Infinite randomness with continuously varying critical exponents in the random XYZ spin chain

We study the antiferromagnetic XYZ spin chain with quenched bond randomness, focusing on a critical line between localized Ising magnetic phases. A previous calculation using the spectrum-bifurcation renormalization group, and assuming marginal many-body localization, proposed that critical indices vary continuously. In this work, we solve the low-energy physics using an unbiased numerically exact tensor network method named the ``rigorous renormalization group.'' We find a line of fixed points consistent with infinite-randomness phenomenology, with indeed continuously varying critical exponents for average spin correlations. A self-consistent Hartree--Fock-type treatment of the $z$ couplings as interactions added to the free-fermion random XY model captures much of the important physics including the varying exponents; we provide an understanding of this as a result of local correlation induced between the mean-field couplings. We solve the problem of the locally correlated XY spin chain with an arbitrary degree of correlation and provide analytical strong-disorder renormalization group proofs of continuously varying exponents based on an associated classical random walk problem. This is also 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 an extended region of the critical interacting XYZ spin chain.