Kevin Slagle

Quantum field theory of X-cube fracton topological order and robust degeneracy from geometry

We propose a quantum field theory description of the X-cube model of fracton topological order. The field theory is not (and cannot be) a topological quantum field theory (TQFT), since unlike the X-cube model, TQFTs are invariant (i.e. symmetric) under continuous spacetime transformations. However, the theory is instead invariant under a certain subgroup of the conformal group. We describe how braiding statistics and ground state degeneracy are reproduced by the field theory, and how the the X-cube Hamiltonian and field theory can be minimally coupled to matter fields. We also show that even on a manifold with trivial topology, spatial curvature can induce a ground state degeneracy that is stable to arbitrary local perturbations! Our formalism may allow for the description of other fracton field theories, where the only necessary input is an equation of motion for a charge density.

Fracton topological order from nearest-neighbor two-spin interactions and dualities

Fracton topological order describes a remarkable phase of matter which can be characterized by fracton excitations with constrained dynamics and a ground state degeneracy that increases exponentially with the length of the system on a three-dimensional torus. However, previous models exhibiting this order require many-spin interactions which may be very difficult to realize in a real material or cold atom system. In this work, we present a more physically realistic model which has the so-called X-cube fracton topological order but only requires nearest-neighbor two-spin interactions. The model lives on a three-dimensional honeycomb-based lattice with one to two spin-1/2 degrees of freedom on each site and a unit cell of 6 sites. The model is constructed from two orthogonal stacks of

Out-of-Time-Order Correlation in Marginal Many-Body Localized Systems

Z_2

X-Cube Fracton Model on Generic Lattices: Phases and Geometric Order

topologically ordered Kitaev honeycomb layers, which are coupled together by a two-spin interaction. It is also shown that a four-spin interaction can be included to instead stabilize 3+1D

Exotic quantum phase transitions of strongly interacting topological insulators

Z_2

Quantum phase transition between theZ2spin liquid and valence bond crystals on a triangular lattice

topological order. We also find dual descriptions of four quantum phase transitions in our model, all of which appear to be discontinuous first order transitions.

Wave Function and Strange Correlator of Short Range Entangled states

We show that the out-of-time-order correlation (OTOC)

Many-Body Localization of Symmetry Protected Topological States

\langle W(t)^\dagger V(0)^\dagger W(t)V(0)\rangle

Fracton Models on General Three-Dimensional Manifolds

in many-body localized (MBL) and marginal MBL systems can be efficiently calculated by the spectrum bifurcation renormalization group (SBRG). We find that in marginal MBL systems, the scrambling time

Disordered XYZ Spin Chain Simulations using the Spectrum Bifurcation Renormalization Group

t_\text{scr}