Critical behavior and entanglement of the random transverse-field Ising model between one and two dimensions

TL;DR

This study investigates the critical behavior and entanglement entropy of disordered ladder systems in the transverse-field Ising model, revealing their connection to the two-dimensional model's critical properties through numerical analysis.

Contribution

It provides the first detailed numerical analysis of the critical exponents and entanglement properties of the 2D disordered transverse-field Ising model using ladder geometries.

Findings

Critical exponents for 2D model: ν(2d)=1.25(3), x(2d)=0.996(10), ψ(2d)=0.51(2)

Critical properties are governed by the infinite disorder fixed point of the chain

Scaling of pseudo-critical points and entanglement entropy supports the 2D critical behavior

Abstract

We consider disordered ladders of the transverse-field Ising model and study their critical properties and entanglement entropy for varying width, $w \le 20$, by numerical application of the strong disorder renormalization group method. We demonstrate that the critical properties of the ladders for any finite $w$ are controlled by the infinite disorder fixed point of the random chain and the correction to scaling exponents contain information about the two-dimensional model. We calculate sample dependent pseudo-critical points and study the shift of the mean values as well as scaling of the width of the distributions and show that both are characterized by the same exponent, $\nu(2d)$. We also study scaling of the critical magnetization, investigate critical dynamical scaling as well as the behavior of the critical entanglement entropy. Analyzing the $w$-dependence of the results we have obtained accurate estimates for the critical exponents of the two-dimensional model: $\nu(2d)=1.25(3)$, $x(2d)=0.996(10)$ and $\psi(2d)=0.51(2)$.