A discrete density matrix theory for atoms in strong magnetic fields

Quantum magnetism in low dimensions has been one of the central areas of theoretical research for many decades now. One of the key reasons for the long standing interest in this field has been the existence of simplified models, which serve as paradigms for understanding the role of strong interactions in many-electron systems. Although simple, these models quite often can not be solved exactly. In this review, we discuss a variety of analytical and numerical methods, which t...

Density-functional theory is used to study the electronic structure of quantum dots in a magnetic field. New series of magic numbers are found for the total angular momentum of electrons. The empirical formula for the plateau width is obtained. The effect of a charged impurity on the electronic structure of a quantum dot has been studied.

In the Dirac operator framework we characterize and estimate the ground state energy of relativistic hydrogenic atoms in a constant magnetic field and describe the asymptotic regime corresponding to a large field strength using relativistic Landau levels. We also define and estimate a critical magnetic field beyond which stability is lost.

We consider a one-dimensional model for many-electron atoms in strong magnetic fields in which the Coulomb potential and interactions are replaced by one-dimensional regularizations associated with the lowest Landau level. For this model we show that the maximum number of electrons is bounded above by 2Z+1 + c sqrt{B}. We follow Lieb's strategy in which convexity plays a critical role. For the case of two electrons and fractional nuclear charge, we also discuss the critical...

The problem of a hydrogen atom in a strong magnetic field is a notorious example of a quantum system that has genuinely different asymptotic behaviors in different directions. In the direction perpendicular to the magnetic field the motion is quadratically confined, while in the direction along the field line the motion is a Coulomb-distorted free motion. In this work, we identify the asymptotically relevant parts of the Hamiltonian and cast the problem into a Lippmann-Schwin...

We present a new pseudospectral algorithm for the calculation of the structure of atoms in strong magnetic fields. We have verified this technique for one, two and three-electron atoms in zero magnetic fields against laboratory results and find typically better than one-percent accuracy. We further verify this technique against the state-of-the-art calculations of hydrogen, helium and lithium in strong magnetic fields (up to about $2\times 10^{6}$ T) and find a similar level ...

We present new ab initio calculations of the electronic structure of various atoms and molecules in strong magnetic fields ranging from B=10^12 G to 2x10^15 G, appropriate for radio pulsars and magnetars. For these field strengths, the magnetic forces on the electrons dominate over the Coulomb forces, and to a good approximation the electrons are confined to the ground Landau level. Our calculations are based on the density functional theory, and use a local magnetic exchange...

Asymptotics of the ground state energy of the heavy atoms and molecules in the self-generated magnetic field has been derived and for minimal energy positions of nuclei remainder estimate $O(N^{16/9})$ has been recovered.

We present a new method for calculating ground state properties of quantum dots in high magnetic fields. It takes into account the equilibrium positions of electrons in a Wigner cluster to minimize the interaction energy in the high field limit. Assuming perfect spin alignment the many-body trial function is a single Slater determinant of overlapping oscillator functions from the lowest Landau level centered at and near the classical equilibrium positions. We obtain an analyt...

In this review article we provide an overview of the field of atomic structure of light atoms in strong magnetic fields. There is a very rich history of this field which dates back to the very birth of quantum mechanics. At various points in the past significant discoveries in science and technology have repeatedly served to rejuvenate interest in atomic structure in strong fields, broadly speaking, resulting in three eras in the development of this field; the historical, the...