This review summarizes recent developments in the theory of spin glasses, as well as pertinent experimental data. The most characteristic properties of spin glass systems are described, and related phenomena in other glassy systems (dielectric and orientational glasses) are mentioned. The Edwards-Anderson model of spin glasses and its treatment within the replica method and mean-field theory are outlined, and concepts such as "frustration," "broken replica symmetry," "broken ergodicity," etc., are discussed. The dynamic approach to describing the spin glass transition is emphasized. Monte Carlo simulations of spin glasses and the insight gained by them are described. Other topics discussed include site-disorder models, phenomenological theories for the frozen phase and its excitations, phase diagrams in which spin glass order and ferromagnetism or antiferromagnetism compete, the Ne\'el model of superparamagnetism and related approaches, and possible connections between spin glasses and other topics in the theory of disordered condensed-matter systems.

Spin glasses: Experimental facts, theoretical concepts, and open questions

This is an introductory review of the physics of quantum spin liquid states. Quantum magnetism is a rapidly evolving field, and recent developments reveal that the ground states and low-energy physics of frustrated spin systems may develop many exotic behaviors once we leave the regime of semiclassical approaches. The purpose of this article is to introduce these developments. The article begins by explaining how semiclassical approaches fail once quantum mechanics become important and then describe the alternative approaches for addressing the problem. Mainly spin-1/2 systems are discussed, and most of the time is spent in this article on one particular set of plausible spin liquid states in which spins are represented by fermions. These states are spin-singlet states and may be viewed as an extension of Fermi liquid states to Mott insulators, and they are usually classified in the category of so-called SU(2), U(1), or Z2 spin liquid states. A review is given of the basic theory regarding these states and the extensions of these states to include the effect of spin-orbit coupling and to higher spin (S>1/2) systems. Two other important approaches with strong influences on the understanding of spin liquid states are also introduced: (i) matrix product states and projected entangled pair states and (ii) the Kitaev honeycomb model. Experimental progress concerning spin liquid states in realistic materials, including anisotropic triangular-lattice systems [κ-(ET)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2], kagome-lattice system [ZnCu3(OH)6Cl2], and hyperkagome lattice system (Na4Ir3O8), is reviewed and compared against the corresponding theories.

Quantum spin liquid states

A generalized frustrated Ising model on a two-dimensional lattice is considered. This model is paramagnetic at zero temperature but ferromagnetic provided 0 < T < T c. The effect of dilution on this system is also investigated, and long range order is shown to be restored in the dilute model under certain conditions involving concentration, temperature and interactions which are discussed in comparison with usual percolation.

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Order as an effect of disorder

In materials with strong local Coulomb interactions, simple defects such as atomic substitutions strongly affect both macroscopic and local properties of the system. A nonmagnetic impurity, for instance, is seen to induce magnetism nearby. Even without disorder, models of such correlated systems are generally not soluble in 2 or 3 dimensions, and so few exact results are known for the properties of such impurities. Nevertheless, some simple physical ideas have emerged from experiments and approximate theories. Here, we first review what we can learn about this problem from 1D antiferromagnetically correlated systems. We then discuss experiments on the high Tc cuprate normal state which probe the effect of impurities on local charge and spin degrees of freedom, and compare with theories of single impurities in correlated hosts, as well as phenomenological effective Kondo descriptions. Subsequently, we review theories of impurities in d-wave superconductors including residual quasiparticle interactions, and compare with experiments in the superconducting state. We argue that existing data exhibit a remarkable similarity to impurity-induced magnetism in the 1D case, implying the importance of electronic correlations for the understanding of these phenomena, and suggesting that impurities may provide excellent probes of the still poorly understood ground state of the cuprates.

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Defects in correlated metals and superconductors

Quantum simulation using synthetic systems is a promising route to solve outstanding quantum many-body problems in regimes where other approaches, including numerical ones, fail1. Many platforms are being developed towards this goal, in particular based on trapped ions2–4, superconducting circuits5–7, neutral atoms8–11 or molecules12,13. All of these platforms face two key challenges: scaling up the ensemble size while retaining high-quality control over the parameters, and validating the outputs for these large systems. Here we use programmable arrays of individual atoms trapped in optical tweezers, with interactions controlled by laser excitation to Rydberg states11, to implement an iconic many-body problem—the antiferromagnetic two-dimensional transverse-field Ising model. We push this platform to a regime with up to 196 atoms manipulated with high fidelity and probe the antiferromagnetic order by dynamically tuning the parameters of the Hamiltonian. We illustrate the versatility of our platform by exploring various system sizes on two qualitatively different geometries—square and triangular arrays. We obtain good agreement with numerical calculations up to a computationally feasible size (approximately 100 particles). This work demonstrates that our platform can be readily used to address open questions in many-body physics. Programmable quantum simulation of two-dimensional antiferromagnets is achieved with up to 196 neutral atoms, and the capability of the platform is demonstrated on square and triangular arrays.

https://hal.archives-ouvertes.fr/hal-03282018/document

Quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms.

We present exact results for various frustrated Ising models in two dimensions with periodic interactions. None of them gives rise to what could be regarded as spin glass order. The only long range orders encountered are of ferro- or antiferromagnetic type but the effect of frustration manifests itself at low temperature (entropy, susceptibilities). The analysis of these results provides some indications concerning a necessary condition for ordering in such systems and the possible nature of the spin glass order.

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Frustration in periodic systems : exact results for some 2D Ising models

Exact results are obtained for two‐dimensional Ising models in which periodic conflicting interactions induce frustration effects. A brief review of the remarkable thermodynamic and magnetic properties of these models is presented. For specific choices of the interactions, the main features predicted are: (1) The existence of systems with a highly degenerate level of lowest energy, leading to a residual 0K entropy per spin. (2) According to the distribution of interactions, the existence of a residual 0K entropy is not an impediment to the onset of long range order at finite temperatures. However, if such an order takes place, the corresponding order parameter may not be saturated at 0K, and the associated susceptibility will diverge at 0K as well as at the transition temperatures. (3) Long range spin correlations 〈S(O)S(R) 〉 at 0K averaged over all ground states are studied in one of the models (which includes the ’’odd model’’) for simple crystallographic directions of R. They are shown to decrease as f (R) ⋅R−1/2 where f (R) is an oscillatory factor, proper to each R direction, which results in marked anisotropy effects.

Frustration effects in 2D regular Ising models

The main interest of the domino model is to be tractable by analytic methods. Its properties are only of interest if they have some generality. i) Temperature-induced order is probably a fairly common property. In particular it may be expected in three-dimensional systems with ground state entropy proportional to N1/3, from low-temperature expansions. It is probably more exceptional in two-dimensional systems. ii) Order induced by stoechiometric disorder is probably exceptional in Ising models. The domino model seems to be very spec.ial. iii) The fact that X″ can be strictly smaller than the concentration threshold X is an interesting feature of the domino model. It would be of interest to consider this possibility in other frustrated systems.

J.-P. Carton

Papers

Order as an effect of disorder

Frustration in periodic systems : exact results for some 2D Ising models

Frustration effects in 2D regular Ising models

Order as a consequence of disorder in frustrated Ising models