Chern-Simons superconductors and their instabilities

Abstract

Two-dimensional quantum antiferromagnets host rich physics including long-range ordering, high-Tc superconductivity, quantum spin liquid behavior, topological ordering, variety of other exotic phases, and quantum criticalities. Frustrating perturbations in antiferromagnets may give rise to strong quantum fluctuations, challenging the theoretical understanding of the many-body ground state. Here we develop a method to describe the quantum antiferromagnets using fermionic degrees of freedom. The method is based on a formally exact mapping between spin-exchange models and theories describing fermionic matter with the emergent U (1) Chern-Simons gauge field. For the planar Néel state, this mapping self-consistently generates the Chern-Simons superconductor mean-field ground state of introduced fermions. We systematically compare the Chern-Simons superconductor state with the planar Néel state at the level of collective modes and order parameters. We reveal qualitative and quantitative correspondences between these states. Such a description of the Néel order, constructed from the fractionalized fermion excitations and emergent gauge fields, can be applied to the quantum spin-liquids. More importantly, it allows us to keep track of the unconventional phase transitions from ordered states to the spin-liquids. We show that such confinement-deconfinement transitions are signaled and characterized by the Chern-Simons superconductor instabilities, driven by strong frustration. These results provide a systematic parton mean-field approach that accounts for the magnetically ordered state, the spin-liquids, and the unconventional phase transitions in a unified physical picture. The findings suggest observing and classifying descendant states, including quantum spin-liquids and unconventional superconductors.

Quantum correlations in the frustrated XY model on the honeycomb lattice

“…A distinctive study based on the Chern-Simons fermionisation of the spin 1/2 operators reveals a complex structure of ground state order within the intermediate regime. This structure is characterised by the coexistence of out-of-plane long-range N' eel ordering and in-plane chiral spin-liquid ordering 40 .…”

Emergent Kondo behavior from gauge fluctuations in spin liquids

“…Our work therefore opens an unprecedented avenue to explore many-body resonances with new mechanisms, which may unveil the mysteries of the emergent gauge fluctuations in QSLs. based on the Chern-Simons (CS) representation [30][31][32][33][34][35][36], which will facilitate the study of impurity problem. The spin-raising and lowering operators are statistically equivalent to hardcore bosons.…”

Chern-Simons approach to atmospheric dynamics

“…In their simplest form, the CS equations are first order linear differential equations for a three-component field theory. CS models have been proposed to describe other 2+1 dimensional systems like, for instance, in the fractional quantum Hall effect, anyons, 2+1 vortices [3], or the electron gas in the two-dimensional planes of high temperature superconductors [4][5][6], gravity in a 2+1 dimensional spacetime [7] or graphene [8].…”