Chiral topological spin liquids with projected entangled pair states

Abstract

Topological chiral phases are ubiquitous in the physics of the Fractional Quantum Hall Effect. Non-chiral topological spin liquids are also well known. Here, using the framework of projected entangled pair states (PEPS), we construct a family of chiral spin liquids on the square lattice which are generalized spin-1/2 Resonating Valence Bond (RVB) states obtained from deformed local tensors with $d+id$ symmetry. On a cylinder, we construct four topological sectors with even or odd number of spinons on the boundary and even or odd number of (${\mathbb{Z}}_2$) fluxes penetrating the cylinder which, we argue, remain orthogonal in the limit of infinite perimeter. The analysis of the transfer matrix provides evidence of short-range (long-range) triplet (singlet) correlations as for the critical (non-chiral) RVB state. The Entanglement Spectrum exhibits chiral edge modes, which we confront to predictions of Conformal Field Theory, and the corresponding Entanglement Hamiltonian is shown to be long ranged.

7 pages, 6 figures, Final version (small changes)

References in corpus (6)

• Non-Abelian Anyons and Topological Quantum Computation
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Criticality, the area law, and the computational power of PEPS
• Resonating valence bond states in the PEPS formalism
• Chiral projected entangled-pair state with topological order
• Critical Correlations for Short-Range Valence-Bond Wave Functions on the Square Lattice

Cited by in corpus (5)

• Systematic construction of spin liquids on the square lattice from tensor networks with SU(2) symmetry
• Emergence of Chiral Spin Liquids via Quantum Melting of Non-Coplanar Magnetic Orders
• Towards a mathematical formalism for classifying phases of matter
• Investigation of the chiral antiferromagnetic Heisenberg model using PEPS
• Infinite Matrix Product States vs Infinite Projected Entangled-Pair States on the Cylinder: a comparative study