7 research outputs found
Non-local scaling operators with entanglement renormalization
The multi-scale entanglement renormalization ansatz (MERA) can be used, in
its scale invariant version, to describe the ground state of a lattice system
at a quantum critical point. From the scale invariant MERA one can determine
the local scaling operators of the model. Here we show that, in the presence of
a global symmetry , it is also possible to determine a class of
non-local scaling operators. Each operator consist, for a given group element
, of a semi-infinite string \tGamma_g with a local operator
attached to its open end. In the case of the quantum Ising model,
, they correspond to the disorder operator ,
the fermionic operators and , and all their descendants.
Together with the local scaling operators identity , spin
and energy , the fermionic and disorder scaling operators ,
and are the complete list of primary fields of the Ising
CFT. Thefore the scale invariant MERA allows us to characterize all the
conformal towers of this CFT.Comment: 4 pages, 4 figures. Revised versio
Entanglement renormalization and boundary critical phenomena
The multiscale entanglement renormalization ansatz is applied to the study of
boundary critical phenomena. We compute averages of local operators as a
function of the distance from the boundary and the surface contribution to the
ground state energy. Furthermore, assuming a uniform tensor structure, we show
that the multiscale entanglement renormalization ansatz implies an exact
relation between bulk and boundary critical exponents known to exist for
boundary critical systems.Comment: 6 pages, 4 figures; for a related work see arXiv:0912.164
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