We study the effect of the magnetic field in a one-dimensional attractive interacting system with an extended Fermi surface. By the application of Abelian bosonization, we are able to show that elementary excitations in different regions of momentum space behave differently. There is evidence of a mixed phase. The system possess a paramagnetic gapless excitation in the presence of an infinitesimal magnetic field, though the system has a spin gap. We calculate the susceptibilities at different regions of momentum space. We also discuss the effect of finite temperature, and the interesting behavior of the spin component of the specific heat.
We study the effect of the magnetic field in a one-dimensional attractive interacting system with an extended Fermi surface. By the application of Abelian bosonization, we are able to show that elementary excitations in different regions of momentum space behave differently. There is evidence of a mixed phase. The system possess a paramagnetic gapless excitation in the presence of an infinitesimal magnetic field, though the system has a spin gap. We calculate the susceptibilities at different regions of momentum space. We also discuss the effect of finite temperature, and the interesting behavior of the spin component of the specific heat.
We study the effect of the long-range random potential on optical conductivity in a one-dimensional interacting electron system with extended-Fermi surface. We apply Abelian bosonization to show that in one part of the momentum space the system has a metallic behavior with a gap in the spin sector, while in the other region of momentum space it behaves like a gapless Luttinger liquid (paramagnetic metallic phase). Consequently we consider the scattering of electrons with the long-range random potential (forward scattering disorder) in that region of momentum space, where the system is in gapless Luttinger liquid phase. The real part of the optical conductivity has no Drude peak for small frequency $(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\omega}}0),$ but the Drude weight is nonzero and it has the doping dependence, while the imaginary part of the optical conductivity shows the usual $1/\ensuremath{\omega}$ behavior, like in the clean system, and it has no doping dependence. We explain the doping dependence with the help of one-dimensional exact density of states.
A system of a finite number of harmonically trapped fermions in one dimension, in the presence of a static magnetic field, is studied within the framework of the static fluctuation approximation, for different repulsive and attractive potential strengths. Specifically, the thermodynamic properties of the system (the chemical potential, total energy, heat capacity, and entropy), as well as its magnetic properties (the magnetization and susceptibility), are calculated. It is observed that the system remains in an ordered phase for a small number of particles N, even at high temperatures T. Disorder sets in for large N, even at low T. The effect of the potential strength on the heat capacity is particularly tangible in the region bordering the quantum and classical regimes. The effect of the temperature (representing disorder) is directly opposite to that of the magnetic field (representing order), as expected on basic physical grounds. These features are consistent with experimental results.
We investigate magnetic properties and statistical effects in one-dimensional (1D) strongly repulsive two-component fermions and in a 1D mixture of strongly repulsive polarized fermions and bosons. Universality in the characteristics of phase transitions, magnetization, and susceptibility in the presence of an external magnetic field H are analyzed from the exact thermodynamic Bethe ansatz solution. We show explicitly that polarized fermions with a repulsive interaction have antiferromagnetic behavior at zero temperature. A universality class of linear field-dependent magnetization persists for weak and finite strong interaction. The system is fully polarized when the external field exceeds the critical value ${H}_{c}^{F}\ensuremath{\approx}\frac{8}{\ensuremath{\gamma}}{E}_{F}$, where EF is the Fermi energy and $\ensuremath{\gamma}$ is the dimensionless interaction strength. In contrast, the mixture of polarized fermions and bosons in an external field exhibits square-root field-dependent magnetization in the vicinities of H=0 and the critical value $H={H}_{c}^{M}\ensuremath{\approx}\frac{16}{\ensuremath{\gamma}}{E}_{F}$. We find that a pure boson phase occurs in the absence of the external field, fully polarized fermions and bosons coexist for 0<H<HcM, and a fully polarized fermion phase occurs for $H\ensuremath{\geqslant}{H}_{c}^{M}$. This phase diagram for the Bose-Fermi mixture is reminiscent of weakly attractive fermions with population imbalance, where the interacting fermions with opposite spins form singlet pairs.
A model of one-dimensional fermions characterized by a large momentum-transfer interaction g1 and a small momentum-transfer interaction g2 is considered. Results obtained previously by the renormalization-group method are extended by studying the triplet Cooper-pair response function and uniform charge and spin response functions. The sign of g1 dominates the behavior of the system. For g1>0, ${g}_{1}\ensuremath{-}2{g}_{2}>0$ the triplet Cooper response diverges as $T\ensuremath{\rightarrow}0$ and is seen to dominate the singlet Cooper response which is also divergent. The uniform static spin susceptibility is nondivergent for g1>0 and diverges to zero for g1<0. The specific heat is found to be linear in temperature in all regions. These results, obtained by the second-order renormalization group, yield the correct qualitative results in regions where exact solutions are available.
We address the problem of a magnetic impurity in a two-dimensional U(1) spin liquid where the spinons have gapless excitations near the Fermi surface and are coupled to an emergent gapless gauge field. Using a large N expansion, we analyze the strong coupling behavior and obtain the Kondo temperature which was found to be the same as for a Fermi liquid. In this approximation, we also study the specific heat and the magnetic susceptibility of the impurity. These quantities present no deviations from the Fermi liquid ones, consistent with the notion that the magnetic impurity is only sensitive to the local density of fermionic states.
We present a bosonized effective field theory for a 2d Fermi surface in a weak magnetic field using the coadjoint orbit approach, which was recently developed as a nonlinear bosonization method in phase space for Fermi liquids and non-Fermi liquids. We show that by parametrizing the phase space with the guiding center and the mechanical momentum, and by using techniques in noncommutative field theory, the physics of Landau levels and Landau level degeneracy (NΦ) naturally arises. For a parabolic dispersion, the resulting theory describes NΦ flavors of free chiral bosons propagating in \emph{momentum space}. In addition, the action contains a linear term in the bosonic field, which upon mode expansion becomes a topological θ-term. By properly quantizing this theory, we reproduce the well-known thermal and magnetic responses of a Fermi surface, including linear-in-T specific heat, Landau diamagnetism, and the de Haas-van Alphen effect. {In particular, the de Haas-van Alphen effect is shown to be a direct consequence of the topological θ-term.} Our theory paves the way toward understanding correlated gapless fermionic systems in a magnetic field using the powerful approach of bosonization.