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
Abstract:
Fracton phases are recent entrants to the roster of topological phases in three dimensions. They are characterized by subextensively divergent topological degeneracy and excitations that are constrained to move along lower dimensional subspaces, including the eponymous fractons that are immobile in isolation. We develop correlation function diagnostics to characterize Type I fracton phases which build on their exhibiting partial deconfinement. These are inspired by similar diagnostics from standard gauge theories and utilize a generalized gauging procedure that links fracton phases to classical Ising models with subsystem symmetries. En route, we explicitly construct the spacetime partition function for the plaquette Ising model which, under such gauging, maps into the X-cube fracton topological phase. We numerically verify our results for this model via Monte Carlo calculations.Viewpoint: Topological insulators turn a corner
Physics American Physical Society 10 (2017) 1-3
Non-Fermi glasses: Localized descendants of fractionalized metals
Physical Review Letters American Physical Society 119:14 (2017) 1-5
Abstract:
Non-Fermi liquids are metals that cannot be adiabatically deformed into free fermion states. We argue for the existence of "non-Fermi glasses" phases of interacting disordered fermions that are fully many-body localized (MBL), yet cannot be deformed into an Anderson insulator without an eigenstate phase transition. We explore the properties of such non-Fermi glasses, focusing on a specific solvable example. At high temperature, non-Fermi glasses have qualitatively similar spectral features to Anderson insulators. We identify a diagnostic, based on ratios of correlators, that sharply distinguishes between the two phases even at infinite temperature. Our results and diagnostic should generically apply to the high-temperature behavior of MBL descendants of fractionalized phases.Filling-enforced nonsymmorphic Kondo semimetals in two dimensions
Physical Review B 96:8 (2017)