Quantum criticality of hot random spin chains

Abstract

We study the infinite-temperature properties of an infinite sequence of random quantum spin chains using a real-space renormalization group approach, and demonstrate that they exhibit non-ergodic behavior at strong disorder. The analysis is conveniently implemented in terms of SU(2)${}_k$ anyon chains that include the Ising and Potts chains as notable examples. Highly excited eigenstates of these systems exhibit properties usually associated with quantum critical ground states, leading us to dub them "quantum critical glasses". We argue that random-bond Heisenberg chains self-thermalize and that the excited-state entanglement crosses over from volume-law to logarithmic scaling at a length scale that diverges in the Heisenberg limit $k\to \infty$. The excited state fixed points are generically distinct from their ground state counterparts, and represent novel non-equilibrium critical phases of matter.

4.5+12 pages. 2 figures. v5: Published version

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• Eigenstate phases with finite on-site non-Abelian symmetry
• Probability distribution of the entanglement across a cut at an infinite-randomness fixed point
• Entanglement scaling in fermion chains with a localization-delocalization transition and inhomogeneous modulations
• Pair localization in dipolar systems with tunable positional disorder
• Universal crossover from ground state to excited-state quantum criticality
• Random Transverse Field Spin-Glass Model on the Cayley tree : phase transition between the two Many-Body-Localized Phases
• Many-body localization with mobility edges
• Universality in Non-Equilibrium Quantum Systems