Research

Correlation effects in one-dimensional metallic quantum wires under various confinements

Dynamical response theory is employed to investigate the effects of various transverse confinements on electron correlations in the ground state of a ferromagnetic one-dimensional quantum wire for different wire widths $b$ and density parameters $r_\text{s}$. In the regime of a thin quantum wire, electrons are treated as a one-dimensional gas under different confinement models via effective electron-electron interaction potentials. Using the first-order random phase approximation (FRPA) including self-energy and exchange contribution, which provides the ground state structure beyond the random phase approximation, we numerically compute the structure factor, pair-correlation function, correlation energy, and ground-state energy for various values of $b$ and $r_\text{s}$. Our results reveal that the correlation energy depends on the choice of confinement model. For the ultrathin wire $(b\rightarrow 0)$ in the high-density limit, we find that the correlation energy for transverse confinement models $V_1(q)$ (harmonic), $V_2(q)$ (cylindrical), and $V_5(q)$ (harmonic-delta) approaches $\epsilon_\text{c}(r_\text{s})= - \pi^2/360 \sim -0.02741$ a.u., which agrees with the exact results in this limit [P.-F.\ Loos, J.\ Chem.\

Phys.\ \textbf{138}, 064108 (2013), Vinod Ashokan \textit{et al.}, Phys.\ Rev.\ B \textbf{101}, 075130 (2020)]. This clearly illustrates that for at least these three confinement potentials, the one-dimensional Coulomb potential can be regularized at interparticle distance $x=0$ to yield the same correlation energy. In contrast, other confinement potentials, $V_3(q)$ (infinite square well), $V_4(q)$ (infinite square-infinite triangular well), and $V_6(q)$ (infinite square-delta well), do not approach the same high-density limit; instead, the correlation energy tends to $\epsilon_\text{c} \sim -0.03002$ a.u.\ for these potentials. The percentage difference in correlation energy between the confinement models $V_1(q)$, $V_2(q)$, $V_5(q)$ and $V_3(q)$, $V_4(q)$, $V_6(q)$ is within about $10\%$  in the high-density limit. The ground-state properties obtained from the FRPA are compared with the available quantum Monte Carlo results in the high-density regime. We observe that the peak height in the static structure factor at $k=2k_\text{F}$ depends significantly on the confinement model. These prominent peaks at $k=2k_\text{F}$ are fitted with a function based on our finite wire-width theory, guided by insights from bosonization, demonstrating good agreement with our FRPA theory. 

 Physical Review B 112, 245426 (2025)] 

Electronic quantum wires in extended quasiparticle picture

Expanding the two-particle Green’s functions determines the self-energy and the polarization as well as the response function on the same footing. 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 self-energy in agreement with perturbation theory, provided one works in the extended quasiparticle picture. 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. While the on-shell selfenergies are strictly zero due to Pauli-blocking of elastic scattering, the off-shell behavior 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 behavior. A renormalization procedure is proposed by subtracting an energy constant to render the Fock exchange energy finite. The effective mass derived from meanfield approximation shows a dip analogous to the onset of Peierls instability. The reduced density matrix or momentum distribution is calculated with the help of a Padé regularization repairing deficiencies of the perturbation theory. A seemingly finite step at the Fermi energy indicating Fermi-liquid behavior is repaired in this way. 

PHYSICAL REVIEW B 109, 205116 (2024) 

Static structure factor crossover 2kF →4kF in one-dimensional paramagnetic electron gases

We use the variational quantum Monte Carlo (VMC) method to study the wire-width (b) and electron-density (rs) 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 = 2kF to k = 4kF. It is found that, for a fixed electron density, in the charge structure factor the crossover from the dominant peak occurring at 2kF to 4kF occurs as the wire width decreases. Our study suggests that the crossover is due to the interplay of both rs and b < rs. The finite wire-width correlation effect is reflected in the peak height of the charge and spin structure factors. We fit the dominant peaks of the charge and spin structure factors assuming fit functions based on our finite wire-width theory and clues from bosonization, resulting in a good fit of the VMC data. The pronounced peaks in the charge and spin structure factors at 4kF and 2kF, respectively, indicate the complete decoupling of the charge and spin degrees of freedom. Furthermore, the wire-width dependence of the electron correlation energy and the Tomonaga-Luttinger parameter Kρ is found to be significant.

PHYSICAL REVIEW B 107, 115414 (2023) 

Electron correlation and confinement effects in quasi-one-dimensional quantum wires at high density

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 rs. The correlationenergy, pair-correlation function, static structure factor, and momentum density are calculated at high density. It is observed that the peak in the static structure factor at k = 2kF grows as the wire width decreases. We obtain the Tomonaga-Luttinger liquid parameter Kρ from the momentum density. It is found that Kρ 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  rs < 1. It is found that the correlation energy varies as b2 for b  rs 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 rs  1. These are compared with the QMC results in the range of applicability of the theory.

PHYSICAL REVIEW B 105, 115140 (2022) 

Ground-state properties of electron-electron biwire systems

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 (rs) 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 → 0 and it decreases as d−2 when d →∞. 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 rs to a single monowire of density parameter rs/2 as d is reduced from infinity to zero. The MD reveals Tomonaga-Luttinger (TL) liquid behavior with a power-law nature near kF 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 k < kF and increases for k > kF, similar to its behavior with increasing rs. The TL liquid exponent is extracted by fitting the MD data near kF, from which the TL liquid interaction parameter Kρ 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.

PHYSICAL REVIEW B 104, 035149 (2021) 

Exact ground-state properties of the one-dimensional electron gas at high density

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 a one-dimensional (1D) electron gas in the limit of infinitely thin cylindrical and harmonic wires. The structure factor for these wires is also obtained analytically in the high-density or small rs limit. This structure factor allows to get the 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 analytical expression for the pair correlation function is also presented for small distances and provides a justification for the small rs expansion as long as rs < 3/2 ( π2/(π2+3) ) = 1.15.

PHYSICAL REVIEW B 101, 075130 (2020) 

Conditions where random phase approximation becomes exact in the high-density limit

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 − β − α of the Fermi momentum if the relation between Fermi energy and Fermi momentum is f ∼ pβf and the interacting potential possesses a momentum power law of ∼p−α. The condition d − β −α < 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 is found to be independent of the width parameter of the wire. The proposed high-density expansion agrees with the quantum Monte Carlo simulations.

PHYSICAL REVIEW B 97, 155147 (2018) 

One-dimensional electron fluid at high density

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 rs . The extracted exponent α of the momentum density for k ∼ kF is used to determine the Tomonaga-Luttinger parameter Kρ as a function of rs in the high-density regime. 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)].

PHYSICAL REVIEW B 98, 125139 (2018)