Abstract
Quantum magnets provide the simplest example of strongly interacting quantum matter, yet they continue to resist a comprehensive understanding above one spatial dimension. We explore a promising framework in two dimensions, the Dirac spin liquid (DSL) — quantum electrodynamics (QED3) with 4 Dirac fermions coupled to photons. Importantly, its excitations include magnetic monopoles that drive confinement. We address previously open key questions — the symmetry actions on monopoles on square, honeycomb, triangular and kagome lattices. The stability of the DSL is enhanced on triangular and kagome lattices compared to bipartite (square and honeycomb) lattices. We obtain the universal signatures of the DSL on triangular and kagome lattices, including those of monopole excitations, as a guide to numerics and experiments on existing materials. Even when unstable, the DSL helps unify and organize the plethora of ordered phases in correlated two-dimensional materials.
Highlights
Quantum magnets provide the simplest example of strongly interacting quantum matter, yet they continue to resist a comprehensive understanding above one spatial dimension
We show that a trivial monopole appears in the square lattice Dirac spin liquid (DSL), consistent with duality-based arguments[44] and earlier calculations[38] and does not contradict the Lieb–Schultz–Mattis–Oshikawa–Hastings theorem (LSMOH) theorem
Our calculation of symmetry quantum numbers of monopole excitations in the QED3 Dirac spin liquid theory on different 2D lattices indicates that the DSL on triangular and kagome lattices may be a stable phase
Summary
Quantum magnets provide the simplest example of strongly interacting quantum matter, yet they continue to resist a comprehensive understanding above one spatial dimension. Starting with a Schwinger boson-based representation of spins, a Z2 gapped spin liquid is the natural ‘mother’ state for describing non-bipartite lattices[9,10,11,12,13], while the similar procedure for the bipartite case indicated Neel and valence bond crystal phases for bipartite lattices, separated by a deconfined quantum critical point[3,4,14]. These paradigms which are based on quantum disordering an initial classical ordered state (noncolinear versus colinear order on the non-bipartite and bipartite lattices, respectively) represent significant progress towards a synthesis. The Luttinger liquid theory can be reformulated in terms of Dirac fermions coupled to a U(1) gauge field, and can be viewed as the one-dimensional version of U(1) Dirac spin liquid[17,18,19]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
