Journal of Physics A Mathematical and General

Conformal field theory in the Tomonaga–Luttinger model with the 1/rβ long-range interaction

Hokuto Inoue, K. Nomura

Published May 16, 2006• 0 citations

Abstract

The authors have discovered some errors in the references of their paper. For corrections, please refer to the PDF of this corrigendum.

DOI: 10.1088/0305-4470/39/22/c01

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Journal of Physics A Mathematical and General

Conformal field theory in the Tomonaga–Luttinger model with the 1/rβ long-range interaction

Hokuto Inoue, K. Nomura

Published May 16, 2006• 0 citations

Publisher

Abstract

The authors have discovered some errors in the references of their paper. For corrections, please refer to the PDF of this corrigendum.

DOI: 10.1088/0305-4470/39/22/c01

Related papers

Conformal field theory in the Tomonaga–Luttinger model with the 1/rβlong-range interaction

Hitoshi Inoue, K. Nomura

We attempt to construct U (1) conformal field theory (CFT) in the Tomonaga–Luttinger (TL) liquid with the 1/ r β long-range interaction (LRI). Treating the long-range forward scattering as a perturbation and applying CFT to it, we derive finite size scalings which depend on the power of the LRI. The obtained finite size scalings give nontrivial behaviours when β is odd and is close to 2. We find consistency between the analytical arguments and numerical results in the finite size scaling of energy.We attempt to construct U (1) conformal field theory (CFT) in the Tomonaga–Luttinger (TL) liquid with the 1/ r β long-range interaction (LRI). Treating the long-range forward scattering as a perturbation and applying CFT to it, we derive finite size scalings which depend on the power of the LRI. The obtained finite size scalings give nontrivial behaviours when β is odd and is close to 2. We find consistency between the analytical arguments and numerical results in the finite size scaling of energy.

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We discuss effects of $1/r^β$ type long-range (LR) interactions in a tight-binding model by utilizing the bosonization technique, renormalization group and conformal field theory (CFT). We obtain the low energy action known for Kibble's model which generates the mass gap in 3 dimension when $β=1$ , the Coulomb force case. In one dimension, the dispersion relations predict that the system remains gapless even for $β=1$ and the existences of Tomonaga-Luttinger liquid (TLL) when $β> 1$ . When $β=1$ , the LR interactions break TLL in the long wavelength limits, even if the strength is very small. We make the more precise arguments from the stand point of the renormalization group and CFT. Finally we derive the accurate finite size scaling of energies and thermodynamics. Moreover we proceed to numerical calculations, considering the LR umklapp process terms. We conclude that the TLL phase become wider in the strength space of interactions as the power $β$ approaches to 1.We discuss effects of $1/r^β$ type long-range (LR) interactions in a tight-binding model by utilizing the bosonization technique, renormalization group and conformal field theory (CFT). We obtain the low energy action known for Kibble's model which generates the mass gap in 3 dimension when $β=1$, the Coulomb force case. In one dimension, the dispersion relations predict that the system remains gapless even for $β=1$ and the existences of Tomonaga-Luttinger liquid (TLL) when $β> 1$. When $β=1$, the LR interactions break TLL in the long wavelength limits, even if the strength is very small. We make the more precise arguments from the stand point of the renormalization group and CFT. Finally we derive the accurate finite size scaling of energies and thermodynamics. Moreover we proceed to numerical calculations, considering the LR umklapp process terms. We conclude that the TLL phase become wider in the strength space of interactions as the power $β$ approaches to 1.

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Kazuki Yamamoto, Norio Kawakami

Universal scaling relations for dissipative Tomonaga-Luttinger (TL) liquids with $\mathrm{SU}(N$ ) spin symmetry are obtained for both fermions and bosons, by using asymptotic Bethe-ansatz solutions and conformal field theory (CFT) in one-dimensional non-Hermitian quantum many-body systems with $\mathrm{SU}(N$ ) symmetry. We uncover that the spectrum of dissipative TL liquids with $\mathrm{SU}(N$ ) spin symmetry is described by the sum of one charge mode characterized by a complex generalization of $c=1$ U(1) Gaussian CFT, and $N\ensuremath{-}1$ spin modes characterized by level- $1\phantom{\rule{4pt}{0ex}}\mathrm{SU}(N$ ) Kac-Moody algebra with the conformal anomaly $c=N\ensuremath{-}1$, and thereby dissipation only affects the charge mode as a result of spin-charge separation in one-dimensional non-Hermitian quantum systems. The derivation is based on a complex generalization of Haldane's ideal-gas description, which is implemented by the $\mathrm{SU}(N$ ) Calogero-Sutherland model with inverse-square long-range interactions.Universal scaling relations for dissipative Tomonaga-Luttinger (TL) liquids with $\mathrm{SU}(N$) spin symmetry are obtained for both fermions and bosons, by using asymptotic Bethe-ansatz solutions and conformal field theory (CFT) in one-dimensional non-Hermitian quantum many-body systems with $\mathrm{SU}(N$) symmetry. We uncover that the spectrum of dissipative TL liquids with $\mathrm{SU}(N$) spin symmetry is described by the sum of one charge mode characterized by a complex generalization of $c=1$ U(1) Gaussian CFT, and $N\ensuremath{-}1$ spin modes characterized by level-$1\phantom{\rule{4pt}{0ex}}\mathrm{SU}(N$) Kac-Moody algebra with the conformal anomaly $c=N\ensuremath{-}1$, and thereby dissipation only affects the charge mode as a result of spin-charge separation in one-dimensional non-Hermitian quantum systems. The derivation is based on a complex generalization of Haldane's ideal-gas description, which is implemented by the $\mathrm{SU}(N$) Calogero-Sutherland model with inverse-square long-range interactions.

arXiv:2207.04395Physical review. B./Physical review. BJan 9, 202330 citations

Correlation functions for a one-dimensional Fermi system with long-range interaction (Tomonaga model)

I. E. Dzyaloshinskiǐ, A. I. Larkin

Journal of Experimental and Theoretical PhysicsJan 1, 197428 citations

Scaling theory in Tomonaga-Luttinger liquid with

1/r^β

type long-range interactions

We discuss effects of

1/r^β

type long-range (LR) interactions in a tight-binding model by utilizing the bosonization technique, renormalization group and conformal field theory (CFT). We obtain the low energy action known for Kibble's model which generates the mass gap in 3 dimension when

β=1

, the Coulomb force case. In one dimension, the dispersion relations predict that the system remains gapless even for

β=1

and the existences of Tomonaga-Luttinger liquid (TLL) when

β> 1

. When

β=1

, the LR interactions break TLL in the long wavelength limits, even if the strength is very small. We make the more precise arguments from the stand point of the renormalization group and CFT. Finally we derive the accurate finite size scaling of energies and thermodynamics. Moreover we proceed to numerical calculations, considering the LR umklapp process terms. We conclude that the TLL phase become wider in the strength space of interactions as the power

β

approaches to 1.

Universal scaling relations for dissipative Tomonaga-Luttinger (TL) liquids with

\mathrm{SU}(N

) spin symmetry are obtained for both fermions and bosons, by using asymptotic Bethe-ansatz solutions and conformal field theory (CFT) in one-dimensional non-Hermitian quantum many-body systems with

\mathrm{SU}(N

) symmetry. We uncover that the spectrum of dissipative TL liquids with

\mathrm{SU}(N

) spin symmetry is described by the sum of one charge mode characterized by a complex generalization of

c=1

U(1) Gaussian CFT, and $N\ensuremath{-}1$ spin modes characterized by level-

1\phantom{\rule{4pt}{0ex}}\mathrm{SU}(N

) Kac-Moody algebra with the conformal anomaly $c=N\ensuremath{-}1$, and thereby dissipation only affects the charge mode as a result of spin-charge separation in one-dimensional non-Hermitian quantum systems. The derivation is based on a complex generalization of Haldane's ideal-gas description, which is implemented by the

\mathrm{SU}(N

) Calogero-Sutherland model with inverse-square long-range interactions.