scholarly journals Vertical density matrix algorithm: A higher-dimensional numerical renormalization scheme based on the tensor product state ansatz

2001 ◽  
Vol 64 (1) ◽  
Author(s):  
Nobuya Maeshima ◽  
Yasuhiro Hieida ◽  
Yasuhiro Akutsu ◽  
Tomotoshi Nishino ◽  
Kouichi Okunishi
Keyword(s):  
Density Matrix ◽  
Tensor Product ◽  
Renormalization Scheme ◽  
Product State ◽  
Matrix Algorithm ◽  
Higher Dimensional ◽  
Vertical Density

COMPLEXITY RELAXATION OF THE TENSOR PRODUCT MODEL TRANSFORMATION FOR HIGHER DIMENSIONAL PROBLEMS

2008 ◽  
Vol 9 (2) ◽  
pp. 195-200 ◽  
Author(s):  
Péter Baranyi ◽  
Zoltén Petres ◽  
Péter Korondi ◽  
Yeung Yam ◽  
Hideki Hashimoto
Keyword(s):  
Tensor Product ◽  
Model Transformation ◽  
Product Model ◽  
Higher Dimensional

scholarly journals Perfect hypercomplex algebras: Semi-tensor product approach

2021 ◽  
Vol 1 (4) ◽  
pp. 177-187
Author(s):  
Daizhan Cheng ◽  
◽  
Zhengping Ji ◽  
Jun-e Feng ◽  
Shihua Fu ◽  
...  
Keyword(s):  
Tensor Product ◽  
Sufficient Conditions ◽  
Characteristic Functions ◽  
Hypercomplex Numbers ◽  
3 Dimensional ◽  
Zero Sets ◽  
Higher Dimensional ◽  
Product Approach ◽  
Necessary And Sufficient

<abstract><p>The set of associative and commutative hypercomplex numbers, called the perfect hypercomplex algebras (PHAs) is investigated. Necessary and sufficient conditions for an algebra to be a PHA via semi-tensor product (STP) of matrices are reviewed. The zero sets are defined for non-invertible hypercomplex numbers in a given PHA, and characteristic functions are proposed for calculating zero sets. Then PHA of various dimensions are considered. First, classification of $ 2 $-dimensional PHAs are investigated. Second, all the $ 3 $-dimensional PHAs are obtained and the corresponding zero sets are calculated. Finally, $ 4 $- and higher dimensional PHAs are also considered.</p></abstract>

scholarly journals THE COMBINATORICS OF TENSOR PRODUCTS OF HIGHER AUSLANDER ALGEBRAS OF TYPE A

2020 ◽  
pp. 1-21
Author(s):  
JORDAN MCMAHON ◽  
NICHOLAS J. WILLIAMS
Keyword(s):  
Tensor Product ◽  
Tensor Products ◽  
Type A ◽  
Coordinate Ring ◽  
Preprojective Algebra ◽  
Finite Algebras ◽  
Plücker Coordinates ◽  
Higher Dimensional ◽  
Dimensional Version

Abstract We consider maximal non-l-intertwining collections, which are a higher-dimensional version of the maximal non-crossing collections which give clusters of Plücker coordinates in the Grassmannian coordinate ring, as described by Scott. We extend a method of Scott for producing such collections, which are related to tensor products of higher Auslander algebras of type A. We show that a higher preprojective algebra of the tensor product of two d-representation-finite algebras has a d-precluster-tilting subcategory. Finally, we relate mutations of these collections to a form of tilting for these algebras.

FOCK SPACE FOR GENERALIZED STATISTICS AND BOSON-FERMION SUPERSELECTION RULE

1996 ◽  
Vol 10 (21) ◽  
pp. 1035-1041
Author(s):  
L. DE FALCO ◽  
R. MIGNANI ◽  
R. SCIPIONI
Keyword(s):  
Quantum Gravity ◽  
Density Matrix ◽  
Tensor Product ◽  
Fock Space ◽  
Superselection Rule ◽  
Expectation Values ◽  
Ladder Operators ◽  
Von Neumann ◽  
Von Neumann Equation ◽  
Natural Way

We introduce a generalized Fock space for a recently proposed operatorial deformation of the Heisenberg-Weyl (HW) algebra, aimed at describing statistics different from the Bose or Fermi ones. The new Fock space is obtained by the tensor product of the usual Fock space and the space spanned by the eigenstates of the deformation operator ĝ. We prove a “statistical Ehrenfest-like theorem”, stating that the expectation values of the ladder operators of the generalized HW algebra — taken in the ĝ-subspace — are creation and annihilation operators defined in the usual Fock space and obeying the ordinary statistics, according to the ĝ-eigenvalues. Moreover, such a “statistics” operator ĝ can be regarded as the generator of a boson-fermion superselection rule. As a consequence, the generalized Fock space decomposes into incoherent sectors, and therefore one gets a density matrix diagonal in the ĝ eigenstates. This leads, under suitable conditions, to the possibility of continuously interpolating between different statistics. In particular, it is necessary to assume a nonstandard Liouville-Von Neumann equation for the density matrix, of the type already considered e.g. in the framework of quantum gravity. It is also preliminarily shown that our formalism leads in a natural way — due to the very properties of the operator ĝ — to a grading of the HW algebra, and therefore to a supersymmetrical scheme.

scholarly journals Subdivision Depth Computation for Tensor Productn-Ary Volumetric Models

2011 ◽  
Vol 2011 ◽  
pp. 1-22 ◽  
Author(s):  
Ghulam Mustafa ◽  
Muhammad Sadiq Hashmi
Keyword(s):  
Tensor Product ◽  
Error Bounds ◽  
Error Control ◽  
Computational Formula ◽  
Evaluation Technique ◽  
Volumetric Models ◽  
Higher Dimensional ◽  
Special Cases ◽  
Subdivision Depth ◽  
Control Tool

We offer computational formula of subdivision depth for tensor productn-ary (n⩾2) volumetric models based on error bound evaluation technique. This formula provides and error control tool in subdivision schemes over regular hexahedron lattice in higher-dimensional spaces. Moreover, the error bounds of Mustafa et al. (2006) are special cases of our bounds.

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