We study a system of one-dimensional (iso)spin-1/2 bosons in the regime of strong repulsive interactions. We argue that the low-energy spectrum of the system consists of acoustic density waves and the spin excitations described by an effective ferromagnetic spin chain with a small exchange constant J. We use this description to compute the dynamic spin structure factor and the spectral functions of the system.

arXiv:0808.0681Physical Review LettersOct 23, 200848 citations

Physica B+C

Excitation spectrum and structure factor for interacting bosons

Kapil M. Khanna, S. Chauba Singh, O. P. Sinha

Published Aug 1, 1982• 0 citations

Publisher

DOI: 10.1016/0378-4363(82)90031-6

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Excitation spectrum for interacting bosons

Kapil M. Khanna, B.K. Das

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Bosonization approach to charge and spin dynamics of one-dimensional spin- 12 fermions with band curvature in a clean quantum wire

S. Teber

We consider one-dimensional spin- $\frac{1}{2}$ fermions in a clean quantum wire, with forward scattering interactions and a nonlinear single-particle spectrum ${\ensuremath{\xi}}_{k}=v\ensuremath{\mid}k\ensuremath{\mid}+{k}^{2}∕2m$, where $v$ is the Fermi velocity and $1∕m$ is the band curvature. We calculate the dynamical structure factor (DSF) of the model at small wave vector $q$ with the help of the bosonization technique. For spinless fermions, we show that, starting from the single-parametric spectrum $\ensuremath{\omega}=u\ensuremath{\mid}q\ensuremath{\mid}$, bosonization emulates the two-parametric excitation spectrum $\ensuremath{\omega}=u\ensuremath{\mid}q\ensuremath{\mid}\ifmmode\pm\else\textpm\fi{}{q}^{2}∕2{m}^{*}$, where ${m}^{*}$ decreases with increasing repulsive interactions. Moreover, away from the excitation cone, i.e., $\ensuremath{\omega}⪢u\ensuremath{\mid}q\ensuremath{\mid}$, bosonization yields the two-pair excitation continuum of the DSF. For spinful fermions, we show that the spin-charge coupling (SCC) due to band curvature affects the charge and spin DSFs in an asymmetric way. For the charge DSF, SCC manifests as a two-peak structure: a charge peak at $\ensuremath{\omega}={u}_{\ensuremath{\rho}}\ensuremath{\mid}q\ensuremath{\mid}$ but also a spin peak at $\ensuremath{\omega}={u}_{\ensuremath{\sigma}}\ensuremath{\mid}q\ensuremath{\mid}$, as charge fluctuations may decay via chargeless spin-singlet excitations. For the magnetic DSF, SCC manifests as a continuous transfer of magnetic spectral weight to frequencies $\ensuremath{\omega}>{u}_{\ensuremath{\sigma}}\ensuremath{\mid}q\ensuremath{\mid}$, as spin fluctuations decay via pairs of chargeless spin and spinless charge-neutral excitations.We consider one-dimensional spin-$\frac{1}{2}$ fermions in a clean quantum wire, with forward scattering interactions and a nonlinear single-particle spectrum ${\ensuremath{\xi}}_{k}=v\ensuremath{\mid}k\ensuremath{\mid}+{k}^{2}∕2m$, where $v$ is the Fermi velocity and $1∕m$ is the band curvature. We calculate the dynamical structure factor (DSF) of the model at small wave vector $q$ with the help of the bosonization technique. For spinless fermions, we show that, starting from the single-parametric spectrum $\ensuremath{\omega}=u\ensuremath{\mid}q\ensuremath{\mid}$, bosonization emulates the two-parametric excitation spectrum $\ensuremath{\omega}=u\ensuremath{\mid}q\ensuremath{\mid}\ifmmode\pm\else\textpm\fi{}{q}^{2}∕2{m}^{*}$, where ${m}^{*}$ decreases with increasing repulsive interactions. Moreover, away from the excitation cone, i.e., $\ensuremath{\omega}⪢u\ensuremath{\mid}q\ensuremath{\mid}$, bosonization yields the two-pair excitation continuum of the DSF. For spinful fermions, we show that the spin-charge coupling (SCC) due to band curvature affects the charge and spin DSFs in an asymmetric way. For the charge DSF, SCC manifests as a two-peak structure: a charge peak at $\ensuremath{\omega}={u}_{\ensuremath{\rho}}\ensuremath{\mid}q\ensuremath{\mid}$ but also a spin peak at $\ensuremath{\omega}={u}_{\ensuremath{\sigma}}\ensuremath{\mid}q\ensuremath{\mid}$, as charge fluctuations may decay via chargeless spin-singlet excitations. For the magnetic DSF, SCC manifests as a continuous transfer of magnetic spectral weight to frequencies $\ensuremath{\omega}>{u}_{\ensuremath{\sigma}}\ensuremath{\mid}q\ensuremath{\mid}$, as spin fluctuations decay via pairs of chargeless spin and spinless charge-neutral excitations.

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Experimental signatures of bosonic pairing in a two-component Bose gas

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Two-component bosonic droplets are commonly described within Bogoliubov theory, where beyond-mean-field quantum fluctuations stabilize the system against mean-field collapse. In the interaction regime where droplets form, however, the Bogoliubov excitation spectrum contains an imaginary branch associated with the underlying instability, which is typically omitted when evaluating the beyond-mean-field energy. Bosonic pairing theory provides an alternative description with a fully real excitation spectrum. In this work, we reformulate bosonic pairing theory within an operator formalism, making its underlying approximations transparent, and compare its predictions with those of Bogoliubov theory for a homonuclear binary Bose mixture across the crossover from a weakly interacting gas to the droplet regime. Working at fixed particle density, we determine the variational parameters of bosonic pairing theory self-consistently and focus on the regime in which both theories possess real excitation spectra, allowing a direct comparison. We find that bosonic pairing theory yields a lower grand potential than Bogoliubov theory and predicts qualitatively distinct correlation signatures, including enhanced long-wavelength interspecies momentum-space correlations and a finite density static structure factor at experimentally accessible low momenta. These differences persist over a broad range of interaction strengths and suggest that correlation and structure-factor measurements can provide direct experimental tests of bosonic pairing across the gas-to-droplet crossover.Two-component bosonic droplets are commonly described within Bogoliubov theory, where beyond-mean-field quantum fluctuations stabilize the system against mean-field collapse. In the interaction regime where droplets form, however, the Bogoliubov excitation spectrum contains an imaginary branch associated with the underlying instability, which is typically omitted when evaluating the beyond-mean-field energy. Bosonic pairing theory provides an alternative description with a fully real excitation spectrum. In this work, we reformulate bosonic pairing theory within an operator formalism, making its underlying approximations transparent, and compare its predictions with those of Bogoliubov theory for a homonuclear binary Bose mixture across the crossover from a weakly interacting gas to the droplet regime. Working at fixed particle density, we determine the variational parameters of bosonic pairing theory self-consistently and focus on the regime in which both theories possess real excitation spectra, allowing a direct comparison. We find that bosonic pairing theory yields a lower grand potential than Bogoliubov theory and predicts qualitatively distinct correlation signatures, including enhanced long-wavelength interspecies momentum-space correlations and a finite density static structure factor at experimentally accessible low momenta. These differences persist over a broad range of interaction strengths and suggest that correlation and structure-factor measurements can provide direct experimental tests of bosonic pairing across the gas-to-droplet crossover.

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The Excitation Spectrum for Weakly Interacting Bosons

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Excitation spectrum for interacting bosons high-density calculations

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Spectral Functions of Strongly Interacting Isospin- 12 Bosons in One Dimension

К. А. Матвеев, Akira Furusaki

arXiv:0808.0681Physical Review LettersOct 23, 200848 citations

We consider one-dimensional spin-

\frac{1}{2}

fermions in a clean quantum wire, with forward scattering interactions and a nonlinear single-particle spectrum ${\ensuremath{\xi}}_{k}=v\ensuremath{\mid}k\ensuremath{\mid}+{k}^{2}∕2m$, where

v

is the Fermi velocity and

1∕m

is the band curvature. We calculate the dynamical structure factor (DSF) of the model at small wave vector

q

with the help of the bosonization technique. For spinless fermions, we show that, starting from the single-parametric spectrum $\ensuremath{\omega}=u\ensuremath{\mid}q\ensuremath{\mid}$, bosonization emulates the two-parametric excitation spectrum $\ensuremath{\omega}=u\ensuremath{\mid}q\ensuremath{\mid}\ifmmode\pm\else\textpm\fi{}{q}^{2}∕2{m}^{*}$, where

{m}^{*}

decreases with increasing repulsive interactions. Moreover, away from the excitation cone, i.e., $\ensuremath{\omega}⪢u\ensuremath{\mid}q\ensuremath{\mid}$, bosonization yields the two-pair excitation continuum of the DSF. For spinful fermions, we show that the spin-charge coupling (SCC) due to band curvature affects the charge and spin DSFs in an asymmetric way. For the charge DSF, SCC manifests as a two-peak structure: a charge peak at $\ensuremath{\omega}={u}_{\ensuremath{\rho}}\ensuremath{\mid}q\ensuremath{\mid}$ but also a spin peak at $\ensuremath{\omega}={u}_{\ensuremath{\sigma}}\ensuremath{\mid}q\ensuremath{\mid}$, as charge fluctuations may decay via chargeless spin-singlet excitations. For the magnetic DSF, SCC manifests as a continuous transfer of magnetic spectral weight to frequencies $\ensuremath{\omega}>{u}_{\ensuremath{\sigma}}\ensuremath{\mid}q\ensuremath{\mid}$, as spin fluctuations decay via pairs of chargeless spin and spinless charge-neutral excitations.