We study possible gapless edge states of translation-symmetric ${\mathbb{Z}}_{2}$ spin liquids. The gapless edge states emerge from dangling Majorana fermions at the boundary. We construct a series of mean-field Hamiltonians of ${\mathbb{Z}}_{2}$ spin liquids on the square lattice; these models can be obtained by generalization of Wen's exactly solvable plaquette model. We also study the details of the edge theory of these ${\mathbb{Z}}_{2}$ spin liquids and find their effective background field (BF) theory descriptions. The effective BF theories are shown to describe the crystal momenta of the ground states and their degeneracies and to predict the edge theories of these ${\mathbb{Z}}_{2}$ spin liquids. As a by-product, we obtained a way to classify the BF theories reflecting the lattice symmetries. We discuss in closing three-dimensional ${\mathbb{Z}}_{2}$ spin liquids with gapless surface states on the cubic lattice.We study possible gapless edge states of translation-symmetric ${\mathbb{Z}}_{2}$ spin liquids. The gapless edge states emerge from dangling Majorana fermions at the boundary. We construct a series of mean-field Hamiltonians of ${\mathbb{Z}}_{2}$ spin liquids on the square lattice; these models can be obtained by generalization of Wen's exactly solvable plaquette model. We also study the details of the edge theory of these ${\mathbb{Z}}_{2}$ spin liquids and find their effective background field (BF) theory descriptions. The effective BF theories are shown to describe the crystal momenta of the ground states and their degeneracies and to predict the edge theories of these ${\mathbb{Z}}_{2}$ spin liquids. As a by-product, we obtained a way to classify the BF theories reflecting the lattice symmetries. We discuss in closing three-dimensional ${\mathbb{Z}}_{2}$ spin liquids with gapless surface states on the cubic lattice.

arXiv:1206.2295Physical Review BSep 4, 201227 citations

Introduction to Quantum Spin Liquids

C. Lhuillier, Grégoire Misguich

Springer series in solid-state sciencesSep 29, 201011 citations

Mean-field theory of spin-liquid states with finite energy gap and topological orders

Xiao-Gang Wen

The mean-field theory of a T- and P-symmetric spin-liquid state is developed. The quasiparticle excitations in the spin-liquid state are shown to be spin-1/2 neutral fermions (the spinons) and charge e spinless bosons (the holons). The spin-liquid state is shown to be characterized by a nontrivial topological order. Although our discussions are based on the mean-field theory, the concept of the topological order and the associated universal properties (e.g., the quantum number of the quasiparticles) are expected to be valid beyond the mean-field theory. We also discuss the dynamical stability of the mean-field theory.The mean-field theory of a T- and P-symmetric spin-liquid state is developed. The quasiparticle excitations in the spin-liquid state are shown to be spin-1/2 neutral fermions (the spinons) and charge e spinless bosons (the holons). The spin-liquid state is shown to be characterized by a nontrivial topological order. Although our discussions are based on the mean-field theory, the concept of the topological order and the associated universal properties (e.g., the quantum number of the quasiparticles) are expected to be valid beyond the mean-field theory. We also discuss the dynamical stability of the mean-field theory.

Physical review. B, Condensed matterAug 1, 1991627 citations

Gapless and gapped spin liquids in frustrated spin-1/2 models

Federico Becca

Bulletin of the American Physical SocietyMar 5, 20150 citations

Spin liquid states in the vicinity of a metal-insulator transition

Yi Zhou, Tai Kai Ng

We study in this paper quantum spin liquid states (QSLs) at the vicinity of the metal-insulator transition. Assuming that the low-energy excitations in the QSLs are labeled by ``spinon'' occupation numbers with the same Fermi surface structure as in the corresponding metal (Fermi-liquid) side, we propose a phenomenological Landau-like low-energy theory for the QSLs and show that the usual $U(1)$ QSLs is a representative member of this class of spin liquids. Based on our effective low-energy theory, an alternative picture to the Brinkman-Rice picture of the Mott metal-insulator transition is proposed. The charge, spin, and thermal responses of QSLs are discussed under such a phenomenology.We study in this paper quantum spin liquid states (QSLs) at the vicinity of the metal-insulator transition. Assuming that the low-energy excitations in the QSLs are labeled by ``spinon'' occupation numbers with the same Fermi surface structure as in the corresponding metal (Fermi-liquid) side, we propose a phenomenological Landau-like low-energy theory for the QSLs and show that the usual $U(1)$ QSLs is a representative member of this class of spin liquids. Based on our effective low-energy theory, an alternative picture to the Brinkman-Rice picture of the Mott metal-insulator transition is proposed. The charge, spin, and thermal responses of QSLs are discussed under such a phenomenology.

arXiv:1302.0157Physical Review BOct 21, 201315 citations

We study possible gapless edge states of translation-symmetric

{\mathbb{Z}}_{2}

spin liquids. The gapless edge states emerge from dangling Majorana fermions at the boundary. We construct a series of mean-field Hamiltonians of

{\mathbb{Z}}_{2}

spin liquids on the square lattice; these models can be obtained by generalization of Wen's exactly solvable plaquette model. We also study the details of the edge theory of these

{\mathbb{Z}}_{2}

spin liquids and find their effective background field (BF) theory descriptions. The effective BF theories are shown to describe the crystal momenta of the ground states and their degeneracies and to predict the edge theories of these

{\mathbb{Z}}_{2}

spin liquids. As a by-product, we obtained a way to classify the BF theories reflecting the lattice symmetries. We discuss in closing three-dimensional

{\mathbb{Z}}_{2}

spin liquids with gapless surface states on the cubic lattice.

U(1)

QSLs is a representative member of this class of spin liquids. Based on our effective low-energy theory, an alternative picture to the Brinkman-Rice picture of the Mott metal-insulator transition is proposed. The charge, spin, and thermal responses of QSLs are discussed under such a phenomenology.