scholarly journals The AKLT Model on a Hexagonal Chain is Gapped

2019 ◽  
Vol 177 (6) ◽  
pp. 1077-1088 ◽  
Author(s):  
Marius Lemm ◽  
Anders W. Sandvik ◽  
Sibin Yang
Keyword(s):  
Hexagonal Chain ◽  
Aklt Model

scholarly journals Universal Qudit Hamiltonians

2021 ◽  
Author(s):  
Stephen Piddock ◽  
Ashley Montanaro
Keyword(s):  
State Energy ◽  
Entangled State ◽  
Quantum Computers ◽  
List Type ◽  
Universal Family ◽  
Finite Dimensional ◽  
Universal Quantum ◽  
Aklt Model ◽  
Almost All ◽  
Natural Way

AbstractA family of quantum Hamiltonians is said to be universal if any other finite-dimensional Hamiltonian can be approximately encoded within the low-energy space of a Hamiltonian from that family. If the encoding is efficient, universal families of Hamiltonians can be used as universal analogue quantum simulators and universal quantum computers, and the problem of approximately determining the ground-state energy of a Hamiltonian from a universal family is QMA-complete. One natural way to categorise Hamiltonians into families is in terms of the interactions they are built from. Here we prove universality of some important classes of interactions on qudits (d-level systems): We completely characterise the k-qudit interactions which are universal, if augmented with arbitrary Hermitian 1-local terms. We find that, for all $$k \geqslant 2$$ k ⩾ 2 and all local dimensions $$d \geqslant 2$$ d ⩾ 2 , almost all such interactions are universal aside from a simple stoquastic class. We prove universality of generalisations of the Heisenberg model that are ubiquitous in condensed-matter physics, even if free 1-local terms are not provided. We show that the SU(d) and SU(2) Heisenberg interactions are universal for all local dimensions $$d \geqslant 2$$ d ⩾ 2 (spin $$\geqslant 1/2$$ ⩾ 1 / 2 ), implying that a quantum variant of the Max-d-Cut problem is QMA-complete. We also show that for $$d=3$$ d = 3 all bilinear-biquadratic Heisenberg interactions are universal. One example is the general AKLT model. We prove universality of any interaction proportional to the projector onto a pure entangled state.

scholarly journals Omega, Sadhana, and PI Polynomials of Quasi-Hexagonal Benzenoid Chain

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Nazeran Idrees ◽  
Muhammad Jawwad Saif ◽  
Sumiya Nasir ◽  
Fozia Bashir Farooq ◽  
Asia Rauf ◽  
...  
Keyword(s):  
Linear Chain ◽  
Graph Invariants ◽  
Hexagonal Chain ◽  
Pi Index ◽  
Chemical Graphs

Counting polynomials are important graph invariants whose coefficients and exponents are related to different properties of chemical graphs. Three closely related polynomials, i.e., Omega, Sadhana, and PI polynomials, dependent upon the equidistant edges and nonequidistant edges of graphs, are studied for quasi-hexagonal benzenoid chains. Analytical closed expressions for these polynomials are derived. Moreover, relation between Padmakar–Ivan (PI) index of quasi-hexagonal chain and that of corresponding linear chain is also established.

π-ELECTRON CONTENTS OF RINGS IN THE DOUBLE-HEXAGONAL-CHAIN HOMOLOGOUS SERIES (PYRENE, ANTHANTHRENE AND OTHER ACENOACENES)

2005 ◽  
Vol 25 (3) ◽  
pp. 215-226 ◽  
Author(s):  
Ivan Gutman ◽  
Milan Randić ◽  
Alexandru T. Balaban ◽  
Boris Furtula ◽  
Veselin Vuĉković
Keyword(s):  
Homologous Series ◽  
Hexagonal Chain

scholarly journals Valency-Based Topological Properties of Linear Hexagonal Chain and Hammer-Like Benzenoid

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Yi-Xia Li ◽  
Abdul Rauf ◽  
Muhammad Naeem ◽  
Muhammad Ahsan Binyamin ◽  
Adnan Aslam
Keyword(s):  
Graphical Representation ◽  
Structural Features ◽  
Topological Indices ◽  
Quantitative Structure ◽  
Structure Property ◽  
Hexagonal Chain ◽  
Structure Property Relationships ◽  
Quantitative Measurements ◽  
Qsar Modelling ◽  
Quantitative Structure Property Relationships

Topological indices are quantitative measurements that describe a molecule’s topology and are quantified from the molecule’s graphical representation. The significance of topological indices is linked to their use in QSPR/QSAR modelling as descriptors. Mathematical associations between a particular molecular or biological activity and one or several biochemical and/or molecular structural features are QSPRs (quantitative structure-property relationships) and QSARs (quantitative structure-activity relationships). In this paper, we give explicit expressions of two recently defined novel ev-degree- and ve-degree-based topological indices of two classes of benzenoid, namely, linear hexagonal chain and hammer-like benzenoid.

scholarly journals Block spin density matrix of the inhomogeneous AKLT model

2008 ◽  
Vol 7 (4) ◽  
pp. 153-174 ◽  
Author(s):  
Ying Xu ◽  
Hosho Katsura ◽  
Takaaki Hirano ◽  
Vladimir E. Korepin
Keyword(s):  
Density Matrix ◽  
Spin Density ◽  
Spin Density Matrix ◽  
Aklt Model ◽  
Block Spin

Applications on Hyper-Zagreb Index of Generalized Hierarchical Product Graphs

2016 ◽  
Vol 13 (10) ◽  
pp. 7355-7361 ◽  
Author(s):  
Zhaoyang Luo
Keyword(s):  
Connected Graph ◽  
Explicit Formulas ◽  
Zagreb Index ◽  
Hexagonal Chain ◽  
Product Graphs

Let G be a connected graph. The Hyper-Zagreb index of a connected graph G is defined as HM(G) = Σuv∈EG [dG(u)+dG(v)]2, where dG(v) is the degree of the vertex v in G. In this paper, the Hyper-Zagreb Gindex of the generalized hierarchical, Cartesian, cluster, corona products and four new sums of graphs according to some invariants of the factors are computed, respectively. As applications, we present explicit formulas for the HM index of the linear phenylene Fn, the C4 nanotorus Cm□Cn, the C4 nanotubes Pm□Cn, the l-dimensional hypercubes Ql , the zig-zag polyhex nanotube TUHC6[2n, 2], the hexagonal chain ln, the regular dicentric dendrimer DDp,r and so forth.

scholarly journals Deformations of the boundary theory of the square-lattice AKLT model

2020 ◽  
Vol 102 (3) ◽  
Author(s):  
John Martyn ◽  
Kohtaro Kato ◽  
Angelo Lucia
Keyword(s):  
Square Lattice ◽  
Boundary Theory ◽  
Aklt Model
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