Quantum Monte Carlo Study of Long-Range Transverse-Field Ising Models on the Triangular Lattice

Abstract

Motivated by recent experiments with a Penning ion trap quantum simulator, we perform numerically exact Stochastic Series Expansion quantum Monte Carlo simulations of long-range transverse-field Ising models on a triangular lattice for different decay powers $\alpha$ of the interactions. The phase boundary for the ferromagnet is obtained as a function of $\alpha$. For antiferromagnetic interactions, there is strong indication that the transverse field stabilizes a clock ordered phase with sublattice magnetization $(M,-\frac{M}{2},-\frac{M}{2})$ with unsaturated $M<1$ in a process known as "order by disorder" similar to the nearest neighbour antiferromagnet on the triangular lattice. Connecting the known limiting cases of nearest neighbour and infinite-range interactions, a semiquantitative phase diagram is obtained. Magnetization curves for the ferromagnet for experimentally relevant system sizes and with open boundary conditions are presented.

arXiv comment18 pages, 19 figures

References in corpus (16)

• Engineered 2D Ising interactions on a trapped-ion quantum simulator with hundreds of spins
• Effective quantum spin systems with ion traps
• Computational Studies of Quantum Spin Systems
• Ising models of quantum frustration
• Mott Transition from a Spin Liquid to a Fermi Liquid in the Spin-Frustrated Organic Conductor kappa-(ET)2Cu2(CN)3
• Entanglement entropy for the long range Ising chain
• Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections
• Two-dimensional periodic frustrated Ising models in a transverse field
• Stochastic series expansion method for quantum Ising models with arbitrary interactions
• Interplay of quantum and thermal fluctuations in a frustrated magnet
• Anomalous Behavior of Spin Systems with Dipolar Interactions
• Theory of the Magnetic phase diagram of LiHoF${}_4$
• Relaxation timescales and decay of correlations in a long-range interacting quantum simulator
• Statistical Mechanics of systems with long range interactions
• Low-Temperature Properties of Ising Antiferromagnet on a Stacked Triangular Lattice
• Quantum Monte Carlo study of the transverse-field quantum Ising model on infinite-dimensional structures

Cited by in corpus (24)

• Observing the space- and time-dependent growth of correlations in dynamically tuned synthetic Ising antiferromagnets
• Critical behavior of quantum magnets with long-range interactions in the thermodynamic limit
• Fidelity and criticality of quantum Ising chain with long-range interactions
• Fidelity Susceptibility Study of Quantum Long-Range Antiferromagnetic Ising Chain
• Quantum criticality of two-dimensional quantum magnets with long-range interactions
• Criticality of Spin Systems with Weak Long-Range Interactions
• Quantum-critical properties of the long-range transverse-field Ising model from quantum Monte Carlo simulations
• Quantum criticality and excitations of a long-range anisotropic $XY$-chain in a transverse field
• Quantum criticality of the transverse-field Ising model with long-range interactions on triangular-lattice cylinders
• Nonperturbative Waveguide Quantum Electrodynamics
• Scaling at quantum phase transitions above the upper critical dimension
• Phase diagram of the quantum Ising model with long-range interactions on an infinite-cylinder triangular lattice
• Monte Carlo based techniques for quantum magnets with long-range interactions
• Systematic Analysis of Crystalline Phases in Bosonic Lattice Models with Algebraically Decaying Density-Density Interactions
• Study of the long-range transverse field Ising model with fermionic Gaussian states
• Effective-Dimension Theory of Critical Phenomena above Upper Critical Dimensions
• Spin-glass quantum phase transition in amorphous arrays of Rydberg atoms
• Long-range interactions from $U\left(1\right)$ gauge fields via dimensional mismatch
• Stochastic parameter optimization analysis of dynamical quantum critical phenomena in long-range transverse-field Ising chain
• Criticality of the Higgs mass for the long-range quantum $XY$ chain: Amplitude ratio between the Higgs and paramagnetic gaps
• Finding the ground states of symmetric infinite-dimensional Hamiltonians: explicit constrained optimizations of tensor networks
• Deconfined quantum criticality on a triangular Rydberg array
• Criticality of the magnon-bound-state hierarchy for the quantum Ising chain with the long-range interactions
• Numerical Probe of Dynamical Properties of a Two-Dimensional Triangular Ising Lattice with Long-Range Interaction