Article
Materials Science, Multidisciplinary
Kouichi Seki, Toshiya Hikihara, Kouichi Okunishi
Summary: The study introduces a new entanglement-based algorithm for the quantum spin system's strong-disorder renormalization group method. This algorithm demonstrates better accuracy on the square lattice model but lower efficiency on the one-dimensional and triangular lattice models. Possible improvements and theoretical background of the algorithm are also discussed.
Article
Astronomy & Astrophysics
Pablo Bueno, Roberto Emparan, Quim Llorens
Summary: This study focuses on the structure of higher-curvature gravitational densities induced from holographic renormalization in AdS(d+1) and their definition of a higher-curvature gravitational theory on the brane in a braneworld construction. It is found that these densities satisfy a holographic c-theorem in general dimensions and the terms affecting the monotonicity of the holographic c-function are algebraic in curvature and do not involve covariant derivatives of the Riemann tensor.
Article
Computer Science, Interdisciplinary Applications
Takumi Yamashita, Tetsuya Sakurai
Summary: This paper proposes a parallel computing method for the Higher Order Tensor Renormalization Group (HOTRG) applied to a d-dimensional simple lattice model. The method aims to reduce computational cost and memory space requirement by distributing local tensor elements to each process and minimizing communication between processes.
COMPUTER PHYSICS COMMUNICATIONS
(2022)
Article
Materials Science, Multidisciplinary
Patrick C. G. Vlaar, Philippe Corboz
Summary: Tensor network algorithms have been proven to be powerful tools for studying one- and two-dimensional quantum many-body systems, but their application in three-dimensional quantum systems has been limited. This paper develops and benchmarks two contraction approaches for infinite projected entangled-pair states (iPEPS) in 3D, showing competitive results compared to other methods.
Article
Multidisciplinary Sciences
Jacob Price, Brek Meuris, Madelyn Shapiro, Panos Stinis
Summary: This study introduces a time-dependent renormalization approach to address instabilities in reduced order models by controlling the memory decay parameter. Through verification on different equations, it is found that the renormalization coefficients decay algebraically with increasing resolution.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
(2021)
Article
Physics, Multidisciplinary
Ilia A. Luchnikov, Mikhail E. Krechetov, Sergey N. Filippov
Summary: The use of Riemannian optimization in quantum physics and quantum information science has shown effectiveness in solving optimization problems with constraints, such as low-energy spectrum and eigenstates of multipartite Hamiltonians, variational search of tensor networks, preparation of arbitrary quantum states, decomposition of quantum gates, and tomography of quantum states. The universality of this approach allows for its application to complex quantum architectures beyond the problems listed, including optimal control of noisy quantum systems.
NEW JOURNAL OF PHYSICS
(2021)
Article
Physics, Multidisciplinary
Jose Reslen
Summary: The tensor network representation and entanglement distribution of the ground state of a Bethe chain are obtained and studied. The maximum block entanglement is observed at the interplay between single- and many-bodyness. In systems of two fermions, tensor networks with substantial many-body entropy cannot be expressed as a sequence of next-neighbor unitaries applied on an uncorrelated state, but require additional four-next-neighbor unitaries. This finding challenges the idea that ground states can be obtained through next-neighbor operations on an initial tensor network lacking many-body correlations. The work highlights the transcendence of many-bodyness in the implementation of protocols based on matrix product states.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2023)
Article
Optics
Zhao-Yu Sun, Hui-Xin Wen, Meng Li, Bin Guo
Summary: This study analyzed the activity levels of young children with TD, but did not consider the effects of cognitive ability or other developmental factors on motor performance and participation. Furthermore, a detailed description of the functioning profile of ASD was lacking.
Article
Astronomy & Astrophysics
Samuel Goldman, Nima Lashkari, Robert G. Leigh, Mudassir Moosa
Summary: The exact renormalization group is a powerful tool for studying field theories, and by applying it to the flow of wave functionals, a large class of continuous unitary networks can be obtained, including a class of Gaussian continuous multiscale renormalization Ansatze. These generalized wave functional ERG schemes allow for modifications of the dispersion relation, significantly altering the entanglement structure of the ultraviolet states. This construction demonstrates that cMERA can be derived from a more fundamental microscopic principle, opening up avenues for exploring cMERA beyond the free field regime.
Article
Astronomy & Astrophysics
Ming-Xia Ma, Shao-Feng Wu
Summary: In AdS/CFT correspondence, the UV divergence in the field theory generating functional can be eliminated by the IR divergence in gravity, known as holographic renormalization. The standard Fefferman-Graham expansion method is strict and universal but technically cumbersome. To improve the technique, alternative approaches based on the Hamilton-Jacobi formulation of gravity have been developed, allowing for the generation of exact counterterms ansatz. This approach has been successfully applied to various holographic models.
Article
Physics, Multidisciplinary
Cheng-Ju Lin, Zhi Li, Timothy H. Hsieh
Summary: Entanglement renormalization is a method for coarse graining quantum states in real space, and applying the multiscale entanglement renormalization ansatz to finite-temperature states leads to a renormalization scheme. By mapping a two-dimensional toric code to a coarse-grained system with a higher temperature, the lack of topological order is explicitly demonstrated. Additionally, the thermofield double corresponding to critical thermal states in one-dimensional free boson models is described by a Lifshitz theory, demonstrating the relevance and irrelevance of perturbations under real space renormalization.
PHYSICAL REVIEW LETTERS
(2021)
Article
Astronomy & Astrophysics
Israel Quiros, Roberto De Arcia, Ricardo Garcia-Salcedo, Tame Gonzalez, Francisco X. Linares Cedeno, Ulises Nucamendi
Summary: This paper investigates the cosmological dynamics of geometric inflation using the tools of dynamical systems theory, focusing on two explicit models where the infinite series of higher curvature corrections can be summed. The global dynamics of these toy models in phase space is discussed, revealing the quantum origin of primordial inflation.
Article
Physics, Mathematical
Benoit Collins, Razvan Gurau, Luca Lionni
Summary: We discuss the generalization of the Harish-Chandra-Itzykson-Zuber integral to tensors and analyze its asymptotic behavior for large N. Assumptions on the scaling of external tensors with N are made. Our study reveals non-trivial asymptotic regimes for a two-parameter class of scaling ansatze. This research is important for understanding the entanglement properties of multipartite quantum systems and its potential applications to randomized local measurements.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2023)
Article
Astronomy & Astrophysics
ChunJun Cao, Jason Pollack, Yixu Wang
Summary: In this paper, we explore a class of holographic tensor networks that are efficient contractible variational ansatz, manifestly (approximate) quantum error correction codes, and can support power-law correlation functions. We prove that in the case when the network consists of a single type of tensor that also acts as an erasure correction code, it cannot be both locally contractible and sustain power-law correlation functions. Motivated by this no-go theorem and the desire for local contractibility in an efficient variational ansatz, we provide guidelines for constructing networks consisting of multiple types of tensors that can support power-law correlation. We also present an explicit construction of one such network, which approximates the holographic HaPPY pentagon code in the limit where variational parameters are taken to be small.
Article
Materials Science, Multidisciplinary
Hui-Ke Jin, Rong-Yang Sun, Yi Zhou, Hong-Hao Tu
Summary: The article presents an efficient and accurate method for converting Hartree-Fock-Bogoliubov wave functions into matrix product states (MPSs). The method is benchmarked with specific models to validate its performance and shows great potential for applications, especially when combined with the density-matrix renormalization group method.
