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.

4 pages, 2 figures

References in corpus (2)

• Distribution of pseudo-critical temperatures and lack of self-averaging in disordered Poland-Scheraga models with different loop exponents
• Disorder induced rounding of the phase transition in the large q-state Potts model

Cited by in corpus (6)

• Entanglement entropy at infinite randomness fixed points in higher dimensions
• Exact relationship between the entanglement entropies of XY and quantum Ising chains
• Finite-size scaling of the entanglement entropy of the quantum Ising chain with homogeneous, periodically modulated and random couplings
• Random elastic networks : strong disorder renormalization approach
• Entanglement in composite free-fermion systems
• Quantum-critical properties of the one- and two-dimensional random transverse-field Ising model from large-scale quantum Monte Carlo simulations