2016/05/11 by Hyunyong Lee, Hyun‐Yong Lee, Jung Hoon Han · 1 citation
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Condensed matter physics #Homogeneous space #Lattice (music) #Mathematics #Phase (matter) #Phase diagram #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Quantum phase transition #Quantum phases #Quantum spin liquid #Spin polarization #Square lattice #Theoretical physics #Topological order #Valence bond theory #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.94.115150
published as Phys. Rev. B 94, 115150 (2016)
arxiv created 2016/05/11 · openalex publication_date 2016/09/23 · arxiv updated 2016/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Classification of possible quantum spin liquid (QSL) states of interacting spin-1/2's in two dimensions has been a fascinating topic of condensed matter for decades, resulting in enormous progress in our understanding of low-dimensional quantum matter. By contrast, relatively little work exists on the identification, let alone classification, of QSL phases for spin-1 systems in dimensions higher than one. Employing the powerful ideas of tensor network theory and its classification, we develop general methods for writing QSL wave functions of spin-1 respecting all the lattice symmetries, spin rotation, and time reversal with trivial gauge structure on the square lattice. We find 25 distinct classes characterized by five binary quantum numbers. Several explicit constructions of such wave functions are given for bond dimensions D ranging from two to four, along with thorough numerical analyses to identify their physical characters. Both gapless and gapped states are found. The topological entanglement entropy of the gapped states is close to zero, indicative of topologically trivial states. In D=4, several different tensors can be linearly combined to produce a family of states within the same symmetry class. A rich ``phase diagram'' can be worked out among the phases of these tensors, as well as the phase transitions among them. Among the states we identified in this putative phase diagram is the plaquette-ordered phase, gapped resonating valence bond phase, and a critical phase. A continuous transition separates the plaquette-ordered phase from the resonating valence bond phase.