Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0705.2015 · Physical Review Letters

Dynamics of Excitations in a One-Dimensional Bose Liquid

Maxim Khodas, Michael Pustilnik, Alex Kamenev, L. I. Glazman

Published Sep 14, 2007• 70 citations
arXivHTMLPDF

Abstract

We show that the dynamic structure factor of a one-dimensional Bose liquid has a power-law singularity defining the main mode of collective excitations. Using the Lieb-Liniger model, we evaluate the corresponding exponent as a function of the wave vector and the interaction strength.
DOI
10.1103/physrevlett.99.110405

Related papers

Exact Exponents of Edge Singularities in Dynamic Correlation Functions of 1D Bose Gas

Adilet Imambekov, L. I. Glazman

The spectral function and dynamic structure factor of bosons interacting by contact repulsion and confined to one dimension exhibit power-law singularities along the dispersion curves of the collective modes. We find the corresponding exponents exactly, by relating them to the known Bethe ansatz solution of the Lieb-Liniger model. Remarkably, the Luttinger liquid theory predictions for the exponents fail even at low energies, once the immediate vicinities of the edges are considered.

arXiv:0711.2697•Physical Review Letters•May 21, 2008•115 citations

Approximate expression for the dynamic structure factor in the Lieb-Liniger model

Alexander Yu. Cherny, Joachim Brand

Recently, Imambekov and Glazman [Phys. Rev. Lett. 100, 206805 (2008)] showed that the dynamic structure factor (DSF) of the 1D Bose gas demonstrates power-law behaviour along the limiting dispersion curve of the collective modes and calculated the corresponding exponents exactly. Combining these recent results with a previously obtained strong-coupling expansion we present an interpolation formula for the DSF of the 1D Bose gas. The obtained expression is further consistent with exact low energy exponents from Luttinger liquid theory and shows nice agreement with recent numerical results.

arXiv:0906.3446•Journal of Physics Conference Series•Oct 1, 2008•7 citations

Dynamical structure factor of one-dimensional Bose gases: Experimental signatures of beyond-Luttinger-liquid physics

Nicole Fabbri, Miłosz Panfil, David Clément +4 more

Interactions are known to have dramatic effects on bosonic gases in one dimension (1D). Not only does the ground state transform from a condensate like state to an effective Fermi sea, but new fundamental excitations, which do not have any higher-dimensional equivalents, are predicted to appear. In this work, we trace these elusive excitations via their effects on the dynamical structure factor of 1D strongly interacting Bose gases at low temperature. An array of 1D Bose gases is obtained by loading a $^{87}\mathrm{Rb}$ condensate in a two-dimensional lattice potential. The dynamical structure factor of the system is probed by energy deposition through low-momentum Bragg excitations. The experimental signals are compared to recent theoretical predictions for the dynamical structure factor of the Lieb-Liniger model at $T>0$. Our results demonstrate that the main contribution to the spectral widths stems from the dynamics of the interaction-induced excitations in the gas, which cannot be described by the Luttinger liquid theory.

arXiv:1406.2176•Physical Review A•Apr 13, 2015•142 citations

Dynamic and static density-density correlations in the one-dimensional Bose gas: Exact results and approximations

Alexander Yu. Cherny, Joachim Brand

We discuss approximate formulas for the dynamic structure factor of the one-dimensional Bose gas in the Lieb-Liniger model that appear to be applicable over a wide range of the relevant parameters such as the interaction strength, frequency, and wave number. The suggested approximations are consistent with the exact results known in limiting cases. In particular, we encompass exact edge exponents as well as the Luttinger-liquid and perturbation theoretic results. We further discuss derived approximations for the static structure factor and the pair distribution function $g(x)$. The approximate expressions show excellent agreement with numerical results based on the algebraic Bethe ansatz.

arXiv:0812.3264•Physical Review A•Apr 10, 2009•34 citations

Dynamics of a one-dimensional spinor Bose liquid: A phenomenological approach

Alex Kamenev, L. I. Glazman

The ground state of a spinor Bose liquid is ferromagnetic, while the softest excitation above the ground state is the magnon mode. The dispersion relation of the magnon in a one-dimensional liquid is periodic in the wave number $q$ with the period of $2\ensuremath{\pi}n$, determined by the density $n$ of the liquid. Dynamic correlation functions, such as, e.g., spin-spin correlation function, exhibit power-law singularities at the magnon spectrum, $\ensuremath{\omega}\ensuremath{\rightarrow}{\ensuremath{\omega}}_{m}(q,n)$. Without using any specific model of the interparticle interactions, we relate the corresponding exponents to independently measurable quantities $\ensuremath{\partial}{\ensuremath{\omega}}_{m}/\ensuremath{\partial}q$ and $\ensuremath{\partial}{\ensuremath{\omega}}_{m}/\ensuremath{\partial}n$.

arXiv:0808.0479•Physical Review A•Jul 16, 2009•59 citations

Exact results of dynamical structure factor of Lieb–Liniger model

Run-Tian Li, Song Cheng, Yang-Yang Chen +1 more

Abstract The dynamical structure factor (DSF) represents a measure of dynamical density–density correlations in a quantum many-body system. Due to the complexity of many-body correlations and quantum fluctuations in a system of an infinitely large Hilbert space, such kind of dynamical correlations often impose a big theoretical challenge. For one-dimensional (1D) quantum many-body systems, qualitative predictions of dynamical response functions are usually carried out by using the Tomonaga– Luttinger liquid (TLL) theory. In this scenario, a precise evaluation of the DSF for a 1D quantum system with arbitrary interaction strength remains a formidable task. In this paper, we use the form factor approach based on algebraic Bethe ansatz theory to calculate precisely the DSF of Lieb–Liniger model with an arbitrary interaction strength at a large scale of particle number. We find that the DSF for a system as large as 2000 particles enables us to depict precisely its line-shape from which the power-law singularity with corresponding exponents in the vicinities of spectral thresholds naturally emerge. It should be noted that, the advantage of our algorithm promises an access to the threshold behavior of dynamical correlation functions, further confirming the validity of nonlinear TLL theory besides Kitanine et al (2012 J. Stat. Mech. P09001). Finally we discuss a comparison of results with the results from the ABACUS method by J-S Caux (2009 J. Math. Phys. 50 095214) as well as from the strongly coupling expansion by Brand and Cherny (2005 Phys. Rev. A 72 033619).

arXiv:2303.09208•Journal of Physics A Mathematical and Theoretical•Jul 17, 2023•10 citations
Recently, Imambekov and Glazman [Phys. Rev. Lett. 100, 206805 (2008)] showed that the dynamic structure factor (DSF) of the 1D Bose gas demonstrates power-law behaviour along the limiting dispersion curve of the collective modes and calculated the corresponding exponents exactly. Combining these recent results with a previously obtained strong-coupling expansion we present an interpolation formula for the DSF of the 1D Bose gas. The obtained expression is further consistent with exact low energy exponents from Luttinger liquid theory and shows nice agreement with recent numerical results.
Interactions are known to have dramatic effects on bosonic gases in one dimension (1D). Not only does the ground state transform from a condensate like state to an effective Fermi sea, but new fundamental excitations, which do not have any higher-dimensional equivalents, are predicted to appear. In this work, we trace these elusive excitations via their effects on the dynamical structure factor of 1D strongly interacting Bose gases at low temperature. An array of 1D Bose gases is obtained by loading a 87Rb^{87}\mathrm{Rb}87Rb condensate in a two-dimensional lattice potential. The dynamical structure factor of the system is probed by energy deposition through low-momentum Bragg excitations. The experimental signals are compared to recent theoretical predictions for the dynamical structure factor of the Lieb-Liniger model at T>0T>0T>0. Our results demonstrate that the main contribution to the spectral widths stems from the dynamics of the interaction-induced excitations in the gas, which cannot be described by the Luttinger liquid theory.
We discuss approximate formulas for the dynamic structure factor of the one-dimensional Bose gas in the Lieb-Liniger model that appear to be applicable over a wide range of the relevant parameters such as the interaction strength, frequency, and wave number. The suggested approximations are consistent with the exact results known in limiting cases. In particular, we encompass exact edge exponents as well as the Luttinger-liquid and perturbation theoretic results. We further discuss derived approximations for the static structure factor and the pair distribution function g(x)g(x)g(x). The approximate expressions show excellent agreement with numerical results based on the algebraic Bethe ansatz.
The ground state of a spinor Bose liquid is ferromagnetic, while the softest excitation above the ground state is the magnon mode. The dispersion relation of the magnon in a one-dimensional liquid is periodic in the wave number qqq with the period of $2\ensuremath{\pi}n$, determined by the density nnn of the liquid. Dynamic correlation functions, such as, e.g., spin-spin correlation function, exhibit power-law singularities at the magnon spectrum, $\ensuremath{\omega}\ensuremath{\rightarrow}{\ensuremath{\omega}}_{m}(q,n)$. Without using any specific model of the interparticle interactions, we relate the corresponding exponents to independently measurable quantities $\ensuremath{\partial}{\ensuremath{\omega}}_{m}/\ensuremath{\partial}q$ and $\ensuremath{\partial}{\ensuremath{\omega}}_{m}/\ensuremath{\partial}n$.
Abstract The dynamical structure factor (DSF) represents a measure of dynamical density–density correlations in a quantum many-body system. Due to the complexity of many-body correlations and quantum fluctuations in a system of an infinitely large Hilbert space, such kind of dynamical correlations often impose a big theoretical challenge. For one-dimensional (1D) quantum many-body systems, qualitative predictions of dynamical response functions are usually carried out by using the Tomonaga– Luttinger liquid (TLL) theory. In this scenario, a precise evaluation of the DSF for a 1D quantum system with arbitrary interaction strength remains a formidable task. In this paper, we use the form factor approach based on algebraic Bethe ansatz theory to calculate precisely the DSF of Lieb–Liniger model with an arbitrary interaction strength at a large scale of particle number. We find that the DSF for a system as large as 2000 particles enables us to depict precisely its line-shape from which the power-law singularity with corresponding exponents in the vicinities of spectral thresholds naturally emerge. It should be noted that, the advantage of our algorithm promises an access to the threshold behavior of dynamical correlation functions, further confirming the validity of nonlinear TLL theory besides Kitanine et al (2012 J. Stat. Mech. P09001). Finally we discuss a comparison of results with the results from the ABACUS method by J-S Caux (2009 J. Math. Phys. 50 095214) as well as from the strongly coupling expansion by Brand and Cherny (2005 Phys. Rev. A 72 033619).