Critical properties of the Néel–algebraic-spin-liquid transition

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 (QED3), and power-law correlations with universal exponents. The prototypical algebraic spin liquid is the Affleck-Marston π-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 Néel order and drive a direct quantum phase transition to the π-flux phase. We show this transition is in the universality class of the chiral Heisenberg QED3-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 kagomé lattice. Using an 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-antiferromagnetic insulator transition in graphene. arXiv:1905.03719v1 [cond-mat.str-el]

Dynamics of compact quantum electrodynamics at large fermion flavor

“…Looking forward, better algorithm in QMC simulations would certainly be desirable to access larger system sizes and lower temperatures. In particular, the critical properties of the U1D-VBS transition, that of the QED 3 -GN types, have already been discussed in the high-order perturbative RG calculations [42][43][44][45], but the system sizes in this work is too small to extract accurate values of the critical exponents. Further developments, in terms of algorithm improvement and more focus close to the QED 3 -GN critical points, are on-going.…”

“…The gapless excitation close to (π, 0) are the critical fluctuations associated with the QED 3 -GN transition. With larger system sizes and lower temperature in the future QMC studies, one will be able to measure the anomalous dimension exponent η from the momentum and frequency dependence of such critical fluctuation, and could compare with the predictions of QED 3 -GN transitions from the recent perturbative RG calculations [42][43][44][45].…”

“…[1], there are recently several analytical works addressing the critical properties of them [42][43][44][45][46][47]. And the conclusions drawn there are that the U(1)-to-AFM and U(1)-to-VBS phase transitions are indeed possible and the higher-order perturbative RG calculations performed also suggest the possible range of critical exponents of these QED 3 -GN transitions within 1/N f and 4 − expansions [42][43][44][45][46][47].…”

Abelian Higgs model at four loops, fixed-point collision, and deconfined criticality

“…The next-to-leading order loop expansion, on the other hand, shows a dramatic reduction of the critical n c , but due to the large magnitude of this correction, it remains rather inconclusive [16,17] and has led to the belief that a perturbative RG is not well-suited for the question at hand. Therefore, despite the tremendous recent advances in higher-loop calculations for (quasi)relativistic field theories [22][23][24][25][26][27][28][29][30][31][32][33], further efforts to improve the description of the n-component Abelian Higgs model have not been undertaken for many years. In this work, we fill this long-standing void by performing a perturbative RG calculation to four-loop order and in the parameter = 4 − d, primarily to provide an improved estimate for the critical number of complex scalars n c above which the transition becomes continuous.…”

Revealing fermionic quantum criticality from new Monte Carlo techniques

“…The continuous confined transitions from U1D to AFM or VBS we found should be described by QED 3 -Gross-Neveu O (2) or O(3) universality, depending on the symmetry group that the fermion bilinears break in the confined phase, and further carefully study of the critical properties of these transitions via QMC simulations and analytical calculations is certainly worthwhile [93]. Recently perturbative renormalization group calculations to higher orders have been carried out in attempt to accquire the critical properties of the deconfinement to confinement transition in form of QED 3 -Gross-Neveu universality classes [120][121][122][123][124][125] and to address the relevance or irrelevance of the monopole operators to the stability of the U1D phase [126][127][128], show substantial interests and great ongoing efforts along this direction.…”