scholarly journals Dyonic objects and tensor network representation

2020 ◽  
pp. 2050336
Author(s):  
A. Belhaj ◽  
Y. El Maadi ◽  
S-E. Ennadifi ◽  
Y. Hassouni ◽  
M. B. Sedra
Keyword(s):  
Particle Physics ◽  
Network Representation ◽  
Tensor Network ◽  
Arbitrary Dimensions

Motivated by particle physics results, we investigate certain dyonic solutions in arbitrary dimensions. Concretely, we study the stringy constructions of such objects from concrete compactifications. Then, we elaborate their tensor network realizations using multistate particle formalism.

scholarly journals Boson condensation and instability in the tensor network representation of string-net states

2018 ◽  
Vol 98 (12) ◽  
Author(s):  
Sujeet K. Shukla ◽  
M. Burak Şahinoğlu ◽  
Frank Pollmann ◽  
Xie Chen
Keyword(s):  
Network Representation ◽  
Tensor Network

scholarly journals Sparse sampling and tensor network representation of two-particle Green's functions

2020 ◽  
Vol 8 (1) ◽  
Author(s):  
Hiroshi Shinaoka ◽  
Dominique Geffroy ◽  
Markus Wallerberger ◽  
Junya Otsuki ◽  
Kazuyoshi Yoshimi ◽  
...  
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Mean Field Theory ◽  
Mean Field ◽  
Sparse Sampling ◽  
Compact Representation ◽  
Hubbard Models ◽  
Network Representation ◽  
Tensor Network ◽  
Particle Level

Many-body calculations at the two-particle level require a compact representation of two-particle Green’s functions. In this paper, we introduce a sparse sampling scheme in the Matsubara frequency domain as well as a tensor network representation for two-particle Green’s functions. The sparse sampling is based on the intermediate representation basis and allows an accurate extraction of the generalized susceptibility from a reduced set of Matsubara frequencies. The tensor network representation provides a system independent way to compress the information carried by two-particle Green’s functions. We demonstrate efficiency of the present scheme for calculations of static and dynamic susceptibilities in single- and two-band Hubbard models in the framework of dynamical mean-field theory.

scholarly journals Loop-free tensor networks for high-energy physics

2021 ◽  
Vol 380 (2216) ◽  
Author(s):  
Simone Montangero ◽  
Enrique Rico ◽  
Pietro Silvi
Keyword(s):  
Particle Physics ◽  
Information Science ◽  
High Energy Physics ◽  
High Energy ◽  
Lattice Gauge ◽  
Tensor Networks ◽  
Sign Problem ◽  
Tensor Network ◽  
Network Methods ◽  
Energy Physics

This brief review introduces the reader to tensor network methods, a powerful theoretical and numerical paradigm spawning from condensed matter physics and quantum information science and increasingly exploited in different fields of research, from artificial intelligence to quantum chemistry. Here, we specialize our presentation on the application of loop-free tensor network methods to the study of high-energy physics problems and, in particular, to the study of lattice gauge theories where tensor networks can be applied in regimes where Monte Carlo methods are hindered by the sign problem. This article is part of the theme issue ‘Quantum technologies in particle physics’.

scholarly journals Abelian and non-Abelian chiral spin liquids in a compact tensor network representation

2020 ◽  
Vol 101 (3) ◽  
Author(s):  
Hyun-Yong Lee ◽  
Ryui Kaneko ◽  
Tsuyoshi Okubo ◽  
Naoki Kawashima
Keyword(s):  
Spin Liquids ◽  
Network Representation ◽  
Tensor Network

scholarly journals Semidual Kitaev lattice model and tensor network representation

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Florian Girelli ◽  
Prince K. Osei ◽  
Abdulmajid Osumanu
Keyword(s):  
Hopf Algebra ◽  
Quantum Group ◽  
Lattice Models ◽  
Cross Product ◽  
Network Representation ◽  
Finite Dimensional ◽  
Tensor Network ◽  
Exactly Solvable ◽  
Definition Of ◽  
Born Reciprocity

Abstract Kitaev’s lattice models are usually defined as representations of the Drinfeld quantum double D(H) = H ⋈ H*op, as an example of a double cross product quantum group. We propose a new version based instead on M(H) = Hcop ⧑ H as an example of Majid’s bicrossproduct quantum group, related by semidualisation or ‘quantum Born reciprocity’ to D(H). Given a finite-dimensional Hopf algebra H, we show that a quadrangulated oriented surface defines a representation of the bicrossproduct quantum group Hcop ⧑ H. Even though the bicrossproduct has a more complicated and entangled coproduct, the construction of this new model is relatively natural as it relies on the use of the covariant Hopf algebra actions. Working locally, we obtain an exactly solvable Hamiltonian for the model and provide a definition of the ground state in terms of a tensor network representation.

scholarly journals Isometric tensor network representation of string-net liquids

2020 ◽  
Vol 101 (8) ◽  
Author(s):  
Tomohiro Soejima ◽  
Karthik Siva ◽  
Nick Bultinck ◽  
Shubhayu Chatterjee ◽  
Frank Pollmann ◽  
...  
Keyword(s):  
Network Representation ◽  
Tensor Network

scholarly journals Explicit tensor network representation for the ground states of string-net models

2009 ◽  
Vol 79 (8) ◽  
Author(s):  
Oliver Buerschaper ◽  
Miguel Aguado ◽  
Guifré Vidal
Keyword(s):  
Ground States ◽  
Network Representation ◽  
Tensor Network
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