@article { ISI:000535205600016,
title = {Hilbert-Space Fragmentation from Strict Confinement},
journal = {Phys. Rev. Lett.},
volume = {124},
number = {20},
year = {2020},
month = {MAY 22},
pages = {207602},
publisher = {AMER PHYSICAL SOC},
type = {Article},
abstract = {We study one-dimensional spin-1/2 models in which strict confinement of Ising domain walls leads to the fragmentation of Hilbert space into exponentially many disconnected subspaces. Whereas most previous works emphasize dipole moment conservation as an essential ingredient for such fragmentation, we instead require two commuting U(1) conserved quantities associated with the total domain-wall number and the total magnetization. The latter arises naturally from the confinement of domain walls. Remarkably, while some connected components of the Hilbert space thermalize, others are integrable by Bethe ansatz. We further demonstrate how this Hilbert-space fragmentation pattern arises perturbatively in the confining limit of Z(2) gauge theory coupled to fermionic matter, leading to a hierarchy of timescales for motion of the fermions. This model can be realized experimentally in two complementary settings.},
issn = {0031-9007},
doi = {10.1103/PhysRevLett.124.207602},
author = {Yang, Zhi-Cheng and Liu, Fangli and Gorshkov, V, Alexey and Iadecola, Thomas}
}
@article {ISI:000465163400005,
title = {Hierarchical Majoranas in a programmable nanowire network},
journal = {Phys. Rev. B},
volume = {99},
number = {15},
year = {2019},
month = {APR 19},
pages = {155138},
publisher = {AMER PHYSICAL SOC},
type = {Article},
abstract = {We propose a hierarchical architecture for building {\textquoteleft}{\textquoteleft}logical{{\textquoteright}{\textquoteright}} Majorana zero modes using {\textquoteleft}{\textquoteleft}physical{{\textquoteright}{\textquoteright}} Majorana zero modes at the Y-junctions of a hexagonal network of semiconductor nanowires. Each Y-junction contains three {\textquoteleft}{\textquoteleft}physical{{\textquoteright}{\textquoteright}} Majoranas, which hybridize when placed in close proximity, yielding a single effective Majorana mode near zero energy. The hybridization of effective Majorana modes on neighboring Y-junctions is controlled by applied gate voltages on the links of the honeycomb network. This gives rise to a tunable tight-binding model of effective Majorana modes. We show that selecting the gate voltages that generate a Kekule vortex pattern in the set of hybridization amplitudes yields an emergent {\textquoteleft}{\textquoteleft}logical{{\textquoteright}{\textquoteright}} Majorana zero mode bound to the vortex core. The position of a logical Majorana can be tuned adiabatically, without moving any of the {\textquoteleft}{\textquoteleft}physical{{\textquoteright}{\textquoteright}} Majoranas or closing any energy gaps, by programming the values of the gate voltages to change as functions of time. A nanowire network supporting multiple such {\textquoteleft}{\textquoteleft}logical{{\textquoteright}{\textquoteright}} Majorana zero modes provides a physical platform for performing adiabatic non-Abelian braiding operations in a fully controllable manner.},
issn = {2469-9950},
doi = {10.1103/PhysRevB.99.155138},
author = {Yang, Zhi-Cheng and Iadecola, Thomas and Chamon, Claudio and Mudry, Christopher}
}