Possibility of deconfined criticality in SU(N) Heisenberg models at smallN

Abstract

To examine the validity of the scenario of the deconfined critical phenomena, we carry out a quantum Monte Carlo simulation for the SU(N ) generalization of the Heisenberg model with four-body and six-body interactions. The quantum phase transition between the SU(N ) Néel and valence-bond solid phases is characterized for N = 2, 3, and 4 on the square and honeycomb lattices. While finite-size scaling analysis works well up to the maximum lattice size (L = 256) and indicates the continuous nature of the phase transition, a clear systematic change towards the first-order transition is observed in the estimates of the critical exponent y ≡ 1/ν as the system size increases. We also confirm the relevance of a squared valence-bond solid field 2 for the SU(3) model.

Necessary Condition for Emergent Symmetry from the Conformal Bootstrap

“…In [24], they obtained ∆ 1 = 0.785, so our necessary condition implies that it can show the second order phase transition on the square lattice but it cannot on the rectangular lattice, in agreement with what is observed. The direct measurement of ∆ 2 = 2.0 there turns out to be close to but slightly below our bound with ∆ 1 = 0.785.…”

“…In [24] they obtained ∆ 1 = 0.865, and our condition predicts that the charge two monopole operator is relevant. On the other hand in [23], they claim that the charge two monopole operator is irrelevant and the phase transition is second order on the rectangular lattice.…”

“…From the effective field theory viewpoint, a difficulty comes from the existence of monopole operators. One can argue that the lattice symmetry forbids the smallest charged monopole operator, but not necessarily so for the higher charged monopole operators [23,24]. For instance, if we use the rectangular lattice, one can only preserve the Z 2 subgroup of the U (1) monopole charge, and if we use the honeycomb lattice it is Z 3 and if we use the square lattice it is Z 4 .…”

Transitions to valence-bond solid order in a honeycomb lattice antiferromagnet

“…In parallel work, other studies have tried to access the physics of deconfined criticality in three dimensional classical models [45][46][47][48][49][50][51][52][53][54][55] . On the square lattice (with q = 4), QMC simulations [28][29][30][31][33][34][35][36][37]39,40,42,44,45 find no direct signature of first-order behavior even at the largest sizes studied. This is true both for SU(2) symmetric models, as well as spin models with enhanced SU(N) symmetry, which are expected to exhibit a transition in the NCCP N −1 universality class.…”

“…This theory of deconfined criticality has motivated several numerical studies [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45] of model quantum Hamiltonians designed 9 to host a Néel-VBS columnar transition. In parallel work, other studies have tried to access the physics of deconfined criticality in three dimensional classical models [45][46][47][48][49][50][51][52][53][54][55] .…”