Degeneracy of the 1/8 Plateau and Antiferromagnetic Phases in the Shastry-Sutherland Magnet TmB_{4}

Simulations of frustrated Ising Hamiltonians using quantum approximate optimization

Novel magnetic materials are important for future technological advances. Theoretical and numerical calculations of ground-state properties are essential in understanding these materials, however, computational complexity limits conventional methods for studying these states. Here we investigate an alternative approach to preparing materials ground states using the quantum approximate optimization algorithm (QAOA) on near-term quantum computers. We study classical Ising spin models on unit cells of square, Shastry-Sutherland and triangular lattices, with varying field amplitudes and couplings in the material Hamiltonian. We find relationships between the theoretical QAOA success probability and the structure of the ground state, indicating that only a modest number of measurements ([Formula: see text]) are needed to find the ground state of our nine-spin Hamiltonians, even for parameters leading to frustrated magnetism. We further demonstrate the approach in calculations on a trapped-ion quantum computer and succeed in recovering each ground state of the Shastry-Sutherland unit cell with probabilities close to ideal theoretical values. The results demonstrate the viability of QAOA for materials ground state preparation in the frustrated Ising limit, giving important first steps towards larger sizes and more complex Hamiltonians where quantum computational advantage may prove essential in developing a systematic understanding of novel materials. This article is part of the theme issue 'Quantum annealing and computation: challenges and perspectives'.

Ground state and thermodynamic properties of the coupled double-Ising model: application to rare-earth tetraborides

A combination of the standard Metropolis algorithm and the parallel tempering method is used to study ground-state and thermodynamic properties of the coupled double Ising (CDI) model on the Shastry-Sutherland lattice (SSL). This model is derived from the complex spin-electron model, in which electrons described by the Hubbard model and spins described by the Ising model interact via the anisotropic spin-dependent interaction of the Ising type, under the following three conditions: (a) the Hubbard interaction between electrons in the conduction band is sufficiently large; (b) the number of conduction electrons is equal to the number of the lattice points; (c) there is the easy axis spin anisotropy in the system. The model is solved numerically for the selected combinations of spins from the electron (s=1/2) and spin (S=1,3/2,2) Ising branch which represent very realistically the situation in TmB₄, ErB₄and HoB₄compounds, where in addition all three conditions are simultaneously satisfied. It is shown that the interlpay between the electron and spin branch of the CDI model leads to the suppression of the 1/3 magnetization plateau (the main magnetization plateau found in the ordinary Ising model on the SSL) and the stabilization of magnetization plateaus withm∼1/2, which is in perfect agreement with the experimental measurements in TmB₄and ErB₄compounds. A nice correspondence between theoretical and experimental results is also obtained for the temperature dependence of the specific heat capacity, where the low-temperature peak corresponding to the electron branch of the CDI model is followed by high-temperature peak of the spin branch. This opens a new route for exploring the physics of other complex spin-electron systems in which the above-mentioned conditions (a)-(c) are fulfilled.

Ground state and stability of the fractional plateau phase in metallic Shastry-Sutherland system TmB4

We present a study of the ground state and stability of the fractional plateau phase (FPP) with M/M_sat = 1/8 in the metallic Shastry-Sutherland system TmB₄. Magnetization (M) measurements show that the FPP states are thermodynamically stable when the sample is cooled in constant magnetic field from the paramagnetic phase to the ordered one at 2 K. On the other hand, after zero-field cooling and subsequent magnetization these states appear to be of dynamic origin. In this case the FPP states are closely associated with the half plateau phase (HPP, M/M_sat = ½), mediate the HPP to the low-field antiferromagnetic (AF) phase and depend on the thermodynamic history. Thus, in the same place of the phase diagram both, the stable and the metastable (dynamic) fractional plateau (FP) states, can be observed, depending on the way they are reached. In case of metastable FP states thermodynamic paths are identified that lead to very flat fractional plateaus in the FPP. Moreover, with a further decrease of magnetic field also the low-field AF phase becomes influenced and exhibits a plateau of the order of 1/1000 M_sat.

Insulator-metal transition and quasi-flat-band of Shastry-Sutherland lattice

Insulator-metal transition is investigated self-consistently on the frustrated Shastry-Sutherland lattice in the framework of Slave-Boson mean-field theory. Due to the presence of quasi-flat band structure characteristic, the system displays a spin-density-wave (SDW) insulating phase at the weak doping levels, which is robust against frustration, and it will be transited into an SDW metallic phase at high doping levels. As further increasing the doping, the temperature or the frustration on the diagonal linking bonds, the magnetic order m will be monotonically suppressed, resulting in the appearance of a paramagnetic metallic phase. Although the Fermi surface of the SDW metallic phase may be immersed by temperature, the number of mobile charges is robust against temperature at weak doping levels.