Related papers: On the geometry of tensor network states
One of the challenging problems in the condensed matter physics is to understand the quantum many-body systems, especially, their physical mechanisms behind. Since there are only a few complete analytical solutions of these systems, several…
Over the last decade tensor network states (TNS) have emerged as a powerful tool for the study of quantum many body systems. The matrix product states (MPS) are one particular class of TNS and are used for the simulation of…
The main goal of this paper is to study the geometric structures associated with the representation of tensors in subspace based formats. To do this we use a property of the so-called minimal subspaces which allows us to describe the tensor…
Although tensor networks are powerful tools for simulating low-dimensional quantum physics, tensor network algorithms are very computationally costly in higher spatial dimensions. We introduce quantum gauge networks: a different kind of…
Tensor network states are an indispensable tool for the simulation of strongly correlated quantum many-body systems. In recent years, tree tensor network states (TTNS) have been successfully used for two-dimensional systems and to benchmark…
This is a short review on selected theory developments on Tensor Network (TN) states for strongly correlated systems. Specifically, we briefly review the effect of symmetries in TN states, fermionic TNs, the calculation of entanglement…
We study the existence and limitations for hyperinvariant tensor networks incorporating a local SU(2) symmetry. As discrete implementations of the anti de-Sitter/conformal field theory (AdS/CFT) correspondence, such networks have created…
Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. We discuss how to incorporate a global symmetry, given by a…
Extending tensor models at the field theoretical level, tensor field theories are nonlocal quantum field theories with Feynman graphs identified with simplicial complexes. They become relevant for addressing quantum topology and geometry in…
We introduce a new basis on the state space of non-perturbative quantum gravity. The states of this basis are linearly independent, are well defined in both the loop representation and the connection representation, and are labeled by a…
In this paper we propose a space-time random tensor network approach for understanding holographic duality. Using tensor networks with random link projections, we define boundary theories with interesting holographic properties, such as the…
Tensor networks are an efficient platform to represent interesting quantum states of matter as well as to compute physical observables and information-theoretic quantities. We present a general protocol to construct fixed-point tensor…
We study the entanglement structure of states dual to multiboundary wormhole geometries using tensor network models. Perfect and random tensor networks tiling the hyperbolic plane have been shown to provide good models of the entanglement…
Formulating non-Abelian gauge theories as a tensor network is known to be challenging due to the internal degrees of freedom that result in the degeneracy in the singular value spectrum. In two dimensions, it is straightforward to 'trace…
In recent years, the import of quantum information techniques in quantum gravity opened new perspectives in the study of the microscopic structure of spacetime. We contribute to such a program by establishing a precise correspondence…
Several tensor networks are built of isometric tensors, i.e. tensors satisfying $W^\dagger W = \mathrm{I}$. Prominent examples include matrix product states (MPS) in canonical form, the multiscale entanglement renormalization ansatz (MERA),…
Random matrix ensembles are introduced that respect the local tensor structure of Hamiltonians describing a chain of $n$ distinguishable spin-half particles with nearest-neighbour interactions. We prove a central limit theorem for the…
Situated as a language between computer science, quantum physics and mathematics, tensor network theory has steadily grown in popularity and can now be found in applications ranging across the entire field of quantum information processing.…
We show that general string-net condensed states have a natural representation in terms of tensor product states (TPS) . These TPS's are built from local tensors. They can describe both states with short-range entanglement (such as the…
This review elaborates on the foundation, the advantages, and the prospects of tensor network representations for quantum states in vibrational spectroscopy. The focus is on the recently introduced matrix product state decomposition of…