Impurity spin texture at a deconfined quantum critical point

Abstract

The spin texture surrounding a non-magnetic impurity in a quantum antiferromagnet is a sensitive probe of the novel physics of a class of quantum phase transitions between a Neel ordered phase and a valence bond solid phase in square lattice S=1/2 antiferromagnets. Using a newly developed T=0 Quantum Monte Carlo technique, we compute this spin texture at these transitions and find that it does not obey the universal scaling form expected at a scale invariant quantum critical point. We also identify the precise logarithmic form of these scaling violations. Our results are expected to yield important clues regarding the probable theory of these unconventional transitions.Comment: 4+ pages, 2 columns, 4 figure

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

“…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. Further, critical properties fit reasonably well to standard scaling predictions for second-order transitions [28][29][30][33][34][35][36][37]39,44 . The corresponding values of η N and η D , the anomalous exponents governing power-law decays of the Néel order parameter n and the VBS order parameter ψ, are relatively large 28,40,44 , as expected from the theory of deconfined criticality.…”

“…At or close to this critical point, histograms of the phase of ψ exhibit near-perfect U(1) symmetry 29,33,40 , consistent with the idea that the irrelevance of the 4-fold monopole insertion operator Ψ 4 implies, via the identification Ψ ∼ ψ, the irrelevance of the 4-fold anisotropy in the phase of the VBS order parameter ψ. However, in the SU(2) case, slow (perhaps logarithmic) drifts with increasing linear size L are clearly visible 31,[34][35][36][37]45 in certain dimensionless quantities which are expected to be scaleinvariant at a conventional second-order critical point in three space-time dimensions -examples include the spin stiffness and vacancy-induced spin textures. Since histograms of phase of ψ exhibit U(1) symmetry characteristic of the non-compact theory, it seems plausible that these drifts are intrinsic properties of the non-compact critical point.…”

“…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] .…”

Néel to staggered dimer order transition in a generalized honeycomb lattice Heisenberg model

“…This should be contrasted with studies of very similar "JQ" models on the square lattice, with the plaquette interactions chosen to favour columnar order 7 . Extensive numerical work on these models has led to the conclusion that the transition from Néel to columnar valence bond solid order is indeed a continuous transition, [8][9][10] although the critical point exhibits logarithmic violations of standard finite size scaling 8,11 . These violations of scaling have also been interpreted as possible evidence of first order behaviour 12 .…”