Asymptotic freedom, Haldane gap and edge states of SU(N) spin chains
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Motivated by the rich phase diagrams recently unveiled in frustrated spin-1 chains with competing next-nearest-neighbor and four-spin interactions, we investigate the nature of the elementary excitations of spin-1 chains in the vicinity of phase transition ...
In recent years, topology gained a central role in physics. We learnt that energetics could be often explained better by classes of objects defined by having qualitative differences. In today's jargon, we say they are topologically distinct. The process of ...
Symmetry and topology are fundamental properties of nature. Mathematics provides us with a general framework to understand these concepts. On one side, symmetry describes the invariance properties of an object for specific transformations. On the other sid ...
Using the Matrix Product State framework, we generalize the Affleck-Kennedy-Lieb-Tasaki (AKLT) construction to one-dimensional spin liquids with global color SU(N) symmetry, finite correlation lengths, and edge states that can belong to any self-conjugate ...
Building on the mapping of large-S spin chains onto the O(3) nonlinear sigma model with coupling constant 2/S, and on general properties of that model (asymptotic freedom, implying that perturbation theory is valid at high energy, and Elitzur's conjecture ...
This thesis explores various approaches of studying the long-range colour order of antiferromagnetic SU(N) Heisenberg models with the linear flavour-wave theory (LFWT). The LFWT is an extension of the well-known SU(2) spin-wave theory to SU(N), and this se ...
We generalize the construction of the spin-1/2 SU(2) resonating valence bond (RVB) state to the case of the self-conjugate 6 representation of SU(4). As for the case of SU(2) [J.-Y. Chen and D. Poilblanc, Phys. Rev. B 97, 161107(R) (2018)], we use the proj ...
Motivated by the recent generalization of the Haldane conjecture to SU(3) chains [Lajko et al., Nucl. Phys. B924, 508 (2017)] according to which a Haldane gap should be present for symmetric representations if the number of boxes in the Young diagram is a ...
We study the zero-temperature phase diagram of the spin-1/2 Heisenberg model with breathing anisotropy (i.e., with different coupling strength on the upward and downward triangles) on the kagome lattice. Our study relies on large scale tensor network simul ...
We perform a systematic DMRG investigation of the two natural spin-1 generalizations of the spin-1/2 Majumdar-Ghosh chain, the spin-1 J(1)-J(2) Heisenberg chain, where J(2) is a next-nearest-neighbor Heisenberg coupling, and the spin-1 J(1)-J(3) model, whe ...