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Register a new userNon-Abelian quasiholes in lattice Moore-Read states and parent Hamiltonians
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This work concerns Ising quasiholes in Moore-Read type lattice wave functions derived from conformal field theory. We commence with constructing Moore-Read type lattice states and then add quasiholes to them. By use of Metropolis Monte Carlo simulations, we analyze the features of the quasiholes, such as their size, shape, charge, and braiding properties. The braiding properties, which turn out to be the same as in the continuum Moore-Read state, demonstrate the topological attributes of the Moore-Read lattice states in a direct way. We also derive parent Hamiltonians for which the states with quasiholes included are ground states. One advantage of these Hamiltonians lies therein that we can now braid the quasiholes just by changing the coupling strengths in the Hamiltonian since the Hamiltonian is a function of the positions of the quasiholes. The methodology exploited in this article can also be used to construct other kinds of lattice fractional quantum Hall models containing quasiholes, for example investigation of Fibonacci quasiholes in lattice Read-Rezayi states.
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Moore-Read states can be expressed as conformal blocks of the underlying rational conformal field theory, which provides a well explored description for the insertion of quasiholes. It is known, however, that quasielectrons are more difficult to describe in continuous systems, since the natural guess for how to construct them leads to a singularity. In this work, we show that the singularity problem does not arise for lattice Moore-Read states. This allows us to construct Moore-Read Pfaffian states on lattices for filling fraction 5/2 with both quasiholes and quasielectrons in a simple way. We investigate the density profile, charge, size and braiding properties of the anyons by means of Monte Carlo simulations. Further we derive an exact few-body parent Hamiltonian for the states. Finally, we compare our results to the density profile, charge and shape of anyons in the Kapit-Mueller model by means of exact diagonalization.
We use conformal field theory to construct model wavefunctions for a gapless interface between latti
The non-Abelian topological order has attracted a lot of attention for its fundamental importance and exciting prospect of topological quantum computation. However, explicit demonstration or identification of the non-Abelian states and the associated statistics in a microscopic model is very challenging. Here, based on density-matrix renormalization group calculation, we provide a complete characterization of the universal properties of bosonic Moore-Read state on Haldane honeycomb lattice model at filling number $ u=1$ for larger systems, including both the edge spectrum and the bulk anyonic quasiparticle (QP) statistics. We first demonstrate that there are three degenerating ground states, for each of which there is a definite anyonic flux threading through the cylinder. We identify the nontrivial countings for the entanglement spectrum in accordance with the corresponding conformal field theory. Through inserting the $U(1)$ charge flux, it is found that two of the ground states can be adiabatically connected through a fermionic charge-$textit{e}$ QP being pumped from one edge to the other, while the ground state in Ising anyon sector evolves back to itself. Furthermore, we calculate the modular matrices $mathcal{S}$ and $mathcal{U}$, which contain all the information for the anyonic QPs. In particular, the extracted quantum dimensions, fusion rule and topological spins from modular matrices positively identify the emergence of non-Abelian statistics following the $SU(2)_2$ Chern-Simons theory.
We characterize the conditions under which a translationally invariant matrix product state (MPS) is invariant under local transformations. This allows us to relate the symmetry group of a given state to the symmetry group of a simple tensor. We exploit this result in order to prove and extend a version of the Lieb-Schultz-Mattis theorem, one of the basic results in many-body physics, in the context of MPS. We illustrate the results with an exhaustive search of SU(2)--invariant two-body Hamiltonians which have such MPS as exact ground states or excitations.
We introduce lattice gauge theories which describe three-dimensional, gapped quantum phases exhibiting the phenomenology of both conventional three-dimensional topological orders and fracton orders, starting from a finite group $G$, a choice of an Abelian normal subgroup $N$, and a choice of foliation structure. These hybrid fracton orders -- examples of which were introduced in arXiv:2102.09555 -- can also host immobile, point-like excitations that are non-Abelian, and therefore give rise to a protected degeneracy. We construct solvable lattice models for these orders which interpolate between a conventional, three-dimensional $G$ gauge theory and a pure fracton order, by varying the choice of normal subgroup $N$. We demonstrate that certain universal data of the topological excitations and their mobilities are directly related to the choice of $G$ and $N$, and also present complementary perspectives on these orders: certain orders may be obtained by gauging a global symmetry which enriches a particular fracton order, by either fractionalizing on or permuting the excitations with restricted mobility, while certain hybrid orders can be obtained by condensing excitations in a stack of initially decoupled, two-dimensional topological orders.
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