2009/07/24 by C. M. S. da Conceição, C. M. S. da Conceicao, E. C. Marino · 2 citations
Mathematics · Physics and Astronomy · #Condensed matter physics #Duality (order theory) #Mathematics #Phase (matter) #Phase diagram #Physics #Quantum #Quantum and electron transport phenomena #Quantum fluctuation #Quantum many-body systems #Quantum mechanics #Quantum phase transition #Quantum phases #Skyrmion #Spin (aerodynamics) #Theoretical and Computational Physics #Topological order #Topology (electrical circuits) #cond-mat.dis-nn
paper · pdf · doi:10.1103/physrevb.80.064422
published in Physical Review B 80(6) (American Physical Society) · 10 pages, 1 figure
arxiv created 2009/07/24 · openalex publication_date 2009/08/27 · arxiv updated 2015/05/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Quantum topological excitations (skyrmions) are analyzed from the point of view of their duality to spin excitations in the different phases of a disordered two-dimensional, short-range interacting, SO(3) quantum magnetic system of Heisenberg type. The phase diagram displays all the phases, which are allowed by the duality relation. We study the large-distance behavior of the two-point correlation function of quantum skyrmions in each of these phases and, out of this, extract information about the energy spectrum and nontriviality of these excitations. The skyrmion correlators present a power-law decay in the spin-glass (SG) phase, indicating that these quantum topological excitations are gapless but nontrivial in this phase. The SG phase is dual to the AF phase, in the sense that topological and spin excitations are, respectively, gapless in each of them. The Berezinskii-Kosterlitz-Thouless mechanism guarantees the survival of the SG phase at T\ensuremath≠0, whereas the AF phase is washed out to T=0 by the quantum fluctuations. Our results suggest a more symmetric way of characterizing a SG phase: one for which both the order and disorder parameters vanish, namely, ⟨\ensuremathσ⟩=0 and ⟨\ensuremathμ⟩=0, where \ensuremathσ is the spin and \ensuremathμ is the topological excitation operators.