Finite-size scaling of pseudo-critical point distributions in the random transverse-field Ising chain

Abstract

We study the distribution of finite size pseudo-critical points in a one-dimensional random quantum magnet with a quantum phase transition described by an infinite randomness fixed point. Pseudo-critical points are defined in three different ways: the position of the maximum of the average entanglement entropy, the scaling behavior of the surface magnetization, and the energy of a soft mode. All three lead to a log-normal distribution of the pseudo-critical transverse fields, where the width scales as $L^{-1/\nu }$ with $\nu =2$ and the shift of the average value scales as $L^{-1/{\nu }_{typ}}$ with ${\nu }_{typ}=1$, which we related to the scaling of average and typical quantities in the critical region.

arXiv comment4 pages, 2 figures

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• Finite-size scaling of the entanglement entropy of the quantum Ising chain with homogeneous, periodically modulated and random couplings
• Critical behavior and entanglement of the random transverse-field Ising model between one and two dimensions
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