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Physical Review Letters

Universal Diamagnetism of Spinless Bose Systems

Barry Simon A

Published May 3, 1976• 66 citations
Publisher

Abstract

I prove that the ground-state energy of an arbitrary system of nonrelativistic spinless Bose particles increases when any (arbitrarily strong or inhomogeneous) magnetic field is turned on.
DOI
10.1103/physrevlett.36.1083

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Simple diamagnetic monotonicities for Schroumloumloumldinger operators with inhomogeneous magnetic fields of constant direction
Under certain simplifying conditions we detect monotonicity properties of the ground-state energy and the canonical-equilibrium density matrix of a spinless charged particle in the Euclidean plane subject to a perpendicular, possibly inhomogeneous magnetic field and an additional scalar potential. Firstly, we point out a simple condition warranting that the ground-state energy does not decrease when the magnetic field and/or the potential is increased pointwise. Secondly, we consider the case in which both the magnetic field and the potential are constant along one direction in the plane and give a genuine path-integral argument for corresponding monotonicities of the density-matrix diagonal and the absolute value of certain off-diagonals. Our results complement to some degree results of Loss and Thaller (1997 Commun. Math. Phys. 186 95) and Erdös (1997 J. Math. Phys. 38 1289).
The magnetic susceptibilities of the degenerate (below the Bose–Einstein condensation temperature) and nondegenerate ideal gases of nonrelativistic charged spinless bosons are presented. In both cases, the boson gas is diamagnetic. The magnetic susceptibility of the degenerate boson gas below the Bose–Einstein condensation temperature increases in modulus as the temperature increases. As expected, the magnetic susceptibility of the nondegenerate boson gas decreases in modulus with increasing temperature according to the Curie law in low magnetic fields.
We study orbital diamagnetism in (2+1)(2+1)(2+1)-dimensional Dirac electrons with a short-range interaction at zero temperature. We introduce orbital magnetic fields into spinless Dirac electrons on the π\piπ-flux square lattice, and analyze them by using infinite density matrix renormalization group. It is found that the diamagnetism remains intact when the short-range interaction VVV is weak, while it is monotonically suppressed for larger interactions. Around the quantum critical point (QCP) of a charge density wave phase transition, we find a scaling behavior of the ground state energy density characteristic of the chiral Ising universality class. This leads to universal orbital diamagnetism in correlated Dirac electrons around the QCP, which may be regarded as a quantum, magnetic analogue of critical Casimir effect which has been widely studied for classical phase transitions.