2017/10/31 by Cécile Monthus, Cecile Monthus
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Geometry #Ground state #Homogeneous space #Invariant (physics) #Mathematical physics #Mathematics #Physics #Physics of Superconductivity and Magnetism #Pure mathematics #Quantum #Quantum many-body systems #Quantum mechanics #Renormalization group #Scale invariance #Tensor (intrinsic definition) #cond-mat.str-el
paper · pdf · doi:10.1088/1751-8121/aaa814
published as 2018 J. Phys. A: Math. Theor. 51 095301 · v2=final version (17 pages)
openalex created_date 2017/10/20 · arxiv created 2018/01/15 · openalex publication_date 2018/02/01 · arxiv updated 2018/02/02 · openalex updated_date 2026/08/05
Abstract For the line of critical antiferromagnetic XXZ chains with coupling J > 0 and anisotropy <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mn>0</mml:mn> <mml:mo><</mml:mo> <mml:mi mathvariant="normal">Δ</mml:mi> <mml:mo>⩽</mml:mo> <mml:mn>1</mml:mn> </mml:mstyle> </mml:math> , we describe how the block-spin renormalization procedure preserving the SU q (2) symmetry introduced by Martin-Delgado and Sierra (1996 Phys. Rev. Lett . 76 1146) can be reformulated as the translation-invariant scale-invariant tree-tensor-state of the smallest dimension that is compatible with the quantum symmetries of the model. The properties of this tree-tensor-state are studied in detail via the ground-state energy, the magnetizations and the staggered magnetizations, as well as the Shannon–Renyi entropies characterizing the multifractality of the components of the wave function.