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Chinese Physics B

Thermodynamic properties of two-dimensional charged spin-1/2 Fermi gases

Jiaying Yang, Xu Liu, Jihong Qin, Huaiming Guo

Published Jan 24, 2022• 1 citation
Publisher

Abstract

Based on the mean-field theory, we investigate the thermodynamic properties of the two-dimensional (2D) charged spin-1/2 Fermi gas. Landé factor g is introduced to measure the strength of the paramagnetic effect. There is a competition between diamagnetism and paramagnetism in the system. The larger the Landé factor, the smaller the entropy and specific heat. Diamagnetism tends to increase the entropy, while paramagnetism leads to the decrease of the entropy. We find that there exists a critical value of Landé factor for the transition point due to the competition. The entropy of the system increases with the magnetic field when g < 0.58. With the growth of paramagnetism, when g > 0.58, the entropy first decreases with the magnetic field, then reaches a minimum value, and finally increases again. Both the entropy and specific heat increase with the temperature, and no phase transition occurs. The specific heat tends to a constant value at the high-temperature limit, and it approaches to zero at very low temperatures, which have been proved by the analytical calculation.

DOI
10.1088/1674-1056/ac4e0b

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Based on the mean-field theory, we investigate the thermodynamic properties of the two-dimensional (2D) charged spin-1/2 Fermi gas. Landé factor g is introduced to measure the strength of the paramagnetic effect. There is a competition between diamagnetism and paramagnetism in the system. The larger the Landé factor, the smaller the entropy and specific heat. Diamagnetism tends to increase the entropy, while paramagnetism leads to the decrease of the entropy. We find that there exists a critical value of Landé factor for the transition point due to the competition. The entropy of the system increases with the magnetic field when g < 0.58. With the growth of paramagnetism, when g > 0.58, the entropy first decreases with the magnetic field, then reaches a minimum value, and finally increases again. Both the entropy and specific heat increase with the temperature, and no phase transition occurs. The specific heat tends to a constant value at the high-temperature limit, and it approaches to zero at very low temperatures, which have been proved by the analytical calculation.
The magnetic properties of a charged spin-1 Bose gas with ferromagnetic interactions are investigated within mean-field theory. It is shown that a competition between paramagnetism, diamagnetism and ferromagnetism exists in this system. It is shown that diamagnetism, being concerned with spontaneous magnetization, cannot exceed ferromagnetism in a very weak magnetic field. The critical value of reduced ferromagnetic coupling of the paramagnetic phase to ferromagnetic phase transition I[combining overline](c) increases with increasing temperature. The Landé-factor g is introduced to describe the strength of the paramagnetic effect which comes from the spin degree of freedom. The magnetization density M[combining overline] increases monotonically with g for fixed reduced ferromagnetic coupling I[combining overline] as I[combining overline] > I[combining overline](c). In a weak magnetic field, ferromagnetism makes an immense contribution to the magnetization density. On the other hand, at a high magnetic field, the diamagnetism tends to saturate. Evidence for condensation can be seen in the magnetization density at a weak magnetic field.
It has been suggested that either the diamagnetism or paramagnetism of Bose gases, due to the charge or spin degrees of freedom respectively, appears solely to be extraordinarily strong. We investigate the magnetic properties of charged spin-1 Bose gases in an external magnetic field, focusing on the competition between the diamagnetism and paramagnetism, using the Lande-factor g of particles to evaluate the strength of the paramagnetic effect. We propose that a gas with g < 1/√8 exhibits diamagnetism at all temperatures, while a gas with g > 1/2 always exhibits paramagnetism. Moreover, a gas with the Lande-factor in between shows a shift from paramagnetism to diamagnetism as the temperature decreases. The paramagnetic and diamagnetic contributions to the total magnetization density are also calculated in order to demonstrate some details of the competition.
Thermodynamics of trapped charged ideal spin-1 bosons confined in a magnetic field are investigated within semi-classical approximation and truncated-summation approach. It is shown that the critical temperature increases slightly at the first, and then decreases slowly with increasing external magnetic field. Charged spin-1 Bose gases present a crossover from diamagnetism to paramagnetism as the spin factor increases. Charged spin-1 Bose gases exhibit distinct thermodynamic behaviors from the spinless case.
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In this thesis, we present a recent study of the one-dimensional attractively interacting two-component Fermi gas with an external magnetic field. We analytically study the quantum phase diagram, equation of state, quantum criticality, and universal scalings of the model, using the thermodynamic Bethe ansatz equations. We present a high precision equation of state from which universal scaling functions are derived; we show that the thermodynamic properties display universal scaling behaviour at quantum criticality. Expression of high-order-accuracy entropy and specific heat are also analytically derived. Moreover, we present an independent confirmation of the equation of state through an efficient numerical approach of treating the thermodynamic Bethe ansatz equations for which the contributions from the spin strings with length larger than a value of ncn_cnc​ are calculated analytically.