics in the Critical Quantum Ising Chain
Austen LamacraftDepartment of Physics, University of Virginia, Charlottesville, Virginia 22904-4714 USAPaul FendleyAll Souls College and the Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, OX1 3NP, United Kingdom
2008en
ABI
Abstract
The probability distribution of the order parameter is expected to take a universal scaling form at a phase transition. In a spin system at a quantum critical point, this corresponds to universal statistics in the distribution of the total magnetization in the low-lying states. We obtain this scaling function exactly for the ground state and first excited state of the critical quantum Ising spin chain. This is achieved through a remarkable relation to the partition function of the anisotropic Kondo problem, which can be computed by exploiting the integrability of the system.
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