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

Abstract

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.

Topological and quantum critical properties of the interacting Majorana chain model

“…By construction the Kitaev chain describes non-interacting Majorana fermions, therefore shortly after the model has been proposed it has also been extended to include interactions of various forms between the Majorana fermions [13][14][15][16][17][18][19]. Interacting Majorana fermions have also been theoretically studied in the presence of quenched disorder [20][21][22][23][24][25][26], in particular more recently in the context of manybody localization physics at high energy [27][28][29][30][31].…”