Quantum annealing: an overview
Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences,
01/2023
Journal Article
We theoretically discuss dynamical properties of spin-12 Heisenberg antiferromagnet on the triangular lattice in magnetic field H. We use the recently proposed bond-operator theory which operates ...with quantum states of the whole magnetic unit cell containing three spins. This technique describes accurately short-range spin correlations and provides a quantitative description of elementary excitations which appear in other approaches as bound states of conventional low-energy quasiparticles (e.g., magnons). In quantitative agreement with previous numerical and analytical findings, we observe four phases with coplanar spin arrangements upon the field increasing: the three-sublattice Y-phase, the collinear “up-up-down” (UUD) state, the non-collinear V-phase, and the collinear fully polarized (FP) state. We demonstrate that apart from magnons (spin-1 quasiparticles) there are spin-0 elementary excitations in the UUD state one of which is long lived and its spectrum lies below magnon branches. This mode originates from a high-energy quasiparticle at H=0 and it produces anomalies only in the longitudinal spin correlator because longitudinal and transverse channels are separated in collinear states. All other spin-0 excitations have finite lifetime and produce visibly anomalies in the dynamical structure factor. In the V-phase, we obtain multiple short-wavelength spin excitations which have no counterparts in the semiclassical spin-wave theory. Besides, we demonstrate a highly nontrivial field evolution of quasiparticles spectra on the way from one collinear state (UUD) to another one (FP) via the non-collinear V-phase (in which the longitudinal and the transverse channels are mixed). In particular, some parts of the spin-0 branch in the UUD state become parts of the spin-1 (magnon) branch in the FP phase whereas some parts of one magnon branch turn into parts of spin-2 branch. Such evolution would be very difficult to find by any conventional analytical approach. Our results are in good agreement with neutron experimental data obtained recently in Ba3CoSb2O9, KYbSe2, and CsYbSe2.
•Dynamics in ordered triangular-lattice spin-1/2 antiferromagnet in magnetic field.•New short-wavelength quasiparticles.•Low-lying spin-0 excitations.•Highly nontrivial field evolution of quasiparticles spectra.•Transition of quasiparticles from longitudinal to transverse channels.
We propose a cold atom implementation to attain the continuum limit of (1+1)-d CP(N−1) quantum field theories. These theories share important features with (3+1)-d QCD, such as asymptotic freedom ...and θ-vacua. Moreover, their continuum limit can be accessed via the mechanism of dimensional reduction. In our scheme, the CP(N−1) degrees of freedom emerge at low energies from a ladder system of SU(N) quantum spins, where the N spin states are embodied by the nuclear Zeeman states of alkaline-earth atoms, trapped in an optical lattice. Based on Monte Carlo results, we establish that the continuum limit can be demonstrated by an atomic quantum simulation by employing the feature of asymptotic freedom. We discuss a protocol for the adiabatic preparation of the ground state of the system, the real-time evolution of a false θ-vacuum state after a quench, and we propose experiments to unravel the phase diagram at non-zero density.
We show that numerical computations based on tensor renormalization group (TRG) methods can be significantly accelerated with PyTorch on graphics processing units (GPUs) by leveraging NVIDIA's ...Compute Unified Device Architecture (CUDA). Here we find improvement in the runtime and its scaling with bond dimension for two-dimensional systems. Our results establish that the utilization of GPU resources is essential for future precision computations with TRG.
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