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International Journal of Modern Physics B

UNIVERSAL DIAMAGNETISM: EXACT RESULTS AND APPLICATIONS

Debnarayan Jana

Published Aug 10, 2001• 0 citations
Publisher

Abstract

Diamagnetism is a universal pheneomenon of spinless boson system at any finite temperature regardless of their interactions. We present here the exact, non-perturbative results of universal diamagnetism of charged scalar fields at any finite temperature. As an application, we study the effect of anisotropy of two coherence lengths on diamagnetic susceptibility of Cooper pairs in an arbitrary d-dimensions above the transition temperature.

DOI
10.1142/s0217979201006379

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Diamagnetism is a universal pheneomenon of spinless boson system at any finite temperature regardless of their interactions. We present here the exact, non-perturbative results of universal diamagnetism of charged scalar fields at any finite temperature. As an application, we study the effect of anisotropy of two coherence lengths on diamagnetic susceptibility of Cooper pairs in an arbitrary d-dimensions above the transition temperature.
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.
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.
In this Rapid Communication, we investigate the universal properties of a spin-polarized two-component Fermi gas in one dimension (1D) using the Bethe ansatz. We discuss the quantum phases and phase transitions by obtaining exact results for the equation of state, the contact, the magnetic susceptibility, and the contact susceptibility, giving a precise understanding of the 1D analog of the Bose-Einstein condensation and Bardeen-Cooper-Schrieffer crossover in three dimensions (3D) and the associated universal magnetic properties. In particular, we obtain the exact form of the magnetic susceptibility $\ensuremath{\chi}\ensuremath{\sim}1/\sqrt{T}exp(\ensuremath{-}\mathrm{\ensuremath{\Delta}}/T)$ at low temperatures, where $\mathrm{\ensuremath{\Delta}}$ is the energy gap and TTT is the temperature. Moreover, we establish exact upper and lower bounds for the relation between polarization PPP and the contact CCC for both repulsive and attractive Fermi gases. Our findings emphasize the role of pair fluctuations in strongly interacting 1D fermion systems that can shed light on higher dimensions.
Abstract We study orbital diamagnetism at zero temperature in (2 + 1)-dimensional Dirac fermions with a short-range interaction which exhibits a quantum phase transition to a charge density wave (CDW) phase. We introduce orbital magnetic fields into spinless Dirac fermions on the π-flux square lattice, and analyze them by using infinite density matrix renormalization group. It is found that the diamagnetism remains intact in the Dirac semimetal regime, while it is monotonically suppressed in the CDW regime. Around the quantum critical point of the CDW phase transition, we find a scaling behavior of the diamagnetism characteristic of the chiral Ising universality class. Besides, the scaling analysis implies that the robust orbital diamagnetism at weak magnetic fields in a Dirac semimetal regime would hold not only in our model but also in other interacting Dirac fermion systems as long as scaling regions are wide enough. The scaling behavior may also be regarded as a quantum, magnetic analogue of the critical Casimir effect which has been widely studied for classical phase transitions.