Haldane predicted that the isotropic quantum Heisenberg spin chain is in a “massive” phase if the spin is integral. The first rigorous example of an isotropic model in such a phase is presented. The Hamiltonian has an exactSO(3) symmetry and is translationally invariant, but we prove the model has a unique ground state, a gap in the spectrum of the Hamiltonian immediately above the ground state and exponential decay of the correlation functions in the ground state. Models in two and higher dimension which are expected to have the same properties are also presented. For these models we construct an exact ground state, and for some of them we prove that the two-point function decays exponentially in this ground state. In all these models exact ground states are constructed by using valence bonds.

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Valence Bond Ground States in Isotropic Quantum Antiferromagnets

Constructing magnetic molecular solids by employing three-atom ligands as bridges

One-dimensional antiferromagnets have exotic disordered ground states. As was first argued by Haldane (1983), there is an excitation gap for integer, but not half-integer, spin. The authors review the arguments for this behaviour based on field-theory mappings, the Lieb-Schultz-Mattis theorem, exactly solvable models, finite-chain diagonalisation and real experiments.

https://iopscience.iop.org/article/10.1088/0953-8984/1/19/001/pdf

Quantum spin chains and the Haldane gap

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

Physical Content, Analytical Derivation, and Rigorous Extraction of Magnetic Hamiltonians Jean Paul Malrieu,† Rosa Caballol,‡ Carmen J. Calzado, Coen de Graaf,‡,∥ and Nathalie Guiheŕy*,† †Laboratoire de Chimie et Physique Quantiques, Universite ́ de Toulouse 3, 118 route de Narbonne, 31062 Toulouse, France ‡Departament de Química Física i Inorgaǹica, Universitat Rovira i Virgili, Marcel·lí Domingo s/n, 43007 Tarragona, Spain Departamento de Química Física, Universidad de Sevilla, Profesor Garcia Gonzalez s/n, 41012 Sevilla, Spain Institucio ́ Catalana de Recerca i Estudis Avanca̧ts (ICREA), Passeig Lluis Companys 23, 08010 Barcelona, Spain

Magnetic interactions in molecules and highly correlated materials: physical content, analytical derivation, and rigorous extraction of magnetic Hamiltonians.

Magnetic susceptibility and inelastic neutron scattering experiments have been performed in the nearly ideal one-dimensional Heisenberg antiferromagnet with spin one, Ni(C2H8N2)2NO2ClO4. The experimental results are consistent with the recent theoretical predictions for a quantum energy gap between the ground state and the first excited states.

http://iopscience.iop.org/article/10.1209/0295-5075/3/8/013/pdf

Presumption for a Quantum Energy Gap in the Quasi-One-Dimensional S?=?1 Heisenberg Antiferromagnet Ni(C2H8N2)2NO2(ClO4)

Following the Haldane conjecture, the antiferromagnetic (AF) Heisenberg chain of integer spins has a singlet ground state separated from the excited states by an energy gap. Recent numerical calculations on finite AF chains with S=1 supported this conjecture and provided an approximate value for the energy gap: EG≂0.4‖ J‖, where J is the intrachain exchange interaction. We report experimental studies on two Ni (II) quasi‐one‐dimensional (1D) AF with large intrachain interaction, J/k≂−50 K, Ni(C2H8N2)2NO2(ClO4) (NENP) and Ni(C3H10N2)2NO2(ClO4), (NINO). In both compounds, the magnetic susceptibility along the three crystal axes steeply decreases below T≂15 K and no 3D long‐range magnetic order could be detected down to 1.2 K. These features are consistent with the Haldane conjecture. Inelastic neutron scattering experiments performed on NENP show two energy gaps, with an average value of about 0.4‖ J‖, which are explained by a splitting of the Haldane gap by single‐ion anisotropy.

/pdf/quantum-energy-gap-in-two-quasi-one-dimensional-s-1-1o4pjr8tvs.pdf

Quantum energy gap in two quasi‐one‐dimensional S=1 Heisenberg antiferromagnets (invited)

The magnetic phase diagram of K2MnF4 has been determined in fields up to 85 kOe. The variation of TC with H is shown to be related to the anisotropy dependence of TC for the 2‐d anisotropic Heisenberg model.

Field dependent neutron scattering study of the quasi 2‐D Heisenberg antiferromagnet K2MnF4

The critical behaviour of the d-dimensional Ising model in a transverse field H⊥ at temperatures near T = 0 and for H⊥ → Hc⊥, are predicted to be the same as for a (d + 1)-dimensional Ising model in zero field as a function of temperature for T → Tc. We present evidence for such a dimensionality cross-over by studying the field-dependent critical behaviour of the staggered magnetization of the d = 3 Ising-type antiferromagnet MnCl24H2O at low temperatures.

http://iopscience.iop.org/article/10.1209/0295-5075/1/1/006/pdf

Observation of crossover to 4-dimensional critical behaviour

The phase diagram of Rb2MnCl4 in magnetic fields up to 8.3 T parallel to the tetragonal axis was determined by neutron scattering. Similar to K2MnF4, but unlike conventional three-dimensional antiferromagnets, the authors experimental data exhibit a bifurcation of the phase boundary uniaxial antiferromagnet/paramagnet into the phase boundaries uniaxial antiferromagnet/spin-flop phase and paramagnet/spin-flop phase at the multicritical point T*=50.5K, H*=5.55 T. The boundary lines between the uniaxial antiferromagnetic phase and the paramagnetic and spin-flop phases are well described by Tc(H)/Tc(0)= alpha (H)n, where alpha (H) is the field-dependent anisotropy and n approximately=0.04 is possibly a universal exponent.

J. Rossat-Mignod

Papers

Presumption for a Quantum Energy Gap in the Quasi-One-Dimensional S?=?1 Heisenberg Antiferromagnet Ni(C2H8N2)2NO2(ClO4)

Quantum energy gap in two quasi‐one‐dimensional S=1 Heisenberg antiferromagnets (invited)

Field dependent neutron scattering study of the quasi 2‐D Heisenberg antiferromagnet K2MnF4

Observation of crossover to 4-dimensional critical behaviour

Magnetic phase diagram of Rb2MnCl4, a quasi-two-dimensional uniaxial antiferromagnet