Random Antiferromagnetic SU(N) Spin Chains

TL;DR

This paper studies random antiferromagnetic SU(N) spin chains, revealing a universal infinite randomness fixed point with N-dependent exponents, distinct from the SU(2) case, and shows the infinite-N limit fails to describe finite N behavior.

Contribution

It analytically characterizes the low-energy fixed point and critical exponents of random SU(N) spin chains, highlighting the differences from the SU(2) case and the limitations of the infinite-N approximation.

Findings

Universal infinite randomness fixed point identified

Energy-length scale relation: Ω∼exp(−L^ψ) with ψ=1/N

Mean correlation function: C̄_{ij}∼(−1)^{i−j}/|i−j|^{φ} with φ=4/N

Abstract

We analyze random isotropic antiferromagnetic SU(N) spin chains using the real space renormalization group. We find that they are governed at low energies by a universal infinite randomness fixed point different from the one of random spin-1/2 chains. We determine analytically the important exponents: the energy-length scale relation is $\Omega\sim\exp(-L^{\psi})$, where $\psi=1/N$, and the mean correlation function is given by $\bar{C_{ij}}\sim(-1)^{i-j}/|i-j|^{\phi}$, where $\phi=4/N$. Our analysis shows that the infinite-N limit is unable to capture the behavior obtained at any finite N.