  The Multiscale Entanglement Renormalization Ansatz (MERA) is a tensor network
based variational ansatz that is capable of capturing many of the key physical
properties of strongly correlated ground states such as criticality and
topological order. MERA also shares many deep relationships with the AdS/CFT
(gauge-gravity) correspondence by realizing a UV complete holographic duality
within the tensor networks framework. Motivated by this, we have re-purposed
the MERA tensor network as an analysis tool to study the real-time evolution of
the 1D transverse Ising model in its low energy excited state sector. We
performed this analysis by allowing the ancilla qubits of the MERA tensor
network to acquire quantum fluctuations, which yields a unitary transform
between the physical (boundary) and ancilla qubit (bulk) Hilbert spaces. This
then defines a reversible quantum circuit which is used as a `holographic
transform' to study excited states and their real-time dynamics from the point
of the bulk ancillae. In the gapped paramagnetic phase of the transverse field
Ising model, we demonstrate the holographic duality between excited states
induced by single spin-flips (Ising `magnons') acting on the ground state and
single ancilla qubit spin-flips. The single ancillae qubit excitation is shown
to be stable in the bulk under real-time evolution and hence defines a stable
holographic quasiparticle which we have named the `hologron'. The `dictionary'
between the bulk and boundary is determined and realizes many features of the
holographic correspondence in a non-CFT limit of the boundary theory. As an
added spin-off, this dictionary together with the extension to multi-hologron
sectors gives us a systematic way to construct quantitatively accurate low
energy effective Hamiltonians.
