Continuously varying infinite randomness in the disordered XYZ spin chain

We study a critical line between localized magnetic phases in the XYZ spin chain with quenched randomness, where a previous strong-disorder RG calculation, assuming marginal MBL, suggested continuously varying critical indices. We do not address the question of MBL but instead solve the low-energy physics using a new unbiased tensor network method. These results are consistent with a line of infinite randomness fixed points. For weak interactions, a self-consistent Hartree–Fock-type treatment captures much of the important physics, including continuously varying exponents. Using a strong-disorder RG based on random walks, we show that local correlation induced between the mean-field couplings is a strictly marginal perturbation. This constitutes an example of a line of fixed points with continuously varying exponents in the equivalent disordered free-fermion chain. We argue that this line of fixed points also controls the critical XYZ spin chain for finite interactions.