Milestones of low-D quantum magnetism

Abstract

There is a long time gap between the formulation of the basic theory of low-dimensional (low-D) magnetism as advanced by Ising, Heisenberg and Bethe and its experimental verification. The latter started not long before the discovery of high-T C superconductivity in cuprates and has been boosted by this discovery result in an impressive succession of newly observed physical phenomena. Milestones on this road were the compounds which reached their quantum ground states upon lowering the temperature either gradually or through different instabilities. The gapless and gapped ground states for spin excitations in these compounds are inherent for isolated half-integer spin and integer spin chains, respectively. The same is true for the compounds hosting odd and even leg spin ladders. Some complex oxides of transition metals reach gapped ground state by means of spin-Peierls transition, charge ordering or orbital ordering mechanisms. However, the overwhelming majority of low-dimensional systems arrive to a long-range ordered magnetic state, albeit quite exotic realizations. Under a magnetic field some frustrated magnets stabilize multipolar order, e.g., showing a spin-nematic state in the simplest quadropolar case. Finally, numerous square, triangular, kagome and honeycomb layered lattices, along with Shastry-Sutherland and Nersesyan-Tsvelik patterns constitute the playground to check the basic concepts of two-dimensional magnetism, including resonating valence bond state, Berezinskii-Kosterlitz-Thouless transition and Kitaev model.

Simulating quantum many-body dynamics on a current digital quantum computer

“…This model was recently studied in the context of many-body localization without disorder [59,60], where Wannier-Stark localization [61] is induced by the linear potential. This family of Hamiltonians covers a large range of physics in condensed matter, from the integrable limit [56], to manybody quantum magnetism [62], to that of many-body localization [63,64]. These Hamiltonians are perfect testbeds for digital quantum simulation since they can be directly simulated on a quantum computer -the spins-1/2 of the former correspond directly to the qubits of the latter, and the local connectivity of the qubits is suited for the local form of the Hamiltonian.…”

Experimental identification of quantum spin liquids

“…For reference, there is a recent review article in this topic in ref. 50. Here, we will focus on QSLs in two or three dimensions.…”

Multiple phase transitions and high-field quadrupolar order in a model for β−TeVO4

“…Lower dimensionality and frustrating interactions further reduce the tendency of spin systems to acquire conventional magnetic order, thereby promoting exotic quantum phenomena [3][4][5][6][7][8]. Often, the interplay among frustrating interactions, lower dimensionality and the intrinsic quantum nature of the degrees of freedom results in unexpected states and complex magnetic phase diagrams [9,10].…”