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Phenomenology of One-Dimensional Quantum Liquids Beyond the Low-Energy Limit

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Adilet Imambekov, Leonid I. Glazman

Strongly Correlated Electrons · Submitted 4 Dec 2008

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim For Galilean-invariant systems, we relate the parameters of such an effective Hamiltonian to the properties of the function $\epsilon (k).$ This allows us to express the exponents which characterize singular response functions of spinless bosonic or fermionic liquids in terms of $\epsilon(k)$ and Luttinger liquid parameters for any $k.$ For an antiferromagnetic Heisenberg spin-1/2 chain in a zero magnetic field, SU(2) invariance fixes the exponents from purely phenomenological considerations.

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arXiv ID0812.1046 (version 2)
Pith IDNADONRHR, Pith's permanent record of this paper and its review
CitationAdilet Imambekov, Leonid I. Glazman. "Phenomenology of One-Dimensional Quantum Liquids Beyond the Low-Energy Limit." arXiv:0812.1046 (2008). https://pith.science/paper/NADONRHR
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,525 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.20 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.09 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We consider zero temperature behavior of dynamic response functions of 1D systems near edges of support in momentum-energy plane $(k, \omega).$ The description of the singularities of dynamic response functions near an edge $\epsilon(k)$ is given by the effective Hamiltonian of a mobile impurity moving in a Luttinger liquid. For Galilean-invariant systems, we relate the parameters of such an effective Hamiltonian to the properties of the function $\epsilon (k).$ This allows us to express the exponents which characterize singular response functions of spinless bosonic or fermionic liquids in terms of $\epsilon(k)$ and Luttinger liquid parameters for any $k.$ For an antiferromagnetic Heisenberg spin-1/2 chain in a zero magnetic field, SU(2) invariance fixes the exponents from purely phenomenological considerations.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We consider zero temperature behavior of dynamic response functions of 1D systems near edges of support in momentum-energy plane $(k, \omega).$ The description of the singularities of dynamic response functions near an edge $\epsilon(k)$ is given by the effective Hamiltonian of a mobile impurity moving in a Luttinger liquid. contribution 0.78 0.57 0.21 asserted 1.00
s1 For Galilean-invariant systems, we relate the parameters of such an effective Hamiltonian to the properties of the function $\epsilon (k).$ This allows us to express the exponents which characterize singular response functions of spinless bosonic or fermionic liquids in terms of $\epsilon(k)$ and Luttinger liquid parameters for any $k.$ For an antiferromagnetic Heisenberg spin-1/2 chain in a zero magnetic field, SU(2) invariance fixes the exponents from purely phenomenological considerations. result 0.51 0.78 0.53 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.72.

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The paper
Original abstract

We consider zero temperature behavior of dynamic response functions of 1D systems near edges of support in momentum-energy plane $(k, \omega).$ The description of the singularities of dynamic response functions near an edge $\epsilon(k)$ is given by the effective Hamiltonian of a mobile impurity moving in a Luttinger liquid. For Galilean-invariant systems, we relate the parameters of such an effective Hamiltonian to the properties of the function $\epsilon (k).$ This allows us to express the exponents which characterize singular response functions of spinless bosonic or fermionic liquids in terms of $\epsilon(k)$ and Luttinger liquid parameters for any $k.$ For an antiferromagnetic Heisenberg spin-1/2 chain in a zero magnetic field, SU(2) invariance fixes the exponents from purely phenomenological considerations.

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  • [ref] Indeed, the results of Ref. [ref] show that the alternative exponent $μ_L(k_F=π/2)$ proposed in Ref. [ref] is inconsistent with universal relations for the phase shifts in the low-energy limit and with the SU(2) symmetry of the model for $V=2$.

    Spectral function of spinless fermions on a one-dimensional lattice · Dynamical structure factor · contest 0.74

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