Projected BCS states and spin Hamiltonians for the SO(n)_1 Wess-Zumino-Witten model

Abstract

We propose a class of projected BCS wave functions and derive their parent spin Hamiltonians. These wave functions can be formulated as infinite Matrix Product States constructed by chiral correlators of Majorana fermions. In 1D, the spin Hamiltonians can be viewed as SO(n) generalizations of Haldane-Shastry models. We numerically compute the spin-spin correlation functions and Renyi entropies for n=5 and 6. Together with the results for n=3 and 4, we conclude that these states are critical and their low-energy effective theory is the SO(n)_1 Wess-Zumino-Witten model. In 2D, we show that the projected BCS states are chiral spin liquids, which support non-Abelian anyons for odd n and Abelian anyons for even n.

5+8 pages, 3 figures, published version

References in corpus (8)

• Entanglement entropy of critical spin liquids
• Non-Abelian Statistics in a Quantum Antiferromagnet
• Class of exactly solvable SO(n) symmetric spin chains with matrix product ground states
• Paired chiral spin liquid with a Fermi surface in S=1 model on the triangular lattice
• String order and hidden topological symmetry in the SO(2n+1) symmetric matrix product states
• Fermionic theory for quantum antiferromagnets with spin S > 1/2
• Quantum criticality in the SO(5) bilinear-biquadratic Heisenberg chain
• Chiral correlators of the Ising conformal field theory

Cited by in corpus (20)

• Microscopic models for Kitaev's sixteenfold way of anyon theories
• Chiral projected entangled-pair state with topological order
• Quantum spin models for the SU(n)_1 Wess-Zumino-Witten model
• Anyon braiding in semi-analytical fractional quantum Hall lattice models
• Infinite Matrix Product States for long range SU(N) spin models
• Lattice effects on Laughlin wave functions and parent Hamiltonians
• Hexagon-singlet solid ansatz for the spin-1 kagome antiferromagnet
• Excited States in Spin Chains from Conformal Blocks
• Parent Hamiltonians for lattice Halperin states from free-boson conformal field theories
• Exact projected entangled pair ground states with topological Euler invariant
• Resonating valence bond realization of spin-1 non-Abelian chiral spin liquid on the torus
• Chiral conformal field theory for topological states and the anyon eigenbasis on the torus
• Symmetry-protected topological phases, conformal criticalities, and duality in exactly solvable SO($n$) spin chains
• Construction of spin models displaying quantum criticality from quantum field theory
• Abelian and non-Abelian quantum spin liquids in a three-component Bose gas on optical Kagome lattices
• Rainbow chains and numerical renormalisation group for accurate chiral conformal spectra
• Bridging conformal field theory and parton approaches to SU(n)_k chiral spin liquids
• Non-Abelian topological order with SO(5)${}_1$ chiral edge states
• Transverse Field $\gamma$-Matrix Spin Chains
• Gapped spinful phases obtained via Gutzwiller projections of Euler states