Disordered XYZ Spin Chain Simulations using the Spectrum Bifurcation Renormalization Group

We study the disordered XYZ spin chain using the recently developed Spectrum Bifurcation Renormalization Group (SBRG) numerical method. With strong disorder, the phase diagram consists of three many body localized (MBL) spin glass phases. We argue that, with sufficiently strong disorder, these spin glass phases are separated by marginally many-body localized (MBL) critical lines. We examine the critical lines of this model by measuring the entanglement entropy and Edwards-Anderson spin glass order parameter, and find that the critical lines are characterized by an effective central charge c'=ln2. Our data also suggests continuously varying critical exponents along the critical lines. We also demonstrate how long-range mutual information can distinguish these phases.