# Critical properties of the N\'eel/algebraic-spin-liquid transition

## TL;DR

This paper investigates the quantum phase transition from Ne9el order to an algebraic spin liquid in 2D systems, identifying its universality class and calculating critical exponents using advanced field-theoretic methods.

## Contribution

It establishes the universality class of the Ne9el/algebraic spin-liquid transition as chiral Heisenberg QED3-Gross-Neveu-Yukawa and computes critical exponents via epsilon and large-Nf expansions.

## Key findings

- The transition is continuous with specific critical exponents.
- The universality class is identified as chiral Heisenberg QED3-Gross-Neveu-Yukawa.
- Critical exponents for thermodynamic and susceptibility quantities are calculated.

## Abstract

The algebraic spin liquid is a long-sought-after phase of matter characterized by the absence of quasiparticle excitations, a low-energy description in terms of emergent Dirac fermions and gauge fields interacting according to (2+1)D quantum electrodynamics (QED$_3$), and power-law correlations with universal exponents. The prototypical algebraic spin liquid is the Affleck-Marston $\pi$-flux phase, originally proposed as a possible ground state of the spin-1/2 Heisenberg model on the 2D square lattice. While the latter model is now known to order antiferromagnetically at zero temperature, recent sign-problem-free quantum Monte Carlo simulations of spin-1/2 fermions coupled to a compact U(1) gauge field on the square lattice have shown that quantum fluctuations can destroy N\'eel order and drive a direct quantum phase transition to the $\pi$-flux phase. We show this transition is in the universality class of the chiral Heisenberg QED$_3$-Gross-Neveu-Yukawa model with a single SU(2) doublet of four-component Dirac fermions (i.e., $N_f=1$), pointing out important differences with the corresponding putative transition on the kagome lattice. Using an $\epsilon$ expansion below four spacetime dimensions to four-loop order, and a large-$N_f$ expansion up to second order, we show the transition is continuous and compute various thermodynamic and susceptibility critical exponents at this transition, setting the stage for future numerical determinations of these quantities. As a byproduct of our analysis, we also obtain charge-density-wave and valence-bond-solid susceptibility exponents at the semimetal-N\'eel transition for interacting fermions on the honeycomb lattice.