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Jeansebastien Caux - One of the best experts on this subject based on the ideXlab platform.
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Dynamical Structure Factor of one dimensional bose gases experimental signatures of beyond luttinger liquid physics
Physical Review A, 2015Co-Authors: Nicole Fabbri, Milosz Panfil, David Clement, L Fallani, M Inguscio, C Fort, Jeansebastien CauxAbstract: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 $Tg0$. 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.
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Revealing elementary excitations of one-dimensionale Bose gases through their Dynamical Structure Factor
2014Co-Authors: Nicole Fabbri, Milosz Panfil, David Clement, L Fallani, M Inguscio, C Fort, Jeansebastien CauxAbstract: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 $^{87}$Rb condensate in a 2D 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.
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comment on revisiting the exact Dynamical Structure Factor of the heisenberg antiferromagnetic model by a h bougourzi
arXiv: Statistical Mechanics, 2014Co-Authors: Jeansebastien CauxAbstract:We point out the erroneous reasoning and disprove the conclusions contained in a recent preprint by A. H. Bougourzi (arxiv:1402.3855v1) concerning the spin Structure Factor of the Heisenberg model at zero field in the thermodynamic limit, as calculated using the vertex operator approach.
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adjacent spin operator Dynamical Structure Factor of the s 1 2 heisenberg chain
Journal of Statistical Mechanics: Theory and Experiment, 2012Co-Authors: Antoine Klauser, Jorn Mossel, Jeansebastien CauxAbstract:Considering the adjacent spin operators SjzSj + 1z and Sj − Sj + 1 − in the S = 1/2 Heisenberg chain, we give a determinant representation of their form Factors. The Dynamical Structure Factors of the respective operators are computed over the whole Brillouin zone in several magnetic fields and the resulting signal is analyzed in terms of excitation types. Among other results, we find that the SjzSj + 1z Dynamical Structure Factor carries a large weight of the four-spinon excitations which are distinguishable from the two-spinon signal because they are located outside the two-spinon spectrum.
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the spin exchange Dynamical Structure Factor of the s 1 2 heisenberg
Physical Review Letters, 2011Co-Authors: Antoine Klauser, Jorn Mossel, Jeansebastien Caux, Jeroen Van Den BrinkAbstract:We determine the spin-exchange Dynamical Structure Factor of the Heisenberg spin chain, as is measured by indirect resonant inelastic x-ray scattering (RIXS). We find that two-spin RIXS excitations nearly entirely fractionalize into two-spinon states. These share the same continuum lower bound as single-spin neutron scattering excitations, even if the relevant final states belong to orthogonal symmetry sectors. The RIXS spectral weight is mainly carried by higher-energy excitations, and is beyond the reach of the low-energy effective theories of Luttinger liquid type.
Fabian H. L. Essler - One of the best experts on this subject based on the ideXlab platform.
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low temperature Dynamical Structure Factor of the two leg spin 1 2 heisenberg ladder
Physical Review B, 2010Co-Authors: Wolf Goetze, Una Karahasanovic, Fabian H. L. EsslerAbstract:We determine the Dynamical Structure Factor of the two-leg spin-$\frac{1}{2}$ Heisenberg ladder at low temperatures in the regime of strong rung coupling. The dominant feature at zero temperature is the coherent triplon mode. We show that the line shape of this mode broadens in a nonsymmetric way at finite temperatures and that the degree of asymmetry increases with temperature. We also show that at low frequencies, a temperature-induced resonance akin to the Villain mode in the spin-$\frac{1}{2}$ Heisenberg Ising chain emerges.
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finite temperature Dynamical Structure Factor of the heisenberg ising chain
Physical Review B, 2009Co-Authors: A. J. A. James, Wolf Goetze, Fabian H. L. EsslerAbstract:We consider the spin-1/2 Heisenberg $XXZ$ chain in the regime of large Ising-type anisotropy $\ensuremath{\Delta}$. By a combination of duality and Jordan-Wigner transformations we derive a mapping to weakly interacting spinless fermions, which represent domain walls between the two degenerate ground states. We develop a perturbative expansion in $1/\ensuremath{\Delta}$ for the transverse Dynamical spin Structure Factor at finite temperatures and in an applied transverse magnetic field. We present a unified description for both the low-energy temperature-activated response and the temperature evolution of the $T=0$ two-spinon continuum. We find that the two-spinon continuum narrows in energy with increasing temperature. At the same time spectral weight is transferred from the two-spinon continuum to the low-energy intraband scattering continuum, which is strongly peaked around the position of the (single) spinon dispersion (``Villain mode'').
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Finite-temperature Dynamical Structure Factor of alternating Heisenberg chains
Physical Review B, 2008Co-Authors: A. J. A. James, Fabian H. L. Essler, Robert KonikAbstract:We develop a low-temperature expansion for the finite temperature Dynamical Structure Factor of the spin half Heisenberg chain with alternating nearest neighbour exchange in the limit of strong alternation of the exchange constants. We determine both the broadening of the low lying triplet lines and the contribution of the thermally activated intraband scattering.
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Dynamical Structure Factor of the anisotropic heisenberg chain in a transverse field
Physical Review B, 2003Co-Authors: Jeansebastien Caux, Fabian H. L. Essler, Ute LowAbstract:We consider the anisotropic Heisenberg spin-1/2 chain in a transverse magnetic field at zero temperature. We first determine all components of the Dynamical Structure Factor by combining exact results with a mean-field approximation recently proposed by Dmitriev et al. [JETP 95, 538 (2002)]. We then turn to the small anisotropy limit, in which we use field theory methods to obtain exact results. We discuss the relevance of our results to neutron scattering experiments on the one-dimensional Heisenberg chain compound ${\mathrm{Cs}}_{2}{\mathrm{CoCl}}_{4}.$
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Dynamical Structure Factor in copper benzoate and other spin 1 2 antiferromagnetic chains
Physical Review B, 2003Co-Authors: Fabian H. L. Essler, Akira Furusaki, Toshiya HikiharaAbstract:Recent experiments of the quasi-one-dimensional spin-$\frac{1}{2}$ antiferromagnet copper benzoate established the existence of a magnetic field induced gap. The observed neutron scattering intensity exhibits resolution limited peaks at both the antiferromagnetic wave number and at incommensurate wave numbers related to the applied magnetic field. We determine the ratio of spectral weights of these peaks within the framework of a low-energy effective field theory description of the problem.
Manas Kulkarni - One of the best experts on this subject based on the ideXlab platform.
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finite temperature Dynamical Structure Factor of the one dimensional bose gas from the gross pitaevskii equation to the kardar parisi zhang universality class of Dynamical critical phenomena
Physical Review A, 2013Co-Authors: Manas Kulkarni, Austen LamacraftAbstract:We study the finite-temperature Dynamical Structure Factor $S(k,\ensuremath{\omega})$ of a one-dimensional Bose gas using numerical simulations of the Gross-Pitaevskii equation appropriate to a weakly interacting system. The line shape of the phonon peaks in $S(k,\ensuremath{\omega})$ has a width $\ensuremath{\propto}$${|k|}^{3/2}$ at low wave vectors. This anomalous width arises from resonant three-phonon interactions, and reveals a remarkable connection to the Kardar-Parisi-Zhang universality class of Dynamical critical phenomena.
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finite temperature Dynamical Structure Factor of the one dimensional bose gas from the gross pitaevskii equation to the kardar parisi zhang universality class of Dynamical critical phenomena
Physical Review A, 2013Co-Authors: Manas Kulkarni, Austen LamacraftAbstract:We study the finite temperature Dynamical Structure Factor $S(k,\omega)$ of a 1D Bose gas using numerical simulations of the Gross--Pitaevskii equation appropriate to a weakly interacting system. The lineshape of the phonon peaks in $S(k,\omega)$ has a width $\propto |k|^{3/2}$ at low wavevectors. This anomalous width arises from resonant three-phonon interactions, and reveals a remarkable connection to the Kardar--Parisi--Zhang universality class of Dynamical critical phenomena.
Austen Lamacraft - One of the best experts on this subject based on the ideXlab platform.
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finite temperature Dynamical Structure Factor of the one dimensional bose gas from the gross pitaevskii equation to the kardar parisi zhang universality class of Dynamical critical phenomena
Physical Review A, 2013Co-Authors: Manas Kulkarni, Austen LamacraftAbstract:We study the finite-temperature Dynamical Structure Factor $S(k,\ensuremath{\omega})$ of a one-dimensional Bose gas using numerical simulations of the Gross-Pitaevskii equation appropriate to a weakly interacting system. The line shape of the phonon peaks in $S(k,\ensuremath{\omega})$ has a width $\ensuremath{\propto}$${|k|}^{3/2}$ at low wave vectors. This anomalous width arises from resonant three-phonon interactions, and reveals a remarkable connection to the Kardar-Parisi-Zhang universality class of Dynamical critical phenomena.
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finite temperature Dynamical Structure Factor of the one dimensional bose gas from the gross pitaevskii equation to the kardar parisi zhang universality class of Dynamical critical phenomena
Physical Review A, 2013Co-Authors: Manas Kulkarni, Austen LamacraftAbstract:We study the finite temperature Dynamical Structure Factor $S(k,\omega)$ of a 1D Bose gas using numerical simulations of the Gross--Pitaevskii equation appropriate to a weakly interacting system. The lineshape of the phonon peaks in $S(k,\omega)$ has a width $\propto |k|^{3/2}$ at low wavevectors. This anomalous width arises from resonant three-phonon interactions, and reveals a remarkable connection to the Kardar--Parisi--Zhang universality class of Dynamical critical phenomena.
J M P Carmelo - One of the best experts on this subject based on the ideXlab platform.
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bethe strings in the spin Dynamical Structure Factor of the mott hubbard phase in the one dimensional fermionic hubbard model
Physical Review B, 2021Co-Authors: J M P Carmelo, Tilen CadežAbstract:The spectra and role in the spin Dynamical properties of bound states of elementary magnetic excitations named Bethe strings that occur in some integrable spin and electronic one-dimensional models have recently been identified and realized in several materials by experiments. Corresponding theoretical studies have usually relied on the one-dimensional spin-$1/2$ Heisenberg antiferromagnet in a magnetic field. At the isotropic point, it describes the large onsite repulsion $U$ limit of the spin degrees of freedom of the one-dimensional fermionic Hubbard model with one electron per site in a magnetic field $h$. In this paper we consider the thermodynamic limit and study the effects of lowering the latter quantum problem ratio $u=U/4t$, where $t$ is the first-neighbor transfer integral, on the line-shape singularities in $(k,\ensuremath{\omega})$-plane regions at and just above the lower thresholds of the transverse and longitudinal spin Dynamical Structure Factors. The most significant spectral weight contribution from Bethe strings leads to a gapped continuum in the spectrum of the spin Dynamical Structure Factor ${S}^{+\ensuremath{-}}(k,\ensuremath{\omega})$. Our study focuses on the line shape singularities at and just above the gapped lower threshold of that continuum, which have been identified in experiments. Our results are consistent with the contribution of Bethe strings to ${S}^{zz}(k,\ensuremath{\omega})$ being small at low spin densities and becoming negligible upon increasing that density. Our results provide physically important information about how electron itinerancy affects the spin dynamics.
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bethe strings in the Dynamical Structure Factor of the spin 1 2 heisenberg xxx chain
Nuclear Physics, 2020Co-Authors: J M P Carmelo, Tilen Cadež, P D SacramentoAbstract:Abstract Recently there has been a renewed interest in the spectra and role in Dynamical properties of excited states of the spin-1/2 Heisenberg antiferromagnetic chain in longitudinal magnetic fields associated with Bethe strings. The latter are bound states of elementary magnetic excitations described by Bethe-ansatz complex non-real rapidities. Previous studies on this problem referred to finite-size systems. Here we consider the thermodynamic limit and study it for the isotropic spin-1/2 Heisenberg XXX chain in a longitudinal magnetic field. We confirm that also in that limit the most significant spectral weight contribution from Bethe strings leads to ( k , ω ) -plane gapped continua in the spectra of the spin Dynamical Structure Factors S + − ( k , ω ) and S x x ( k , ω ) = S y y ( k , ω ) . The contribution of Bethe strings to S z z ( k , ω ) is found to be small at low spin densities m and to become negligible upon increasing that density above m ≈ 0.317 . For S − + ( k , ω ) , that contribution is found to be negligible at finite magnetic field. We derive analytical expressions for the line shapes of S + − ( k , ω ) , S x x ( k , ω ) = S y y ( k , ω ) , and S z z ( k , ω ) valid in the ( k , ω ) -plane vicinity of singularities located at and just above the gapped lower thresholds of the Bethe-string states's spectra. As a side result and in order to provide an overall physical picture that includes the relative ( k , ω ) -plane location of all spectra with a significant amount of spectral weight, we revisit the general problem of the line-shape of the transverse and longitudinal spin Dynamical Structure Factors at finite magnetic field and excitation energies in the ( k , ω ) -plane vicinity of other singularities. This includes those located at and just above the lower thresholds of the spectra that stem from excited states described by only real Bethe-ansatz rapidities.
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exponents of the spectral functions and Dynamical Structure Factor of the 1d lieb liniger bose gas
Annals of Physics, 2016Co-Authors: J M P Carmelo, P D SacramentoAbstract:Abstract We study the ( k , ω ) -plane finite-energy line shape of the zero-temperature one-boson removal spectral function ( ω 0 ) , one-boson addition spectral function ( ω > 0 ) , and charge Dynamical Structure Factor ( ω > 0 ) of the 1D Lieb–Liniger Bose gas with repulsive boson interaction c > 0 . Our analysis of the problem focuses on the line shape at finite excitation energies in the vicinity of these functions spectrum upper ( ω 0 ) or lower ( ω > 0 ) threshold. Specifically, we derive the exact momentum, interaction, and density dependences of the exponents controlling such a line shape in each of the N = 1 , 2 , 3 , … momentum subdomains k ∈ [ ( N − 1 ) 2 π n , N 2 π n ] . Here n = N / L is the boson density, N the boson number, and L the system length. In the thermodynamic limit considered in our study nearly all spectral weight of the Dynamical correlation functions is for large values of n / c contained in the N = 1 momentum subdomain k ∈ [ 0 , 2 π n ] . As n / c decreases a small fraction of that weight is transferred to the remaining set of N = 2 , 3 , 4 , … momentum subdomains, particularly to the N = 2 subdomain. In the case of the momentum subdomain k ∈ [ 0 , 2 π n ] , our exact results agree with those of previous studies. For that subdomain the above exponents are plotted as a function of the momentum for several n / c values. Our derivation of the line shapes of the three Dynamical correlation functions relies on the use of a simplified form of the pseudofermion Dynamical theory of the fermionic 1D Hubbard model suitably modified in this paper for the 1D Bose gas.