27 research outputs found
Double Semion Phase in an Exactly Solvable Quantum Dimer Model on the Kagome Lattice
Quantum dimer models typically arise in various low energy theories like
those of frustrated antiferromagnets. We introduce a quantum dimer model on the
kagome lattice which stabilizes an alternative topological
order, namely the so-called "double semion" order. For a particular set of
parameters, the model is exactly solvable, allowing us to access the ground
state as well as the excited states. We show that the double semion phase is
stable over a wide range of parameters using numerical exact diagonalization.
Furthermore, we propose a simple microscopic spin Hamiltonian for which the
low-energy physics is described by the derived quantum dimer model.Comment: 7 pages, 5 figure
Fermionic topological quantum states as tensor networks
Tensor network states, and in particular projected entangled pair states, play an important role in the description of strongly correlated quantum lattice systems. They do not only serve as variational states in numerical simulation methods, but also provide a framework for classifying phases of quantum matter and capture notions of topological order in a stringent and rigorous language. The rapid development in this field for spin models and bosonic systems has not yet been mirrored by an analogous development for fermionic models. In this work, we introduce a tensor network formalism capable of capturing notions of topological order for quantum systems with fermionic components. At the heart of the formalism are axioms of fermionic matrix-product operator injectivity, stable under concatenation. Building upon that, we formulate a Grassmann number tensor network ansatz for the ground state of fermionic twisted quantum double models. A specific focus is put on the paradigmatic example of the fermionic toric code. This work shows that the program of describing topologically ordered systems using tensor networks carries over to fermionic models
Simulation of anyons with tensor network algorithms
Interacting systems of anyons pose a unique challenge to condensed matter
simulations due to their non-trivial exchange statistics. These systems are of
great interest as they have the potential for robust universal quantum
computation, but numerical tools for studying them are as yet limited. We show
how existing tensor network algorithms may be adapted for use with systems of
anyons, and demonstrate this process for the 1-D Multi-scale Entanglement
Renormalisation Ansatz (MERA). We apply the MERA to infinite chains of
interacting Fibonacci anyons, computing their scaling dimensions and local
scaling operators. The scaling dimensions obtained are seen to be in agreement
with conformal field theory. The techniques developed are applicable to any
tensor network algorithm, and the ability to adapt these ansaetze for use on
anyonic systems opens the door for numerical simulation of large systems of
free and interacting anyons in one and two dimensions.Comment: Fixed typos, matches published version. 16 pages, 21 figures, 4
tables, RevTeX 4-1. For a related work, see arXiv:1006.247
Tensor network states and geometry
Tensor network states are used to approximate ground states of local
Hamiltonians on a lattice in D spatial dimensions. Different types of tensor
network states can be seen to generate different geometries. Matrix product
states (MPS) in D=1 dimensions, as well as projected entangled pair states
(PEPS) in D>1 dimensions, reproduce the D-dimensional physical geometry of the
lattice model; in contrast, the multi-scale entanglement renormalization ansatz
(MERA) generates a (D+1)-dimensional holographic geometry. Here we focus on
homogeneous tensor networks, where all the tensors in the network are copies of
the same tensor, and argue that certain structural properties of the resulting
many-body states are preconditioned by the geometry of the tensor network and
are therefore largely independent of the choice of variational parameters.
Indeed, the asymptotic decay of correlations in homogeneous MPS and MERA for
D=1 systems is seen to be determined by the structure of geodesics in the
physical and holographic geometries, respectively; whereas the asymptotic
scaling of entanglement entropy is seen to always obey a simple boundary law --
that is, again in the relevant geometry. This geometrical interpretation offers
a simple and unifying framework to understand the structural properties of, and
helps clarify the relation between, different tensor network states. In
addition, it has recently motivated the branching MERA, a generalization of the
MERA capable of reproducing violations of the entropic boundary law in D>1
dimensions.Comment: 18 pages, 18 figure
Simulatorgestutztes, modulares Human Factors Training in der Anasthesie. Konzept und Ergebnisse des Trainingsmoduls "Kommunikation und Kooperation im Team". [Simulator-based modular human factor training in anesthesiology. Concept and results of the module "Communication and Team Cooperation"]
Translation invariance, topology, and protection of criticality in chains of interacting anyons
Using finite-size scaling arguments, the critical properties of a chain of interacting anyons can be extracted from the low-energy spectrum of a finite system. Feiguin et al. [Phys. Rev. Lett. 98, 160409 (2007)] showed that an antiferromagnetic chain of Fibonacci anyons on a torus is in the same universality class as the tricritical Ising model and that criticality is protected by a topological symmetry. In the present paper we first review the graphical formalism for the study of anyons on the disk and demonstrate how this formalism may be consistently extended to the study of systems on surfaces of higher genus. We then employ this graphical formalism to study finite rings of interacting anyons on both the disk and the torus and show that analysis on the disk necessarily yields an energy spectrum which is a subset of that which is obtained on the torus. For a critical Hamiltonian, one may extract from this subset the scaling dimensions of the local scaling operators which respect the topological symmetry of the system. Related considerations are also shown to apply for open chains