Deconfined pseudocriticality in a model spin-1 quantum antiferromagnet

Abstract

Berry phase interference arguments that underlie the theory of deconfined quantum criticality (DQC) for spin-$\frac{1}{2}$ antiferromagnets have also been invoked to allow for continuous transitions in spin-1 magnets including a Néel to (columnar) valence bond solid (cVBS) transition. We provide a microscopic model realization of this transition on the square lattice consisting of Heisenberg exchange ($J_H$) and biquadratic exchange ($J_B$) that favor a Néel phase, and a designed $Q$-term ($Q_B$) interaction which favors a cVBS through large-scale quantum Monte Carlo (QMC) simulations. For $J_H=0$, this model is equivalent to the $SU(3)$ $JQ$ model with a Néel-cVBS transition that has been argued to be DQC through QMC. Upon turning on $J_H$ which brings down the symmetry to $SU(2)$, we find multiple signatures -- a single critical point, high quality collapse of correlation ratios and order parameters, "$U(1)$-symmetric" cVBS histograms and lack of double-peak in order parameter histograms for largest sizes studied near the critical point -- that are highly suggestive of a continuous transition scenario. However, Binder analysis finds negative dips that grow sub-extensively that we interpret as these transitions rather being pseudocritical. This along with recent results on spin-$\frac{1}{2}$ models suggests that deconfined pseudocriticality is the more generic scenario.

Several references added. No major changes. 7 pages, 5 figures of main text. 22 pages of supplementary data. Submitted to PRL. Offered PRB. (Review exchange at https://www.dropbox.com/scl/fo/cuzciggsndwwpbznytt5g/AAi9TAQ_eGEL_AQnxU-BbbU?rlkey=0aesnku2bjv62vup1o2ps06sj&dl=0 ; names and accession code redacted)

References in corpus (24)

• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Scaling in the Fan of an Unconventional Quantum Critical Point
• Many-body spin Berry phases emerging from the $\pi$-flux state: antiferromagnetic/valence-bond-solid competition
• From an Antiferromagnet to a Valence Bond Solid: Evidence for a First Order Phase Transition
• Bridging lattice-scale physics and continuum field theory with quantum Monte Carlo simulations
• Deconfined criticality, runaway flow in the two-component scalar electrodynamics and weak first-order superfluid-solid transitions
• Deconfined quantum critical point in one dimension
• Dirac Fermions with Competing Orders: Non-Landau Transition with Emergent Symmetry
• Coulomb gas transitions in three-dimensional classical dimer models
• Gauge theory picture of an ordering transition in a dimer model
• Transitions to valence-bond solid order in a honeycomb lattice antiferromagnet
• Quantum spin nematics, dimerization, and deconfined criticality in quasi-one dimensional spin-1 magnets
• The $\mathrm{SO}(5)$ Deconfined Phase Transition under the Fuzzy Sphere Microscope: Approximate Conformal Symmetry, Pseudo-Criticality, and Operator Spectrum
• Exactly solvable model for a deconfined quantum critical point in 1D
• Quantum phase transitions in bilayer SU(N) anti-ferromagnets
• SU(2)-invariant continuum theory for an unconventional phase transition in a three-dimensional classical dimer model
• A tensor network study of the complete ground state phase diagram of the spin-1 bilinear-biquadratic Heisenberg model on the square lattice
• Dirac fermions with plaquette interactions. I. SU(2) phase diagram with Gross-Neveu and deconfined quantum criticalities
• Classical to quantum mapping for an unconventional phase transition in a three-dimensional classical dimer model
• Dirac fermions with plaquette interactions. III. SU(N) phase diagram with Gross-Neveu criticality and first-order phase transition
• Marshall-positive SU($N$) quantum spin systems and classical loop models: A practical strategy to design sign-problem-free spin Hamiltonians
• Entanglement entropy and deconfined criticality: emergent SO(5) symmetry and proper lattice bipartition