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-TC 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.

/pdf/milestones-of-low-d-quantum-magnetism-azni4q1hf6.pdf

Milestones of low-D quantum magnetism

Author(s): Ma, N; Sun, GY; You, YZ; Xu, C; Vishwanath, A; Sandvik, AW; Meng, ZY | Abstract: Deconfined quantum critical points govern continuous quantum phase transitions at which fractionalized (deconfined) degrees of freedom emerge. Here we study dynamical signatures of the fractionalized excitations in a quantum magnet (the easy-plane J-Q model) that realize a deconfined quantum critical point with emergent O(4) symmetry. By means of large-scale quantum Monte Carlo simulations and stochastic analytic continuation of imaginary-time correlation functions, we obtain the dynamic spin-structure factors in the Sx and Sz channels. In both channels, we observe broad continua that originate from the deconfined excitations. We further identify several distinct spectral features of the deconfined quantum critical point, including the lower edge of the continuum and its form factor on moving through the Brillouin zone. We provide field-theoretical and lattice model calculations that explain the overall shapes of the computed spectra, which highlight the importance of interactions and gauge fluctuations to explain the spectral-weight distribution. We make further comparisons with the conventional Landau O(2) transition in a different quantum magnet, at which no signatures of fractionalization are observed. The distinctive spectral signatures of the deconfined quantum critical point suggest the feasibility of its experimental detection in neutron scattering and nuclear magnetic resonance experiments.

Dynamical signature of fractionalization at a deconfined quantum critical point

At the familiar liquid-gas phase transition in water, the density jumps discontinuously at atmospheric pressure, but the line of these first-order transitions defined by increasing pressures terminates at the critical point, a concept ubiquitous in statistical thermodynamics. In correlated quantum materials, a critical point was predicted and measured terminating the line of Mott metal-insulator transitions, which are also first-order with a discontinuous charge density. In quantum spin systems, continuous quantum phase transitions (QPTs) have been investigated extensively, but discontinuous QPTs have received less attention. The frustrated quantum antiferromagnet SrCu$_2$(BO$_3$)$_2$ constitutes a near-exact realization of the paradigmatic Shastry-Sutherland model and displays exotic phenomena including magnetization plateaux, anomalous thermodynamics and discontinuous QPTs. We demonstrate by high-precision specific-heat measurements under pressure and applied magnetic field that, like water, the pressure-temperature phase diagram of SrCu$_2$(BO$_3$)$_2$ has an Ising critical point terminating a first-order transition line, which separates phases with different densities of magnetic particles (triplets). We achieve a quantitative explanation of our data by detailed numerical calculations using newly-developed finite-temperature tensor-network methods. These results open a new dimension in understanding the thermodynamics of quantum magnetic materials, where the anisotropic spin interactions producing topological properties for spintronic applications drive an increasing focus on first-order QPTs.

A quantum magnetic analogue to the critical point of water

We report heat capacity measurements of ${\mathrm{SrCu}}_{2}({\mathrm{BO}}_{3}{)}_{2}$ under high pressure along with simulations of relevant quantum spin models and map out the $(P,T)$ phase diagram of the material. We find a first-order quantum phase transition between the low-pressure quantum dimer paramagnet and a phase with signatures of a plaquette-singlet state below $T=2\text{ }\text{ }\mathrm{K}$. At higher pressures, we observe a transition into a previously unknown antiferromagnetic state below 4 K. Our findings can be explained within the two-dimensional Shastry-Sutherland quantum spin model supplemented by weak interlayer couplings. The possibility to tune ${\mathrm{SrCu}}_{2}({\mathrm{BO}}_{3}{)}_{2}$ between the plaquette-singlet and antiferromagnetic states opens opportunities for experimental tests of quantum field theories and lattice models involving fractionalized excitations, emergent symmetries, and gauge fluctuations.

Quantum Phases of SrCu 2 ( BO 3 ) 2 from High-Pressure Thermodynamics

A realistic model of a 2D quantum magnet may exhibit a deconfined quantum critical point---a long-sought type of phase transition---that could present itself as a unique signature in phonon and magnon spectra.

https://link.aps.org/pdf/10.1103/PhysRevX.9.041037

Signatures of a Deconfined Phase Transition on the Shastry-Sutherland Lattice: Applications to Quantum Critical SrCu 2 ( BO 3 ) 2

A detailed neutron scattering study of the Shastry–Sutherland material SrCu2(BO3)2 verifies the existence of a 4-spin plaquette singlet phase in this system.

4-spin plaquette singlet state in the Shastry-Sutherland compound SrCu2(BO3)(2)

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4-spin plaquette singlet state in the Shastry-Sutherland compound SrCu2(BO3)(2)