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

Istvan A. Kovacs; Ferenc Igloi

doi:10.1103/physrevb.80.214416

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arXiv · 0909.4442

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

Istvan A. Kovacs·Ferenc Igloi

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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 $\psi(2d)=0.51(2)$.

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Istvan A. Kovacs, Ferenc Igloi. 2009-09-24. Critical behavior and entanglement of the random transverse-field Ising model between one and two dimensions. https://doi.org/10.1103/physrevb.80.214416

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