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Register a new userMagnetic properties of spin-1/2 Fermi gases with ferromagnetic interaction
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We investigate the magnetic properties of spin-$1/2$ charged Fermi gases with ferromagnetic coupling via mean-field theory, and find the interplay among the paramagnetism, diamagnetism and ferromagnetism. Paramagnetism and diamagnetism compete with each other. When increasing the ferromagnetic coupling the spontaneous magnetization occurs in a weak magnetic field. The critical ferromagnetic coupling constant of the paramagnetic phase to ferromagnetic phase transition increases linearly with the temperature. Both the paramagnetism and diamagnetism increase when the magnetic field increases. It reveals the magnetization density $bar M$ increases firstly as the temperature increases, and then reaches a maximum. Finally the magnetization density $bar M$ decreases smoothly in the high temperature region. The domed shape of the magnetization density $bar M$ variation is different from the behavior of Bose gas with ferromagnetic coupling. We also find the curve of susceptibility follows the Curie-Weiss law, and for a given temperature the susceptibility is directly proportional to the Land{e} factor.
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Magnetic properties of a charged spin-1 Bose gas with ferromagnetic interactions is 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 very weak magnetic field. The critical value of reduced ferromagnetic coupling of paramagnetic phase to ferromagnetic phase transition $bar I_{c}$ increases with increasing temperature. The Lande-factor $g$ is introduced to describe the strength of paramagnetic effect which comes from the spin degree of freedom. The magnetization density $bar M$ increases monotonically with $g$ for fixed reduced ferromagnetic coupling $bar I$ as $bar I>bar I_{c}$. In a weak magnetic field, ferromagnetism makes immense contribution to the magnetization density. While at a high magnetic field, the diamagnetism inclines to saturate. Evidence for condensation can be seen in the magnetization density at weak magnetic field.
Within the mean-field theory, we investigate the magnetic properties of a charged spin-1 Bose gas in two dimension. In this system the diamagnetism competes with paramagnetism, where Lande-factor $g$ is introduced to describe the strength of the paramagnetic effect. The system presents a crossover from diamagnetism to paramagnetism with the increasing of Lande-factor. The critical value of the Lande-factor, $g_{c}$, is discussed as a function of the temperature and magnetic field. We get the same value of $g_{c}$ both in the low temperature and strong magnetic field limit. Our results also show that in very weak magnetic field no condensation happens in the two dimensional charged spin-1 Bose gas.
By high temperature series expansion, exact diagonalisation and temperature density-matrix renormalisation the magnetic susceptibility $chi(T)$ and the specific heat $C(T)$ of dimerised and frustrated $S=1/2$ chains are computed. All three methods yield reliable results, in particular for not too small temperatures or not too small gaps. The series expansion results are provided in the form of polynomials allowing very fast and convenient fits in data analysis using algebraic programmes. We discuss the difficulty to extract more than two coupling constants from the temperature dependence of $chi(T)$.
The ground state and thermodynamic properties of spin-1 and spin-3/2 chains are investigated via exactly solved su(3) and su(4) models with physically motivated chemical potential terms. The analysis involves the Thermodynamic Bethe Ansatz and the High Temperature Expansion (HTE) methods. For the spin-1 chain with large single-ion anisotropy, a gapped phase occurs which is significantly different from the valence-bond-solid Haldane phase. The theoretical curves for the magnetization, susceptibility and specific heat are favourably compared with experimental data for a number of spin-1 chain compounds. For the spin-3/2 chain a degenerate gapped phase exists starting at zero external magnetic field. A middle magnetization plateau can be triggered by the single-ion anisotropy term. Overall, our results lend further weight to the applicability of integrable models to the physics of low-dimensional quantum spin systems. They also highlight the utility of the exact HTE method.
In spin chains with local unitary evolution preserving the magnetization $S^{rm z}$, the domain-wall state $left| dots uparrow uparrow uparrow uparrow uparrow downarrow downarrow downarrow downarrow downarrow dots right>$ typically melts. At large times, a non-trivial magnetization profile develops in an expanding region around the initial position of the domain-wall. For non-integrable dynamics the melting is diffusive, with entropy production within a melted region of size $sqrt{t}$. In contrast, when the evolution is integrable, ballistic transport dominates and results in a melted region growing linearly in time, with no extensive entropy production: the spin chain remains locally in states of zero entropy at any time. Here we show that, for the integrable spin-$1/2$ XXZ chain, low-energy quantum fluctuations in the melted region give rise to an emergent Luttinger liquid which, remarkably, differs from the equilibrium one. The striking feature of this emergent Luttinger liquid is its quasi-particle charge (or Luttinger parameter $K$) which acquires a fractal dependence on the XXZ chain anisotropy parameter $Delta$.
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