Competition between Neel, Haldane nematic, plaquette valence bond solid, and $(\pi ,\pi )$ valence bond solid phases in SU(N) analogs of $S=1$ square-lattice antiferromagnets

Abstract

We use stochastic series expansion (SSE) quantum Monte Carlo (QMC) methods to study the phases and transitions displayed by a class of sign-free designer Hamiltonians for SU($N$) analogs of spin $S=1$ quantum antiferromagnets on the square lattice. The SU($N$) spins are generators of the single-row two-column representation (complex conjugate of single-row two-column representation) on $A$ ($B$) sublattices of the square lattice, and the Hamiltonian is designed to explore the competition between the nearest neighbour antiferromagnetic exchange couplings $J$ and four-spin interactions $Q$ that favor a plaquette-ordered valence bond solid (p-VBS) ground state. We find that this state is indeed established at large $Q/J$ for all $N>3$. For $3<N\le 9$, the ground state exhibits a direct first order quantum phase transition from a small-$Q/J$ Néel ordered antiferromagnetic state to this large-$Q/J$ p-VBS state. The ground state at $Q/J=0$ for $N\ge 10$ has been previously reported to be a valence bond nematic state, dubbed the Haldane nematic in recent literature. For small nonzero $Q/J$ and $N\ge 10$, we additionally find an unusual intermediate state in which the bond energy has a Bragg peak at wavevector $(\pi ,\pi )$ with no accompanying Bragg peaks at wavevectors $(\pi ,0)$ and $(0,\pi )$. This $(\pi ,\pi )$ state also appears to be metastable at $Q/J=0$, as evidenced by low temperature histograms of the Haldane nematic and $(\pi ,\pi )$ order parameters. Deep in the p-VBS phase of the ground state phase diagram, we find the temperature-driven melting of the p-VBS order is in the Ashkin-Teller universality class. In this regime, we identify an interesting signature of Ashkin-Teller criticality in bond correlations at wavevector $(\pi ,\pi )$; this is in addition to the expected critical fluctuations of the conventional p-VBS order parameter at wavevectors $(\pi ,0)$ and $(0,\pi )$.

References in corpus (53)

• Quantum Spin Liquids
• "Deconfined" quantum critical points
• Quantum Spin Liquids
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• A Field Guide to Spin Liquids
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Computational Studies of Quantum Spin Systems
• Quantum magnetism and criticality
• Ultracold Fermi Gases with Emergent SU(N) Symmetry
• Ultracold fermions and the SU(N) Hubbard model
• Ultracold Gases of Ytterbium: Ferromagnetism and Mott States in an SU(6) Fermi System
• Cluster algorithms for general-S quantum spin systems
• Quantum criticality with two length scales
• Mott Insulators of Ultracold Fermionic Alkaline Earth Atoms: Underconstrained Magnetism and Chiral Spin Liquid
• Nematicity and quantum paramagnetism in FeSe
• Scaling in the Fan of an Unconventional Quantum Critical Point
• Antiferromagnetic to valence-bond-soild transitions in two-dimensional SU(N) Heisenberg models with multi-spin interactions
• Continuous quantum phase transition between an antiferromagnet and a valence-bond-solid in two dimensions; evidence for logarithmic corrections to scaling
• Hidden symmetry and quantum phases in spin-3/2 cold atomic systems
• A lattice model for the SU(N) Neel-VBS quantum phase transition at large N
• 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
• Fate of CP(N-1) fixed points with q-monopoles
• Deconfined criticality flow in the Heisenberg model with ring-exchange interactions
• Possibility of Deconfined Criticality in SU(N) Heisenberg Models at Small N
• Néel to valence-bond solid transition on the honeycomb lattice: Evidence for deconfined criticality
• Deconfined criticality, runaway flow in the two-component scalar electrodynamics and weak first-order superfluid-solid transitions
• Néel and Spin-Peierls ground states of two-dimensional SU(N) quantum antiferromagnets
• Observation of antiferromagnetic correlations in an ultracold SU($N$) Hubbard model
• The SU(N) Heisenberg model on the square lattice: a continuous-N quantum Monte Carlo study
• Finite-size scaling and boundary effects in two-dimensional valence-bond-solids
• Impurity spin texture at a deconfined quantum critical point
• Random-Singlet Phase in Disordered Two-Dimensional Quantum Magnets
• Transitions to valence-bond solid order in a honeycomb lattice antiferromagnet
• Exotic quantum phases and phase transitions in correlated matter
• Quantum criticality in SU(3) and SU(4) anti-ferromagnets
• Flavour-selective localization in interacting lattice fermions via SU(N) symmetry breaking
• Ground States of the SU(N) Heisenberg Model
• Columnar order and Ashkin-Teller criticality in mixtures of hard-squares and dimers
• Quantum phase transitions in bilayer SU(N) anti-ferromagnets
• Valence-bond solids, vestigial order, and emergent SO(5) symmetry in a two-dimensional quantum magnet
• Selective insulators and anomalous responses in correlated fermions with synthetic extra dimensions
• Dynamical properties of the $S=\frac{1}{2}$ random Heisenberg chain
• Properties of the random-singlet phase: from the disordered Heisenberg chain to an amorphous valence-bond solid
• Vacancy-induced spin texture in a one dimensional $S=1/2$ Heisenberg antiferromagnet
• Impurity spin texture at a Néel-Valence Bond Solid critical point in $d=2$ SU(3) quantum antiferromagnets
• Marshall-positive SU($N$) quantum spin systems and classical loop models: A practical strategy to design sign-problem-free spin Hamiltonians
• Quantum-critical scaling properties of the two-dimensional random-singlet state
• Spin-$S$ designer hamiltonians and the square lattice $S=1$ Haldane nematic
• First-order Néel-cVBS transition in a model square lattice $S=1$ antiferromagnet
• Resummation-based updates for Stochastic Series Expansion Quantum Monte Carlo
• SU(N) Heisenberg model with multi-column representations
• Antiferromagnetic order in systems with doublet $S_{\mathrm{tot}}=1/2$ ground states