[Paper Review] Quantum Electrodynamics in 2+1 Dimensions as the Organizing Principle of a Triangular Lattice Antiferromagnet

Alexander Wietek, Sylvain Capponi+1 more|arXiv (Cornell University)|Mar 2, 2023

Physics of Superconductivity and Magnetism79 references9 citations

TL;DR

The paper provides evidence that QED3 describes the low-energy spectrum of the J1–J2 Heisenberg model on the triangular lattice, by matching a wide set of monopole, bilinear, and vacuum excitations from a π-flux Dirac spin liquid to exact diagonalization spectra on N=36 and N=48 clusters. It suggests QED3 as an organizing principle for phases near a paramagnetic regime and discusses possible emergence of a VBS at a deconfined critical point.

ABSTRACT

Quantum electrodynamics in $2+1$ dimensions (QED$_3$) has been proposed as a critical field theory describing the low-energy effective theory of a putative algebraic Dirac spin liquid or of quantum phase transitions in two-dimensional frustrated magnets. We provide compelling evidence that the intricate spectrum of excitations of the elementary but strongly frustrated $J_1$-$J_2$ Heisenberg model on the triangular lattice is in one-to-one correspondence to a zoo of excitations from QED$_3$, in the quantum spin liquid regime. This includes a large manifold of explicitly constructed monopole and bilinear excitations of QED$_3$, which is thus shown to serve as an organizing principle of phases of matter in triangular lattice antiferromagnets and their low-lying excitations. Moreover, we observe signatures of an emergent valence bond solid (VBS), which suggests a scenario where only the critical point of a transition from the $120^\circ$ Néel order to a VBS is described by QED$_3$. Our results are obtained by comparing ansatz wave functions from a parton construction to exact eigenstates obtained using large-scale exact diagonalization up to $N=48$ sites.

Motivation & Objective

• Motivate QED3 as an effective field theory for algebraic/Dirac spin liquids and transitions in frustrated magnets.
• Show one-to-one correspondence between QED3 excitations and the low-energy spectrum of the J1-J2 triangular Heisenberg model in the paramagnetic regime.
• Demonstrate overlaps between Gutzwiller-projected π-flux Dirac spin liquid states and exact diagonalization eigenstates on finite clusters.
• Explore the potential emergence of a valence bond solid and its relation to deconfined quantum critical points in this system.

Proposed method

• Construct a π-flux Dirac spin liquid on the triangular lattice and generate Gutzwiller-projected ansatz wave functions for the vacuum, bilinears, and monopoles.
• Use centered boundary conditions to minimize mean-field energy and project to a physical spin Hilbert space.
• Compute overlaps o_n between ED eigenstates and ansatz states to identify correspondences.
• Analyze the torus spectrum of QED3 and relate monopole and bilinear quantum numbers to ED states.
• Compare low-energy spectra of the J1–J2 model with the Rokhsar–Kivelson quantum dimer model to assess gauge-field sector signatures.

Experimental results

Research questions

• RQ1 Can QED3 in 2+1 dimensions reproduce the low-energy torus spectrum of the triangular lattice J1–J2 Heisenberg model?
• RQ2 Do monopole and bilinear excitations of the π-flux Dirac spin liquid capture the prominent low-energy singlet and triplet levels seen in ED?
• RQ3 Is there evidence for an emergent valence bond solid or deconfined critical point in the paramagnetic regime?
• RQ4 How do overlaps between Gutzwiller-projected QED3 states and ED eigenstates vary across the phase diagram (N=36 and N=48 clusters)?

Key findings

• The ground state overlaps with the vacuum ansatz reach o_0 ≈ 0.923 at J2/J1 = 0.12, indicating strong correspondence in the paramagnetic regime.
• Singlet and triplet monopole states show significant overlaps with low-energy ED levels at X.A and K.A1, respectively, with o_n ≈ 0.65–0.67.
• Bilinear excitations have sizeable overlaps with low-lying S=1 Γ.B1 and M.B2 levels, and with S=0 M.B2 level, reaching o_n^B ≈ 0.54–0.74.
• A dense low-energy spectrum in the paramagnetic regime is largely captured by overlaps with vacuum, monopoles, or bilinear excitations, suggesting QED3 as an organizing principle.
• The Rokhsar–Kivelson quantum dimer model on the same clusters exhibits qualitative spectral and dimer-correlation parallels to the J1–J2 model, pointing toward a possible VBS instability.
• The work discusses a scenario where a transition from 120-degree Néel order to a 12-site VBS could be described by a deconfined quantum critical point with N_f = 4 QED3, implying an emergent PSU(4) symmetry at criticality.