A system of one-dimensional electrons interacting via a short-range potential described by Hubbard model is considered in the regime of strong coupling using the Bethe ansatz approach. We study its momentum distribution function at zero temperature and find one additional singularity at the $3{k}_{\mathrm{F}}$ point. We identify that the second singularity is of the same Luttinger liquid type as the low-energy one at ${k}_{\mathrm{F}}$ . By calculating the spectral function simultaneously, we show that the second Luttinger liquid at $3{k}_{\mathrm{F}}$ is formed by charge modes only, unlike the known one around ${k}_{\mathrm{F}}$ consisting of both spin and charge modes. This result reveals the ability of the spin-charge separation effect to split the Fermi point of free electrons into two, demonstrating its robustness beyond the low-energy limit of Luttinger liquid where it was originally found.A system of one-dimensional electrons interacting via a short-range potential described by Hubbard model is considered in the regime of strong coupling using the Bethe ansatz approach. We study its momentum distribution function at zero temperature and find one additional singularity at the $3{k}_{\mathrm{F}}$ point. We identify that the second singularity is of the same Luttinger liquid type as the low-energy one at ${k}_{\mathrm{F}}$. By calculating the spectral function simultaneously, we show that the second Luttinger liquid at $3{k}_{\mathrm{F}}$ is formed by charge modes only, unlike the known one around ${k}_{\mathrm{F}}$ consisting of both spin and charge modes. This result reveals the ability of the spin-charge separation effect to split the Fermi point of free electrons into two, demonstrating its robustness beyond the low-energy limit of Luttinger liquid where it was originally found.

arXiv:2203.00982Physical review. B./Physical review. BMar 22, 20227 citations

Bosonization of strongly interacting one-dimensional electrons

К. А. Матвеев, Akira Furusaki, L. I. Glazman

Strong repulsive interactions in a one-dimensional electron system suppress the exchange coupling $J$ of electron spins to a value much smaller than the Fermi energy ${E}_{F}$ . The conventional theoretical description of such systems based on the bosonization approach and the concept of Tomonaga-Luttinger liquid is applicable only at energies below $J$ . In this paper, we develop a theoretical approach valid at all energies below the Fermi energy, including a broad range of energies between $J$ and ${E}_{F}$ . The method involves bosonization of the charge degrees of freedom, while the spin excitations are treated exactly. We use this technique to calculate the spectral functions of strongly interacting electron systems at energies in the range $J⪡\ensuremath{\epsilon}⪡{E}_{F}$. We show that in addition to the expected features at the wave vector $k$ near the Fermi point ${k}_{F}$ , the spectral function has a strong peak centered at $k=0$ . Our theory also provides analytical description of the spectral function singularities near $3{k}_{F}$ (the ``shadow band'' features).Strong repulsive interactions in a one-dimensional electron system suppress the exchange coupling $J$ of electron spins to a value much smaller than the Fermi energy ${E}_{F}$. The conventional theoretical description of such systems based on the bosonization approach and the concept of Tomonaga-Luttinger liquid is applicable only at energies below $J$. In this paper, we develop a theoretical approach valid at all energies below the Fermi energy, including a broad range of energies between $J$ and ${E}_{F}$. The method involves bosonization of the charge degrees of freedom, while the spin excitations are treated exactly. We use this technique to calculate the spectral functions of strongly interacting electron systems at energies in the range $J⪡\ensuremath{\epsilon}⪡{E}_{F}$. We show that in addition to the expected features at the wave vector $k$ near the Fermi point ${k}_{F}$, the spectral function has a strong peak centered at $k=0$. Our theory also provides analytical description of the spectral function singularities near $3{k}_{F}$ (the ``shadow band'' features).

arXiv:0708.0212Physical Review BOct 31, 200732 citations

Effect of Coulomb interaction on the spectral functions of a 1D electron liquid

Yasha Gindikin, Vladimir A. Sablikov

Physics of low-Dimensional structuresJan 1, 20020 citations

Dynamical functions of a 1D correlated quantum liquid

J. M. P. Carmelo, D. Bozi, Karlo Penc

We extend to initial ground states with zero spin density m = 0 the expressions provided by the pseudofermion dynamical theory (PDT) for the finite-energy one- and two-electron spectral-weight distributions of a one-dimensional (1D) correlated metal with on-site particle-particle repulsion. The spectral-function expressions derived in this paper were used in recent successful and detailed theoretical studies of the finite-energy singular features in photoemission of the organic compound tetrathiafulvalene-tetracyanoquinodimethane (TTF-TCNQ) metallic phase. Our studies take into account spectral contributions from types of microscopic processes that do not occur for finite values of the spin density. Expressions for the spectral functions in the vicinity of the singular border lines which also appear in the TTF- TCNQ spectral-weight distribution are derived. In addition, the PDT expressions are generalized for electronic densities in the vicinity of half filling. Further details on the processes involved in the applications to TTF-TCNQ are reported. Our results are useful for the further understanding of the unusual spectral properties observed in low-dimensional organic metals and also provide expressions for the one- and two-atom spectral functions of a correlated quantum system of ultracold fermionic atoms in a 1D optical lattice with on-site two-atom repulsion.We extend to initial ground states with zero spin density m = 0 the expressions provided by the pseudofermion dynamical theory (PDT) for the finite-energy one- and two-electron spectral-weight distributions of a one-dimensional (1D) correlated metal with on-site particle-particle repulsion. The spectral-function expressions derived in this paper were used in recent successful and detailed theoretical studies of the finite-energy singular features in photoemission of the organic compound tetrathiafulvalene-tetracyanoquinodimethane (TTF-TCNQ) metallic phase. Our studies take into account spectral contributions from types of microscopic processes that do not occur for finite values of the spin density. Expressions for the spectral functions in the vicinity of the singular border lines which also appear in the TTF- TCNQ spectral-weight distribution are derived. In addition, the PDT expressions are generalized for electronic densities in the vicinity of half filling. Further details on the processes involved in the applications to TTF-TCNQ are reported. Our results are useful for the further understanding of the unusual spectral properties observed in low-dimensional organic metals and also provide expressions for the one- and two-atom spectral functions of a correlated quantum system of ultracold fermionic atoms in a 1D optical lattice with on-site two-atom repulsion.

arXiv:0808.3001Journal of Physics Condensed MatterSep 5, 200827 citations

3{k}_{\mathrm{F}}

point. We identify that the second singularity is of the same Luttinger liquid type as the low-energy one at

{k}_{\mathrm{F}}

. By calculating the spectral function simultaneously, we show that the second Luttinger liquid at

3{k}_{\mathrm{F}}

is formed by charge modes only, unlike the known one around

{k}_{\mathrm{F}}

consisting of both spin and charge modes. This result reveals the ability of the spin-charge separation effect to split the Fermi point of free electrons into two, demonstrating its robustness beyond the low-energy limit of Luttinger liquid where it was originally found.

Strong repulsive interactions in a one-dimensional electron system suppress the exchange coupling

J

of electron spins to a value much smaller than the Fermi energy

{E}_{F}

. The conventional theoretical description of such systems based on the bosonization approach and the concept of Tomonaga-Luttinger liquid is applicable only at energies below

J

. In this paper, we develop a theoretical approach valid at all energies below the Fermi energy, including a broad range of energies between

J

and

{E}_{F}

. The method involves bosonization of the charge degrees of freedom, while the spin excitations are treated exactly. We use this technique to calculate the spectral functions of strongly interacting electron systems at energies in the range $J⪡\ensuremath{\epsilon}⪡{E}_{F}$. We show that in addition to the expected features at the wave vector

k

near the Fermi point

{k}_{F}

, the spectral function has a strong peak centered at

k=0

. Our theory also provides analytical description of the spectral function singularities near

3{k}_{F}

(the ``shadow band'' features).