Related papers: Entanglement renormalization and topological order
The investigation of strongly-correlated quantum matter is difficult due to the curse of dimensionality and intricate entanglement structures. These challenges are particularly pronounced in the vicinity of continuous quantum phase…
The multi-scale entanglement renormalization ansatz (MERA) postulates the existence of quantum circuits that renormalize entanglement in real space at different length scales. Chern insulators, however, cannot have scale-invariant discrete…
In this work we provide additional support for the proposed connection between the gauge/gravity dualities in string theory and the successful Multi-Scale-Entanglement-Renormalization-anstaz (MERA) method developed for the efficient…
The Ryu-Takayanagi (RT) formula is a crucial concept in current theory of gauge-gravity duality and emergent phenomena of geometry. Recent reinterpretation of this formula in terms of a set of "bit threads" is an interesting effort in…
In this article two new algorithms are presented that convert a given data tensor train into either a Tucker decomposition with orthogonal matrix factors or a multi-scale entanglement renormalization ansatz (MERA). The Tucker core tensor is…
Quantum entanglement is a particularly useful characterization of topological orders which lack conventional order parameters. In this work, we study the entanglement in topologically ordered states between two arbitrary spatial regions,…
We elaborate on a previous proposal by Hartman and Maldacena on a tensor network which accounts for the scaling of the entanglement entropy in a system at a finite temperature. In this construction, the ordinary entanglement renormalization…
It is well known that the matrix product state (MPS) description of a gapped ground state with a global on-site symmetry can exhibit "symmetry fractionalization". Namely, even though the symmetry acts as a linear representation on the…
Kitaev's quantum double models in 2D provide some of the most commonly studied examples of topological quantum order. In particular, the ground space is thought to yield a quantum error-correcting code. We offer an explicit proof that this…
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…
Renormalization group (RG) methods, which model the way in which the effective behavior of a system depends on the scale at which it is observed, are key to modern condensed-matter theory and particle physics. We compare the ideas behind…
In tensor networks, a geometric operation of pushing a bond cut surface toward a minimal surface corresponds to entanglement distillation. Cutting bonds defines a reduced transition matrix on the bond cut surface and the associated quantum…
We investigate a recent conjecture connecting the AdS/CFT correspondence and entanglement renormalization tensor network states (MERA). The proposal interprets the tensor connectivity of the MERA states associated to quantum many body…
The exact renormalization group (ERG) is a powerful tool for understanding the formal properties of field theories. By adapting generalized ERG schemes to the flow of wavefunctionals, we obtain a large class of continuous unitary networks,…
We present a hierarchy of quantum many-body states among which many examples of topological order can be identified by construction. We define these states in terms of a general, basis-independent framework of tensor networks based on the…
In the holographic correspondence of quantum gravity, a global onsite symmetry at the boundary generally translates to a local gauge symmetry in the bulk. We describe one way how the global boundary onsite symmetries can be gauged within…
Entanglement renormalization is a unitary real-space renormalization scheme. The corresponding quantum circuits or tensor networks are known as MERA, and they are particularly well-suited to describing quantum systems at criticality. In…
We give a detailed physical argument for the area law for entanglement entropy in gapped phases of matter arising from local Hamiltonians. Our approach is based on renormalization group (RG) ideas and takes a resource oriented perspective.…
We adapt the techniques of entanglement renormalization tensor networks to weakly interacting quantum field theories in the continuum. A key tool is "quantum circuit perturbation theory," which enables us to systematically construct…
We construct an explicit renormalization group (RG) transformation for Levin and Wen's string-net models on a hexagonal lattice. The transformation leaves invariant the ground-state "fixed-point" wave function of the string-net condensed…