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A one-dimensional quantum wire of Fermions is considered and ground state properties are calculated in the high density regime within the extended quasiparticle picture and Born approximation. Expanding the two-particle Green functions determines the selfenergy and the polarization as well as the response function on the same footing. While the on-shell selfenergies are strictly zero due to Pauli-blocking of elastic scattering, the off-shell behaviour shows a rich structure of a gap in the damping of excitation which is closed when the momentum approaches the Fermi one. The consistent spectral function is presented completing the first two energy-weighted sum rules. The excitation spectrum shows a splitting due to holons and antiholons as non-Fermi liquid behaviour. A renormalization procedure is proposed by subtracting an energy constant to render the Fock exchange energy finite. The effective mass derived from meanfield shows a dip as onset of Peierls instability. The correlation energy is calculated with the help of the extended quasiparticle picture which accounts for off-shell effects. The corresponding response function leads to the same correlation energy as the selfenergy in agreement with perturbation theory. The reduced density matrix or momentum distribution is calculated with the help of a Pad\'e regularization repairing deficiencies of the perturbation theory. A seemingly finite step at the Fermi energy indicating Fermi-liquid behaviour is repaired in this way., Comment: In memory of Paul Ziesche (1933-2022)

The selfenergy in Born approximation including exchange of interacting one-dimensional systems is expressed in terms of a single integral about the potential which allows a fast and precise calculation for any potential analytically. The imaginary part of the self energy as damping of single-particle excitations shows a rich structure of different areas limited by single-particle and collective excitation lines. The corresponding spectral function reveals a pseudogap, a splitting of excitation into holons and antiholons as well as bound states.

We use the variational quantum Monte Carlo (VMC) method to study the wire width ($b$) and electron density ($r_\text{s}$) dependences of the ground-state properties of quasi-one-dimensional paramagnetic electron fluids. The onset of a quasi-Wigner crystal phase is known to depend on electron density, and the crossover occurs in the low density regime. We study the effect of wire width on the crossover of the dominant peak in the static structure factor from $k=2k_\text{F}$ to $k=4k_\text{F}$. It is found that for a fixed electron density, in the charge structure factor the crossover from the dominant peak occurring at $2k_\text{F}$ to $4k_\text{F}$ occurs as the wire width decreases. Our study suggests that the crossover is due to interplay of both $r_\text{s}$ and $b

We study the ground-state properties of ferromagnetic quasi-one-dimensional quantum wires using the quantum Monte Carlo (QMC) method for various wire widths $b$ and density parameters $r_\text{s}$. The correlation energy, pair-correlation function, static structure factor, and momentum density are calculated at high density, $r_\text{s}=0.5$. It is observed that the peak in the static structure factor at $k=2k_\text{F}$ grows as the wire width decreases. We obtain the Tomonaga-Luttinger liquid parameter $K_\rho$ from the momentum density. It is found that $K_\rho$ increases by about $10$\% between wire widths $b=0.01$ and $b=0.5$. We also obtain ground-state properties of finite thickness wires theoretically using the first-order random phase approximation (RPA) with exchange and self-energy contributions, which is exact in the high-density limit. Analytical expressions for the static structure factor and correlation energy are derived for $b \ll r_\text{s}<1$. It is found that the correlation energy varies as $b^2$ for $b \ll r_\text{s}$ from its value for an infinitely thin wire. It is observed that the correlation energy depends significantly on the wire model used (harmonic versus cylindrical confinement). The first-order RPA expressions for the structure factor, pair-correlation function, and correlation energy are numerically evaluated for several values of $b$ and $r_\text{s} \leq 1$. These are compared with the QMC results in the range of applicability of the theory.

The correlation between electrons in different quantum wires is expected to affect the electronic properties of quantum electron-electron biwire systems. Here, we use the variational Monte Carlo method to study the ground-state properties of parallel, infinitely thin electron-electron biwires for several electron densities ($r_\text{s}$) and interwire separations ($d$). Specifically, the ground-state energy, the correlation energy, the interaction energy, the pair-correlation function (PCF), the static structure factor (SSF), and the momentum distribution (MD) function are calculated. We find that the interaction energy increases as $\ln(d)$ for $d\to 0$ and it decreases as $d^{-2}$ when $d\to \infty$. The PCF shows oscillatory behavior at all densities considered here. As two parallel wires approach each other, interwire correlations increase while intrawire correlations decrease as evidenced by the behavior of the PCF, SSF, and MD. The system evolves from two monowires of density parameter $r_\text{s}$ to a single monowire of density parameter $r_\text{s}/2$ as $d$ is reduced from infinity to zero. The MD reveals Tomonaga-Luttinger (TL) liquid behavior with a power-law nature near $k_\text{F}$ even in the presence of an extra interwire interaction between the electrons in biwire systems. It is observed that when $d$ is reduced the MD decreases for $kk_\text{F}$, similar to its behavior with increasing $r_\text{s}$. The TL liquid exponent is extracted by fitting the MD data near $k_\text{F}$, from which the TL liquid interaction parameter $K_{\rho}$ is calculated. The value of the TL parameter is found to be in agreement with that of a single wire for large separation between the two wires.

In this work we model the salient magnetic properties of the alloy lamellar ferrimagnetic nanostructures $[Co_{1-c}Gd_c]_{\ell^{\prime}}[Co]_\ell[Co_{1-c}Gd_c]_{\ell^{\prime}}$ between $Co$ semi-infinite leads. We have employed the Ising spin effective field theory (EFT) to compute the reliable magnetic exchange constants for the pure cobalt $J_{Co-Co}$ and gadolinium $J_{Gd-Gd}$ materials, in complete agreement with their experimental data. The sublattice magnetizations of the $Co$ and $Gd$ sites on the individual hcp atomic (0001) planes of the $Co-Gd$ layered nanostructures are computed for each plane and corresponding sites, by using the combined EFT and mean field theory (MFT) spin methods. The sublattice magnetizations, effective site magnetic moments, and ferrimagnetic compensation characteristics for the individual hcp atomic planes of the embedded nanostructures, are computed as a function of temperature, and for various stable eutectic concentrations in the range $c\leq$ 0.5. The theoretical results for the sublattice magnetizations and the local magnetic variables of these ultrathin ferrimagnetic lamellar nanostructured systems, between cobalt leads, are necessary for the study of their magnonic transport properties, and eventually their spintronic dynamic computations. The method developed in this work is general and can be applied to comparable magnetic systems nanostructured with other materials.

The dynamical response theory is used to obtain an analytical expression for the exchange energy of a quantum wire for arbitrary polarization and width. It reproduces the known form of exchange energy for 1D electron gas in the limit of infinitely thin cylindrical and harmonic wires. The structure factor for these wires are also obtained analytically in the high-density or small $r_s$ limit. This structure factor enables us to get the {\it exact} correlation energy for both the wires and demonstrates that there are at least two methods to get the ideal Coulomb limit in one dimension. The structure factor and the correlation energy are found to be independent of the way the one-dimensional Coulomb potential is regularized. The analytical expression for the pair correlation function is also presented for small distances and provides a justification for the small $r_s$ expansion as long as $r_s< \frac{3}{2} \left(\frac{\pi^2}{\pi^2+3} \right)=1.15$.

We calculate the ground-state energy, pair correlation function, static structure factor, and momentum density of the one-dimensional electron fluid at high density using variational quantum Monte Carlo simulation. For an infinitely thin cylindrical wire the predicted correlation energy is found to fit nicely with a quadratic function of coupling parameter $r_s$. The extracted exponent $\alpha$ of the momentum density for $k\sim k_F$ is used to determine the Tomonaga-Luttinger parameter $K_\rho$ as a function of $r_s$ in the high-density regime for the first time. We find that the simulated static structure factor and pair correlation function for infinitely thin wires agree with our recent high-density theory [K. Morawetz et al., Phys. Rev. B 97, 155147 (2018)].

It is shown that in $d$-dimensional systems, the vertex corrections beyond the random phase approximation (RPA) or GW approximation scales with the power $d-\beta-\alpha$ of the Fermi momentum if the relation between Fermi energy and Fermi momentum is $\epsilon_{\rm f}\sim p_{\rm f}^\beta$ and the interacting potential possesses a momentum-power-law of $\sim p^{-\alpha}$. The condition $d-\beta-\alpha<0$ specifies systems where RPA is exact in the high-density limit. The one-dimensional structure factor is found to be the interaction-free one in the high-density limit for contact interaction. A cancellation of RPA and vertex corrections render this result valid up to second-order in contact interaction. For finite-range potentials of cylindrical wires a large-scale cancellation appears and found to be independent of the width parameter of the wire. The proposed high-density expansion agrees with the Quantum Monte Carlo simulations.

The structure factor and correlation energy of a quantum wire of thickness $b\ll a_B$ are studied in random phase approximation and for the less investigated region $r_s<1$. Using the single-loop approximation, analytical expressions of the structure factor have been obtained. The exact expressions for the exchange energy are also derived for a cylindrical and harmonic wire. The correlation energy $\epsilon_c$ is found to be represented by $\epsilon_c (b,r_s)= \frac{\alpha(r_s)}{b} + \beta(r_s)\; ln(b) + \eta(r_s)$, for small $b$ and high densities. For a pragmatic width of the wire, the correlation energy is in agreement with the quantum Monte Carlo simulation data., Comment: Being slightly modified