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We have developed a tensor network approach to the two-dimensional fully frustrated classical XY spin model on the kagome lattice, and clarified the nature of the possible phase transitions of various topological excitations.We find that…
Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of…
We develop a tensor network technique that can solve universal reversible classical computational problems, formulated as vertex models on a square lattice [Nat. Commun. 8, 15303 (2017)]. By encoding the truth table of each vertex…
We introduce a numerical approach to calculate the statistics of work done on 1D quantum lattice systems initially prepared in thermal equilibrium states. This approach is based on two tensor-network techniques: Time Evolving Block…
The ground state of the toric code, that of the two-dimensional class D superconductor, and the partition sum of the two-dimensional Ising model are dual to each other. This duality is remarkable inasmuch as it connects systems commonly…
In this paper, fast and efficient discrete sine transformation (DST) algorithms are presented based on the factorization of sparse, scaled orthogonal, rotation, rotation-reflection, and butterfly matrices. These algorithms are completely…
Tensor network states provide an efficient class of states that faithfully capture strongly correlated quantum models and systems in classical statistical mechanics. While tensor networks can now be seen as becoming standard tools in the…
Tensor network methods are powerful and efficient tools to study the properties and dynamics of statistical and quantum systems, in particular in one and two dimensions. In recent years, these methods were applied to lattice gauge theories,…
A novel lattice approach is presented for studying systems comprising a large number of interacting nonrelativistic fermions. The construction is ideally suited for numerical study of fermions near unitarity--a strongly coupled regime…
We present and implement an efficient variational method to simulate two-dimensional finite size fermionic quantum systems by fermionic projected entangled pair states. The approach differs from the original one due to the fact that there…
To apply the powerful many-body techniques of tensor networks to massless Dirac fermions one wants to discretize the $p\cdot\sigma$ Hamiltonian and construct a matrix-product-operator (MPO) representation. We compare two alternative…
We propose a single-layer tensor network framework for the variational determination of ground states in two-dimensional quantum lattice models. By combining the nested tensor network method [Phys. Rev. B 96, 045128 (2017)] with the…
In the context of a quantum critical spin chain whose low energy physics corresponds to a conformal field theory (CFT), it was recently demonstrated [A. Milsted G. Vidal, arXiv:1805.12524] that certain classes of tensor networks used for…
This correspondence presents an efficient method for reconstructing a band-limited signal in the discrete domain from its crossings with a sine wave. The method makes it possible to design A/D converters that only deliver the crossing…
Tensor networks provide a natural language for non-invertible symmetries in general Hamiltonian lattice models. We use ZX-diagrams, which are tensor network presentations of quantum circuits, to define a non-invertible operator implementing…
Calculation of observables with three-dimensional projected entangled pair states is generally hard, as it requires a contraction of complex multi-layer tensor networks. We utilize the multi-layer structure of these tensor networks to…
In this paper we explore the practical use of the corner transfer matrix and its higher-dimensional generalization, the corner tensor, to develop tensor network algorithms for the classical simulation of quantum lattice systems of infinite…
We address the problem of decomposing an image into albedo and shading. We propose the Fast Fourier Intrinsic Network, FFI-Net in short, that operates in the spectral domain, splitting the input into several spectral bands. Weights in…
Using the density matrix renormalization group algorithm, we investigate the lattice model for spinless fermions in one dimension in the presence of a strong interaction and disorder. The phase sensitivity of the ground state energy is…
We study lattice fermions from the viewpoint of spectral graph theory (SGT). We find that a fermion defined on a certain lattice is identified as a spectral graph. SGT helps us investigate the number of zero eigenvalues of lattice Dirac…