1,725,271 research outputs found
Dialogue with Akira Sugino
No full textEl profesor Sugino, ex embajador del Japón en Chile y actualmente cooperando con el IRI, con el apoyo de la JICA, en carácter de académico visitante, dialogó con Jorge Di Masi, Coordinador del Departamento de Asia y el Pacífico del Instituto.Sección Diálogos.Instituto de Relaciones Internacionales (IRI
Area law violations and quantum phase transitions in modified Motzkin walk spin chains
No full textArea law violations for entanglement entropy in the form of a square root has recently been studied for one-dimensional frustration-free quantum systems based on the Motzkin walks and their variations. Here we consider a Motzkin walk with a different Hilbert space on each step of the walk spanned by elements of a {\it Symmetric Inverse Semigroup} with the direction of each step governed by its algebraic structure. This change alters the number of paths allowed in the Motzkin walk and introduces a ground state degeneracy sensitive to boundary perturbations. We study the frustration-free spin chains based on three symmetric inverse semigroups, S-1(3), S-2(3), and S-1(2),The system based on S-1(3) and S-2(3) provide examples of quantum phase transitions in one dimensions with the former exhibiting a transition between the area law and a logarithmic violation of the area law and the latter providing an example of transition from logarithmic scaling to a square root scaling in the system size, mimicking a colored S-1(3) system. The system with S-1(2) is much simpler and produces states that continue to obey the area law. © 2018 The Author(s). Published by IOP Publishing Ltd on behalf of SISSA Medialab srl011Nsciescopu
On a sangaku of Sugino\u27o Shrine (Yamagata) and Yamaguchi Kanzan\u27s second trip
Get PDFIn the preamble of the 1818 sangaku tablet of Sugino\u27o Shrine, the proposers acknowledged the help of an unnamed teacher/master in understanding and solving certain mathematical problems. Endō Tadashi argued that this unnamed teacher could be Saitō Naonaka (1773-1844). In this paper, we examine the famous travel diary of Yamaguchi Kanzan (?-1850) especially on his second trip to the Northeast. We compare the content of Yamaguchi\u27s diary with the three problems of Sugino\u27o\u27s tablet. Together with the timing of Yamaguchi\u27s travel, we conclude that Yamaguchi Kanzan was likely the unnamed master mentioned in the preface of the Sugino\u27o Shrine sangaku
Lattice formulation of two-dimensional N=(2,2) SQCD with exact supersymmetry
No full textAbstractWe construct a lattice model for two-dimensional N=(2,2) supersymmetric QCD (SQCD), with the matter multiplets belonging to the fundamental or anti-fundamental representation of the gauge group U(N) or SU(N). The construction is based on the topological field theory (twisted supercharge) formulation and exactly preserves one supercharge along the line of the papers [F. Sugino, JHEP 0401 (2004) 015; F. Sugino, JHEP 0403 (2004) 067; F. Sugino, JHEP 0501 (2005) 016; F. Sugino, Phys. Lett. B 635 (2006) 218] for pure supersymmetric Yang–Mills theories. In order to avoid the species doublers of the matter multiplets, we introduce the Wilson terms and the model is defined for the case of the number of the fundamental matters (n+) equal to that of the anti-fundamental matters (n−). If some of the matter multiplets decouple from the theory by sending the corresponding anti-holomorphic twisted masses to the infinity, we can analyze the general n+≠n− case, although the lattice model is defined for n+=n−. By computing the anomaly of the U(1)A R-symmetry in the lattice perturbation, we see that the decoupling is achieved and the anomaly for n+≠n− is correctly obtained
Highly entangled spin chains and 2D quantum gravity
No full text© 2020 by the authors. Motzkin and Fredkin spin chains exhibit the extraordinary amount of entanglement scaling as a square-root of the volume, which is beyond logarithmic scaling in the ordinary critical systems. Intensive study of such spin systems is urged to reveal novel features of quantum entanglement. As a study of the systems from a different viewpoint, we introduce large-N matrix models with so-called ABAB interactions, in which correlation functions reproduce the entanglement scaling in tree and planar Feynman diagrams. Including loop diagrams naturally defines an extension of the Motzkin and Fredkin spin chains. Contribution from the whole loop effects at large N gives the growth of the power of 3/2 (with logarithmic correction), further beyond the square-root scaling. The loop contribution provides fluctuating two-dimensional bulk geometry, and the enhancement of the entanglement is understood as an effect of quantum gravity.11Nsciescopu
Novel quantum phases on graphs using abelian gauge theory
No full text© 2021 IOP Publishing Ltd and SISSA Medialab srl Graphs are topological spaces that include broader objects than discretized manifolds, making them interesting playgrounds for the study of quantum phases not realized by symmetry breaking. In particular they are known to support anyons of an even richer variety than the two-dimensional space. We explore this possibility by building a class of frustration-free and gapped Hamiltonians based on discrete abelian gauge groups. The resulting models have a ground state degeneracy that can be either a topological invariant, an extensive quantity or a mixture of the two. For two basis of the degenerate ground states which are complementary in quantum theory, the entanglement entropy (EE) is exactly computed. The result for one basis has a constant global term, known as the topological EE, implying long-range entanglement. On the other hand, the topological EE vanishes in the result for the other basis. Comparisons are made with similar occurrences in the toric code. We analyze excitations and identify anyon-like excitations that account for the topological EE. An analogy between the ground states of this system and the theta-vacuum for a U(1) gauge theory on a circle is also drawn.11Nsciescopu
Renyi entropy of highly entangled spin chains
No full textEntanglement is one of the most intriguing features of quantum theory and a main resource in quantum information science. Ground states of quantum many-body systems with local interactions typically obey an area law which means that the entanglement entropy is proportional to the boundary length. It is exceptional when the system is gapless, and the area law had been believed to be violated by at most a logarithm over two decades. Recent discovery of Motzkin and Fredkin spin chain models is striking, since these models provide significant violation of the entanglement beyond the belief, growing as a square root of the volume in spite of local interactions. In this paper, we first analytically compute the R?nyi entropy of the Motzkin and Fredkin models by careful treatment of asymptotic analysis. The R?nyi entropy is an important quantity, since the whole spectrum of an entangled subsystem is reconstructed once the R?nyi entropy is known as a function of its parameter. We find nonanalytic behavior of the R?nyi entropy with respect to the parameter, which is a novel phase transition never seen in any other spin chain studied so far. Interestingly, similar behavior is seen in the R?nyi entropy of Rokhsar-Kivelson states in two dimensions. (c) 2018 World Scientific Publishing Company11Nsciescopu
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