Metamagnetism and zero-scale-factor universality in the two-dimensional $J$-$Q$ model

Abstract

Using a combination of quantum Monte Carlo and exact methods, we study the field-driven saturation transition of the two-dimensional $J$-$Q$ model, in which the antiferromagnetic Heisenberg exchange $(J)$ coupling competes with an additional four-spin interaction $(Q)$ that favors valence-bond solid order. For small values of $Q$, the saturation transition is continuous, and is expected to be governed by zero-scale-factor universality at its upper critical dimension, with a specific form of logarithmic corrections to scaling (first proposed by Sachdev \textit{et al.} [Phys. Rev. B \textbf{50}, 258 (1994)]). Our results conform to this expectation, but the logarithmic corrections to scaling do not match the form predicted by Sachdev \textit{et al.} We also show that the saturation transition becomes first order above a critical coupling ratio $(Q/J{)}_{\min }$ and is accompanied by magnetization jumps---metamagnetism. We obtain an exact solution for $(Q/J{)}_{\min }$ using a high magnetization expansion, and confirm the existence of the magnetization jumps beyond this value of coupling using quantum Monte Carlo simulations.

arXiv comment8 pages, 5 figures

References in corpus (32)

• Exchange Monte Carlo Method and Application to Spin Glass Simulations
• Quantum Monte Carlo with Directed Loops
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Macroscopic magnetization jumps due to independent magnons in frustrated quantum spin lattices
• Quantum criticality with two length scales
• Emergent multipolar spin correlations in a fluctuating spiral - The frustrated ferromagnetic S=1/2 Heisenberg chain in a magnetic field
• Antiferromagnetic to valence-bond-soild transitions in two-dimensional SU(N) Heisenberg models with multi-spin interactions
• Bond-order-wave phase and quantum phase transitions in the one-dimensional extended Hubbard model
• Continuous quantum phase transition between an antiferromagnet and a valence-bond-solid in two dimensions; evidence for logarithmic corrections to scaling
• Finite Temperature Properties of Quantum Antiferromagnets in a Uniform Magnetic Field in One and Two Dimensions
• Magnetization plateaus in frustrated antiferromagnetic quantum spin models
• Frustrated ferromagnetic spin-1/2 chain in a magnetic field: The phase diagram and thermodynamic properties
• Classical percolation transition in the diluted two-dimensional S=1/2 Heisenberg antiferromagnet
• Multi-magnon bound states in the frustrated ferromagnetic 1D chain
• Exact eigenstates and macroscopic magnetization jumps in strongly frustrated spin lattices
• Bridging lattice-scale physics and continuum field theory with quantum Monte Carlo simulations
• Independent magnon states on magnetic polytopes
• Nuclear magnetic resonance signature of the spin-nematic phase in LiCuVO${}_4$ at high magnetic fields
• Frustrated ferromagnetic spin-1/2 chain in the magnetic field
• Frustrated spin chains in strong magnetic field: dilute two-component Bose gas regime
• Metamagnetism in the XXZ model with next-to-nearest-neighbor coupling
• Method to characterize spinons as emergent elementary particles
• Confinement and Deconfinement of Spinons in Two Dimensions
• Quantum Monte Carlo studies of spinons in one-dimensional spin systems
• Vacancy-induced spin texture in a one dimensional $S=1/2$ Heisenberg antiferromagnet
• Chiral phases of two-dimensional hard-core bosons with frustrated ring-exchange
• Resonances in a dilute gas of magnons and metamagnetism of isotropic frustrated ferromagnetic spin chains
• Thermal valence-bond-solid transition of quantum spins in two dimensions
• Magnetization jump in the XXZ chain with next-nearest-neighbor exchange
• Field-driven quantum phase transitions in $S=1/2$ spin chains
• 1D valence bond solids in a magnetic field
• Magnetization jump in one dimensional $J-Q_2$ model with anisotropic exchange

Cited by in corpus (8)

• Random-Singlet Phase in Disordered Two-Dimensional Quantum Magnets
• Intrinsic Jump Character of the First-Order Quantum Phase Transitions
• Quantum-critical scaling properties of the two-dimensional random-singlet state
• Pair hopping in systems of strongly interacting hard-core bosons
• Bose-Einstein condensation of deconfined spinons in two dimensions
• Magnetic effects of non-magnetic impurities in gapped short-range resonating valence bond spin liquids
• Improvements to the Stochastic Series Expansion method for the $J{Q}_2$ model with a magnetic field
• Field-induced freezing in the unfrustrated Ising antiferromagnet