Singular ferromagnetic susceptibility of the transverse-field Ising antiferromagnet on the triangular lattice

Abstract

A transverse magnetic field $\Gamma$ is known to induce antiferromagnetic three-sublattice order of the Ising spins ${\sigma }^z$ in the triangular lattice Ising antiferromagnet at low enough temperature. This low-temperature order is known to melt on heating in a two-step manner, with a power-law ordered intermediate temperature phase characterized by power-law correlations at the three-sublattice wavevector $\mathbf{Q}$: $⟨{\sigma }^z(\vec{R}){\sigma }^z(0)⟩\sim \cos (\mathbf{Q}\cdot \vec{R})/|\vec{R}{|}^{\eta (T)}$ with the temperature-dependent power-law exponent $\eta (T)\in (1/9,1/4)$. Here, we use a newly developed quantum cluster algorithm to study the {\em ferromagnetic} easy-axis susceptibility ${\chi }_u(L)$ of an $L\times L$ sample in this power-law ordered phase. Our numerical results are consistent with a recent prediction of a singular $L$ dependence ${\chi }_u(L)\sim L^{2-9\eta }$ when $\eta (T)$ is in the range $(1/9,2/9)$. This finite-size result implies, via standard scaling arguments, that the ferromagnetic susceptibility ${\chi }_u(B)$ to a uniform field $B$ along the easy axis is singular at intermediate temperatures in the small $B$ limit, ${\chi }_u(B)\sim |B{|}^{-\frac{4-18\eta }{4-9\eta }}$ for $\eta (T)\in (1/9,2/9)$, although there is no ferromagnetic long-range order in the low temperature state.

8 two-column pages; 10 figures

References in corpus (4)

• Stochastic series expansion method for quantum Ising models with arbitrary interactions
• Interplay of quantum and thermal fluctuations in a frustrated magnet
• Melting of three-sublattice order in easy-axis antiferromagnets on triangular and Kagome lattices
• Quantum cluster algorithm for frustrated Ising models in a transverse field

Cited by in corpus (14)

• Kosterlitz-Thouless Melting of Magnetic Order in the Triangular Quantum Ising Material TmMgGaO${}_4$
• Evidence of the Berezinskii-Kosterlitz-Thouless Phase in a Frustrated Magnet
• Intrinsic quantum Ising model on a triangular lattice magnet TmMgGaO${}_4$ and beyond
• Phase Diagram of Triangular Lattice Quantum Ising Model under External Field
• Neutron scattering investigation of proposed Kosterlitz-Thouless transitions in the triangular-lattice Ising antiferromagnet TmMgGaO4
• Intrinsic transverse field in frustrated quantum Ising magnets: its physical origin and quantum effects
• Monte Carlo based techniques for quantum magnets with long-range interactions
• Field-Tuned Quantum Effects in a Triangular-Lattice Ising Magnet
• Tuning the two-step melting of magnetic orders in a dipolar kagome spin ice by quantum fluctuations
• Obstacles to quantum annealing in a planar embedding of XORSAT
• Emergent Berezinskii-Kosterlitz-Thouless and Kugel-Khomskii physics in the triangular lattice bilayer colbaltate
• Quantum robustness of the toric code in a parallel field on the honeycomb and triangular lattice
• Two-step melting of three-sublattice order in $S=1$ easy-axis triangular lattice antiferromagnets
• Unconventional Spin Dynamics and Supersolid Excitations in the Triangular-Lattice XXZ Model