Symmetry fractionalization in the topological phase of the spin-12J1−J2triangular Heisenberg model

2016/06/30 by S. N. Saadatmand, Ian P. McCulloch, I. P. McCulloch · 73 citations
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Antiferromagnetism #Combinatorics #Condensed matter physics #Fractionalization #Geometry #Ground state #Homogeneous space #Lattice (music) #Mathematics #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Spin (aerodynamics) #Spinon #Topological order #Topology (electrical circuits) #cond-mat.str-el

paper · pdf · doi:10.1103/physrevb.94.121111

published in Physical review. B./Physical review. B 94(12) (American Physical Society) · 6 pages, 4 figures, 1 table, and 10 pages of supplemental materials. v3: equivalent to the published version

openalex created_date 2016/06/24 · openalex publication_date 2016/09/13 · arxiv created 2018/04/12 · arxiv updated 2018/04/13 · openalex updated_date 2026/08/05

Abstract

Using density-matrix renormalization-group calculations for infinite cylinders, we elucidate the properties of the spin-liquid phase of the spin-(1)/(2)\phantom\rule4pt0exJ₁\text\ensuremath-J₂ Heisenberg model on the triangular lattice. We find four distinct ground states characteristic of a nonchiral, Z₂ topologically ordered state with vison and spinon excitations. We shed light on the interplay of topological ordering and global symmetries in the model by detecting fractionalization of time-reversal and space-group dihedral symmetries in the anyonic sectors, which leads to the coexistence of symmetry protected and intrinsic topological order. The anyonic sectors, and information on the particle statistics, can be characterized by degeneracy patterns and symmetries of the entanglement spectrum. We demonstrate the ground states on finite-width cylinders are short-range correlated and gapped; however, some features in the entanglement spectrum suggest that the system develops gapless spinonlike edge excitations in the large-width limit.

Citations

• Detection of symmetry-protected topological phases in one dimension
• Lieb-Schultz-Mattis in higher dimensions
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Phase diagram of thespin−12triangularJ1−J2Heisenberg model on a three-leg cylinder
• Mott Transition from a Spin Liquid to a Fermi Liquid in the Spin-Frustrated Organic Conductorκ−(ET)2Cu2(CN)3
• Density-matrix algorithms for quantum renormalization groups
• Constraints on Topological Order in Mott Insulators
• Spin Liquid State in an Organic Mott Insulator with a Triangular Lattice
• Entanglement spectrum of a topological phase in one dimension
• Classification of symmetry enriched topological phases with exactly solvable models
• Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems
• The density-matrix renormalization group in the age of matrix product states
• Fault-tolerant quantum computation by anyons
• Two soluble models of an antiferromagnetic chain
• Anyons in an exactly solved model and beyond
• Quantum orders and symmetric spin liquids

Cited by

• A quantum dipolar spin liquid
• Interplay between spatial anisotropy and next-nearest-neighbor exchange interactions in the triangular Heisenberg model
• Dynamical structure factor of the triangular antiferromagnet: Schwinger boson theory beyond mean field
• Spectrum of conformal gauge theories on a torus
• Symmetry-Projected Spin-AGP Methods Applied to Spin Systems