Related papers: Explicit tensor network representation for the gro…
We describe how to construct generalized string-net models, a class of exactly solvable lattice models that realize a large family of 2D topologically ordered phases of matter. The ground states of these models can be thought of as…
Matrix models, as quantum mechanical systems without explicit spatial dependence, provide valuable insights into higher-dimensional gauge and gravitational theories, especially within the framework of string theory, where they can describe…
Tensor network states provide successful descriptions of strongly correlated quantum systems with applications ranging from condensed matter physics to cosmology. Any family of tensor network states possesses an underlying entanglement…
We use a recently proposed class of tensor-network states to study phase transitions in string-net models. These states encode the genuine features of the string-net condensate such as, e.g., a nontrivial perimeter law for Wilson loops…
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…
We have developed an efficient tensor network algorithm for spin ladders, which generates ground-state wave functions for infinite-size quantum spin ladders. The algorithm is able to efficiently compute the ground-state fidelity per lattice…
We construct a tensor network representation of the partition function for the massless Schwinger model on a two dimensional lattice using staggered fermions. The tensor network representation allows us to include a topological term. Using…
We prove the conjectured classification of topological phases in two spatial dimensions with gappable boundary, in a simplified setting. Two gapped ground states of lattice Hamiltonians are in the same quantum phase of matter, or…
Tensor Network States are ans\"atze for the efficient description of quantum many-body systems. Their success for one dimensional problems, together with the fact that they do not suffer from the sign problem and can address the simulation…
For any D-dimensional quantum lattice system, the fidelity between two ground state many-body wave functions is mapped onto the partition function of a D-dimensional classical statistical vertex lattice model with the same lattice geometry.…
We propose a unified mathematical framework for classifying phases of matter. The framework is based on different types of combinatorial structures with a notion of locality called lattices. A tensor lattice is a local prescription that…
We develop a strategy for tensor network algorithms that allows to deal very efficiently with lattices of high connectivity. The basic idea is to fine-grain the physical degrees of freedom, i.e., decompose them into more fundamental units…
In this article we present analytical results on the exact tensor network representations and correlation functions of the first examples of 2D ground states with quantum phase transitions between area law and extensive entanglement…
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…
Tensor network methods are taking a central role in modern quantum physics and beyond. They can provide an efficient approximation to certain classes of quantum states, and the associated graphical language makes it easy to describe and…
Tensor networks provide a powerful new framework for classifying and simulating correlated and topological phases of quantum matter. Their central premise is that strongly correlated matter can only be understood by studying the underlying…
Tensor network methods have progressed from variational techniques based on matrix-product states able to compute properties of one-dimensional condensed-matter lattice models into methods rooted in more elaborate states such as projected…
Recently, a class of tensor networks called isometric tensor network states (isoTNS) was proposed which generalizes the canonical form of matrix product states to tensor networks in higher dimensions. While this ansatz allows for efficient…
We adapt the bialgebra and Hopf relations to expose internal structure in the ground state of a Hamiltonian with $Z_2$ topological order. Its tensor network description allows for exact contraction through simple diagrammatic rewrite rules.…
We consider a model of strongly correlated electrons in 1D called the t-J model, which was solved by graded algebraic Bethe ansatz. We use it to design graded tensor networks which can be contracted approximately to obtain a Matrix Product…