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Register a new userSpin Hartree-Fock approach to quantum Heisenberg antiferromagnets in low dimensions
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We construct a new mean-field theory for quantum (spin-1/2) Heisenberg antiferromagnet in one (1D) and two (2D) dimensions using a Hartree-Fock decoupling of the four-point correlation functions. We show that the solution to the self-consistency equations based on two-point correlation functions does not produce any unphysical finite-temperature phase transition in accord with Mermin-Wagner theorem, unlike the common approach based on the mean-field equation for the order parameter. The next-neighbor spin-spin correlation functions, calculated within this approach, reproduce closely the strong renormalization by quantum fluctuations obtained via Bethe ansatz in 1D and a small renormalization of the classical antiferromagnetic state in 2D. The heat capacity approximates with reasonable accuracy the full Bethe ansatz result at all temperatures in 1D. In 2D, we obtain a reduction of the peak height in the heat capacity at a finite temperature that is accessible by high-order $1/T$ expansions.
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We report on numerical studies into the interplay of disorder and electron-electron interactions within the integer quantum Hall regime, where the presence of a strong magnetic field and two-dimensional confinement of the electronic system profoundly affects thermodynamic and transport properties. We emphasise the behaviour of the electronic compressibility, the local density of states, and the Kubo conductivity. Our treatment of the electron-electron interactions relies on the Hartree-Fock approximation so as to achieve system sizes comparable to experimental situations. Our results clearly exhibit manifestations of various interaction-mediated features, such as non-linear screening, local charging, and g-factor enhancement, implying the inadequacy of independent-particle models for comparison with experimental results.
Ground state energies are obtained using the unrestricted Hartree Fock method for up to four interacting electrons parabolically confined in a quantum dot subject to a magnetic field. Restoring spin and rotational symmetries we recover Hund first rule. With increasing magnetic field, crossovers between ground states with different quantum numbers are found for fixed electron number that are not reproduced by the unrestricted Hartree Fock approximation. These are consistent with the ones obtained with more refined techniques. We confirm the presence of a spin blockade due to a spin mismatch in the ground states of three and four electrons.
We report results for the ground state energies and wave functions obtained by projecting spatially unrestricted Hartree Fock states to eigenstates of the total spin and the angular momentum for harmonic quantum dots with $Nleq 12$ interacting electrons including a magnetic field states with the correct spatial and spin symmetries have lower energies than those obtained by the unrestricted method. The chemical potential as a function of a perpendicular magnetic field is obtained. Signature of an intrinsic spin blockade effect is found.
We study the anisotropic quantum Heisenberg antiferromagnet for spin-1/2 that interpolates smoothly between the one-dimensional (1D) and the two-dimensional (2D) limits. Using the spin Hartree-Fock approach we construct a quantitative theory of heat capacity in the quasi-1D regime with a finite coupling between spin chains. This theory reproduces closely the exact result of Bethe Ansatz in the 1D limit and does not produces any spurious phase transitions for any anisotropy in the quasi-1D regime at finite temperatures in agreement with the Mermin-Wagner theorem. We study the static spin-spin correlation function in order to analyse the interplay of lattice geometry and anisotropy in these systems. We compare the square and triangular lattice. For the latter we find that there is a quantum transition point at an intermediate anisotropy of $sim0.6$. This quantum phase transition establishes that the quasi-1D regime extends upto a particular point in this geometry. For the square lattice the change from the 1D to 2D occurs smoothly as a function of anisotropy, i.e. it is of the crossover type. Comparing the newly developed theory to the available experimental data on the heat capacity of $rm{Cs}_2rm{CuBr}_4$ and $rm{Cs}_2rm{CuCl}_4$ we extract the microscopic constants of the exchange interaction that previously could only be measured using inelastic neutron scattering in high magnetic fields.
We apply Projected Hartree-Fock theory (PHF) for approximating ground states of Heisenberg spin clusters. Spin-rotational, point-group and complex-conjugation symmetry are variationally restored from a broken-symmetry mean-field reference, where the latter corresponds to a product of local spin states. A fermionic formulation of the Heisenberg model furnishes a conceptual connection to PHF applications in quantum chemistry and detailed equations for a self-consistent field optimization of the reference state are provided. Different PHF variants are benchmarked for ground-state energies and spin-pair correlation functions of antiferromagnetic spin rings and three different polyhedra, with various values of the local spin-quantum number s. The low computational cost and the compact wave-function representation make PHF a promising complement to existing approaches for ground states of molecular spin clusters, particularly for large s and moderately large N. The present work may also motivate future explorations of more accurate post-PHF methods for Heisenberg spin clusters.
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