Localization-protected order in spin chains with non-Abelian discrete symmetries
Physical Review B American Physical Society 98:6 (2018) 064203
Abstract:
We study the nonequilibrium phase structure of the three-state random quantum Potts model in one dimension. This spin chain is characterized by a non-Abelian D 3 symmetry recently argued to be incompatible with the existence of a symmetry-preserving many-body localized (MBL) phase. Using exact diagonalization and a finite-size scaling analysis, we find that the model supports two distinct broken-symmetry MBL phases at strong disorder that either break the Z 3 clock symmetry or a Z 2 chiral symmetry. In a dual formulation, our results indicate the existence of a stable finite-temperature topological phase with MBL-protected parafermionic end zero modes. While we find a thermal symmetry-preserving regime for weak disorder, scaling analysis at strong disorder points to an infinite-randomness critical point between two distinct broken-symmetry MBL phases.Many-body localization, symmetry, and topology
Reports on Progress in Physics IOP Publishing 81:8 (2018) 082501
Abstract:
We review recent developments in the study of out-of-equilibrium topological states of matter in isolated systems. The phenomenon of many-body localization, exhibited by some isolated systems usually in the presence of quenched disorder, prevents systems from equilibrating to a thermal state where the delicate quantum correlations necessary for topological order are often washed out. Instead, many-body localized systems can exhibit a type of eigenstate phase structure wherein their entire many-body spectrum is characterized by various types of quantum order, usually restricted to quantum ground states. After introducing many-body localization and explaining how it can protect quantum order, we then explore how the interplay of symmetry and dimensionality with many-body localization constrains its role in stabilizing topological phases out of equilibrium.Recoverable information and emergent conservation laws in fracton stabilizer codes
Physical Review B American Physical Society 97:13 (2018) 134426
Abstract:
We introduce a new quantity, that we term {\it recoverable information}, defined for stabilizer Hamiltonians. For such models, the recoverable information provides a measure of the topological information, as well as a physical interpretation, which is complementary to topological entanglement entropy. We discuss three different ways to calculate the recoverable information, and prove their equivalence. To demonstrate its utility, we compute recoverable information for {\it fracton models} using all three methods where appropriate. From the recoverable information, we deduce the existence of emergent Z 2 Gauss-law type constraints, which in turn imply emergent Z 2 conservation laws for point-like quasiparticle excitations of an underlying topologically ordered phase.Topological Entanglement Entropy of Fracton Stabilizer Codes
Physical Review B American Physical Society 97 (2018) 125101
Abstract:
Entanglement entropy provides a powerful characterization of two-dimensional gapped topological phases of quantum matter, intimately tied to their description by topological quantum field theories (TQFTs). Fracton topological orders are three-dimensional gapped topologically ordered states of matter that lack a TQFT description. We show that three-dimensional fracton phases are nevertheless characterized, at least partially, by universal structure in the entanglement entropy of their ground-state wave functions. We explicitly compute the entanglement entropy for two archetypal fracton models, the “X-cube model” and “Haah's code,” and demonstrate the existence of a nonlocal contribution that scales linearly in subsystem size. We show via Schrieffer-Wolff transformations that this piece of the entanglement entropy of fracton models is robust against arbitrary local perturbations of the Hamiltonian. Finally, we argue that these results may be extended to characterize localization-protected fracton topological order in excited states of disordered fracton models.Correlation function diagnostics for type-I fracton phases
Physical Review B: Condensed Matter and Materials Physics American Physical Society 97 (2018) 041110