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Register a new userSimulating the Shastry-Sutherland Ising Model using Quantum Annealing
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Frustration represents an essential feature in the behavior of magnetic materials when constraints on the microscopic Hamiltonian cannot be satisfied simultaneously. This gives rise to exotic phases of matter including spin liquids, spin ices, and stripe phases. Here we demonstrate an approach to understanding the microscopic effects of frustration by computing the phases of a 468-spin Shastry-Sutherland Ising Hamiltonian using a quantum annealer. Our approach uses mean-field boundary conditions to mitigate effects of finite size and defects alongside an iterative quantum annealing protocol to simulate statistical physics. We recover all phases of the Shastry-Sutherland Ising model -- including the well-known fractional magnetization plateau -- and the static structure factor characterizing the critical behavior at these transitions. These results establish quantum annealing as an emerging method in understanding the effects of frustration on the emergence of novel phases of matter and pave the way for future comparisons with real experiments.
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We investigate the quantum annealing of the ferromagnetic $ p $-spin model in a dissipative environment ($ p = 5 $ and $ p = 7 $). This model, in the large $ p $ limit, codifies the Grovers algorithm for searching in an unsorted database. The dissipative environment is described by a phonon bath in thermal equilibrium at finite temperature. The dynamics is studied in the framework of a Lindblad master equation for the reduced density matrix describing only the spins. Exploiting the symmetries of our model Hamiltonian, we can describe many spins and extrapolate expected trends for large $ N $, and $ p $. While at weak system bath coupling the dissipative environment has detrimental effects on the annealing results, we show that in the intermediate coupling regime, the phonon bath seems to speed up the annealing at low temperatures. This improvement in the performance is likely not due to thermal fluctuation but rather arises from a correlated spin-bath state and persists even at zero temperature. This result may pave the way to a new scenario in which, by appropriately engineering the system-bath coupling, one may optimize quantum annealing performances below either the purely quantum or classical limit.
Using the density-matrix renormalization group method for the ground state and excitations of the Shastry-Sutherland spin model, we demonstrate the existence of a narrow quantum spin liquid phase between the previously known plaquette-singlet and antiferromagnetic states. Our conclusions are based on finite-size scaling of excited level crossings and order parameters. Together with previous results on candidate models for deconfined quantum criticality and spin liquid phases, our results point to a unified quantum phase diagram where the deconfined quantum-critical point separates a line of first-order transitions and a gapless spin liquid phase. The frustrated Shastry-Sutherland model is close to the critical point but slightly inside the spin liquid phase, while previously studied unfrustrated models cross the first-order line. We also argue that recent heat capacity measurements in SrCu$_2$(BO$_3$)$_2$ show evidence of the proposed spin liquid at pressures between 2.6 and 3 GPa.
Classical models with complex energy landscapes represent a perspective avenue for the near-term application of quantum simulators. Until now, many theoretical works studied the performance of quantum algorithms for models with a unique ground state. However, when the classical problem is in a so-called clustering phase, the ground state manifold is highly degenerate. As an example, we consider a 3-XORSAT model defined on simple hypergraphs. The degeneracy of classical ground state manifold translates into the emergence of an extensive number of $Z_2$ symmetries, which remain intact even in the presence of a quantum transverse magnetic field. We establish a general duality approach that restricts the quantum problem to a given sector of conserved $Z_2$ charges and use it to study how the outcome of the quantum adiabatic algorithm depends on the hypergraph geometry. We show that the tree hypergraph which corresponds to a classically solvable instance of the 3-XORSAT problem features a constant gap, whereas the closed hypergraph encounters a second-order phase transition with a gap vanishing as a power-law in the problem size. The duality developed in this work provides a practical tool for studies of quantum models with classically degenerate energy manifold and reveals potential connections between glasses and gauge theories.
Neutron diffraction measurements were carried out on single crystals and powders of Yb2Pt2Pb, where Yb moments form planes of orthogonal dimers in the frustrated Shastry-Sutherland Lattice (SSL). Yb2Pt2Pb orders antiferromagnetically at TN=2.07 K, and the magnetic structure determined from these measurements features the interleaving of two orthogonal sublattices into a 5*5*1 magnetic supercell that is based on stripes with moments perpendicular to the dimer bonds, which are along (110) and (-110). Magnetic fields applied along (110) or (-110) suppress the antiferromagnetic peaks from an individual sublattice, but leave the orthogonal sublattice unaffected, evidence for the Ising character of the Yb moments in Yb2Pt2Pb. Specific heat, magnetic susceptibility, and electrical resistivity measurements concur with neutron elastic scattering results that the longitudinal critical fluctuations are gapped with E about 0.07 meV.
The phase diagrams of the frustrated classical spin model with Dzyaloshinskii-Moriya (DM) interaction on the Shastry-Sutherland (S-S) lattice are studied by means of Monte Carlo simulation. For ferromagnetic next-nearest-neighboring (J2) interactions, the introduced exchange frustration enhances the effect of the DM interaction, which enlarges the magnetic field-range with the skyrmion lattice phase and increases the skyrmion density. For antiferromagnetic J2 interactions, the so-called 2q phase (two-sublattice skyrmion crystal) and the spin-flop phase are observed in the simulated phase diagram, and their stabilizations are closely dependent on the DM interaction and J2 interaction, respectively. The simulated results are qualitatively explained from the energy landscape, which provides useful information for understanding the intriguing phases in S-S magnets.
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