Majorana Fermi surface state in a network of quantum spin chains

Abstract

Half a century ago, Anderson’s resonating valence bond theory initiated a compelling research subject in condensed matter physics: the exploration of the nature of quantum spin liquids. Today, the understanding of these phases of matter is deeply connected to the concept of quantum entanglement. In a broad context, quantum spin liquids refer to systems wherein the effective degrees of freedom are described by local magnetic moments residing on the lattice, exhibiting an absence of long-range order even at very low temperatures. In addition, the ground-state wave function displays significant entanglement, and excitations manifest fractionalization. In particular, this thesis is focused on the study of the chiral spin liquids that can be found in Mott insulators that break time-reversal and parity symmetry. Starting from junctions composed of critical spin-1 chains, we construct a honeycomb network hosting a chiral spin liquid with gapless spectrum. The low-energy modes are characterized by spin-1 Majorana fermions, which give rise to a legitimate two-dimensional state that harbors a Fermi surface when the interactions at the junctions are adjusted close to chiral fixed points with staggered chirality. We explore the physical properties and stability of the chiral spin liquid phase against boundary perturbations, employing well-controlled analytical methods within the effective field theory of the network. Additionally, we establish evident connections with the excitation spectrum derived from parton constructions on the kagome lattice.