The equation of state is obtained for a degenerate system of non-interacting, relativistic, neutral fermions with spin 1 / 2 in a uniform magnetic field. The question of arbitrarily large fields is addressed, and previous results for the ground state are extended to finite temperatures.
We return to the question of how the choice of stabilizer generators affects the preservation of information on structures whose degenerate ground state encodes a classical redundancy code. Controlled-not gates are used to transform the stabilizer Hamiltonian into a Hamiltonian consisting of uncoupled single spins and/or pairs of spins. This transformation allows us to obtain an analytical partition function and derive closed-form equations for the relative magnetization and susceptibility. These equations are in agreement with the numerical results presented in Viteri et al. [Phys. Rev. A 80, 042313 (2009)] for finite size systems. Analytical solutions show that there is no finite critical temperature, Tc=0, for all of the memory structures in the thermodynamic limit. This is in contrast to the previously predicted finite critical temperatures based on extrapolation. The mismatch is a result of the infinite system being a poor approximation even for astronomically large finite-size systems, where spontaneous magnetization still arises below an apparent finite critical temperature. We extend our analysis to the canonical stabilizer Hamiltonian. Interestingly, Hamiltonians with two-body interactions have a higher apparent critical temperature than the many-body Hamiltonian.
General expressions are obtained in explicit form for the anomalous and normal distribution functions of quasiparticles in nonunitary phases of a superfluid paramagnetic Fermi liquid consisting of electrically neutral fermions with triplet pairing (the pairs have spin s=1 and an arbitrary odd value of the orbital angular momentum l) in a uniform static magnetic field. A generalized Fermi-liquid approach is used which takes into account the exchange Fermi-liquid interaction but does not specify the form of the energy functional of the superfluid Fermi liquid. The results are valid at any temperature in the interval 0⩽T⩽Tc, where Tc is the temperature of the phase transition from the normal to the superfluid state. When an explicit form of the energy functional is specified, the general formulas for the distribution function can be used to describe the various nonunitary phases of a superfluid Fermi liquid of the He3 type in a high magnetic field. In particular, for He3-A1, He3-A2, and the nonunitary two-dimensional phase of He3 in a high magnetic field at 0⩽T⩽Tc, an energy functional quadratic in the distribution function is used to find a system of coupled equations for the order parameter and the effective magnetic field and to obtain an expression is obtained for the nonlinear magnetic susceptibility.
This work presents the theoretical background for the computation of nuclear magnetic shielding, nuclear hyperfine and magnetizability tensors of paramagnetic molecules, using a magnetically induced current density framework to account for both orbital and spin contributions. The resulting magnetizability tensor is fully consistent with the general Van Vleck formulation, recovering the temperature-dependent Curie contribution through the explicit integration of the magnetically induced spin current density. The methodology proposed herein provides a straightforward computational route that bypasses the complex evaluation of g-tensors and Zero-Field Splitting (ZFS) Hamiltonians. While the theoretical framework is general, we present applications rooted on physically motivated approximations where scalar relativistic effects are incorporated through corrections based on the Zeroth-Order Regular Approximation (ZORA) Hamiltonian within the ground-state spin density. This approach combines a relativistic self-consistent field (SCF) calculation for the ground-state spin density with a non-relativistic, origin-independent current density calculation for the orbital contribution. This hybrid strategy is shown to capture the Heavy-Atom Light-Atom (HALA) effect in 1H and 13C shieldings, particularly in paramagnetic molecular systems containing transition metals up to the 3d series. By restricting the relativistic treatment to the spin density, where scalar relativistic effects are dominant, and neglecting such effects on the orbital contribution of light atoms, this method offers a good compromise between computational efficiency and accuracy for the characterization of large open-shell molecular systems.