Absence of Spontaneous Spin Symmetry Breaking in 1D and 2D Quantum Ferromagnetic Systems with Bilinear and Biquadratic Exchange Interactions

Some measurements have shown that the second-order exchange interaction is non-negligible in ferromagnetic compounds whose microscopic interactions are described by means of half-odd integer quantum spins. In these spin systems the ground state is either ferromagnetic or antiferromagnetic when the bilinear exchange interaction is dominant. Instead, in ferromagnetic systems characterized by bilinear and biquadratic exchange interactions of comparable magnitude, the energy minimum occurs when spins are in a canting ground-state. To this aim, a one-dimensional (1D) quantum spin chain and a two-dimensional (2D) lattice of quantum spins subjected to periodic boundary conditions are modeled via the generalized quantum Heisenberg Hamiltonian containing, in addition to the isotropic and short-range bilinear exchange interaction of the Heisenberg type, a second-order interaction, the isotropic and short-range biquadratic exchange interaction between nearest-neighbors quantum spins. For these 1D and 2D quantum systems a generalization of the Mermin–Wagner–Hohenberg theorem (also known as Mermin–Wagner–Berezinksii or Coleman theorem) is given. It is demonstrated, by means of quantum statistical arguments, based on Bogoliubov’s inequality, that, at any finite temperature, (1) there is absence of long-range order and that (2) the law governing the vanishing of the order parameter is the same as in the bilinear case for both 1D and 2D quantum ferromagnetic systems. The physical implications of the absence of a spontaneous spin symmetry breaking in 1D spin chains and 2D spin lattices modeled via a generalized quantum Heisenberg Hamiltonian are discussed.

Prediction of the Curie temperature considering the dependence of the phonon free energy on magnetic states

Prediction of the Curie temperature is of significant importance for the design of ferromagnetic materials. One of the most widely used methods to estimate the Curie temperature from first principles relies on a spin Hamiltonian, for example, the Heisenberg Hamiltonian, and exchange coupling parameters obtained by first-principles calculations at zero temperature. Even though there have been attempts to include the effects of magnetism on phonons, the influence of magnetism-dependent phonons on magnetism has been disregarded in the theoretical estimation of the Curie temperature. Here, we propose a first-principles thermodynamic approach to minimise the total free energy considering both the influences of magnetism on phonons and the feedback effect from phonons to magnetism. By applying our scheme to body-centered cubic Fe, we find a significant reduction of the Curie temperature due to the feedback effect. This result indicates the importance of the feedback effect for a quantitative description of finite-temperature magnetism. In addition, we point out that the reduction in the theoretical Curie temperature arises in a wide range of ferromagnetic materials that exhibit phonon softening due to magnetic disordering.

Two-local qubit Hamiltonians: when are they stoquastic?

We examine the problem of determining if a 2-local Hamiltonian is stoquastic by local basis changes. We analyze this problem for two-qubit Hamiltonians, presenting some basic tools and giving a concrete example where using unitaries beyond Clifford rotations is required in order to decide stoquasticity. We report on simple results for n-qubit Hamiltonians with identical 2-local terms on bipartite graphs. Our most significant result is that we give an efficient algorithm to determine whether an arbitrary n-qubit XYZ Heisenberg Hamiltonian is stoquastic by local basis changes.