Order Parameter Statistics in the Critical Quantum Ising Chain

2008/02/10 by Austen Lamacraft, Paul Fendley · 2 citations
Physics and Astronomy · #Opinion Dynamics and Social Influence #Quantum many-body systems #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.1103/physrevlett.100.165706

published as Phys. Rev. Lett. 100, 165706 (2008)

arxiv created 2008/02/10 · openalex publication_date 2008/04/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• The Bethe ansatz and the Tzitzéica–Bullough–Dodd equation
• Full counting statistics of the subsystem energy for free fermions and quantum spin chains

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