Аннотация:
We develop a form factor approach to the study of dynamical correlation functions of quantum integrable models in the critical regime. As an example, we consider the quantum non-linear Schrödinger model. We derive the long-distance/long-time asymptotic behavior of various two-point functions of this model. We also compute edge exponents and amplitudes characterizing the power-law behavior of dynamical response functions on the particle–hole excitation thresholds. These last results confirm predictions based on the non-linear Luttinger liquid method. Our results rely on a first principles derivation, based on a microscopic analysis of the model, without invoking, at any stage, any correspondence with a continuous field theory. Furthermore, our approach only makes use of certain general properties of the model, so that it should be applicable, possibly with minor modifications, to a wide class of (not necessarily integrable) gapless one-dimensional Hamiltonians.
KKK, JMM, NAS and VT are supported by the CNRS. NK, KKK, JMM and VT are supported by ANR grant ANR-10-BLAN-0120-04-DIADEMS. KKK and NK are supported by the CNRS grant PEPS-PTI-Asymptotique d'integrales multiples. NK is supported by the Burgundy region, FABER grant 2010-9201AAO047S00753. We also acknowledge the support from the GDRI-471 of the CNRS 'French-Russian network in Theoretical and Mathematical Physics'. NAS is also supported by the Program of RAS Basic Problems of Nonlinear Dynamics, RFBR-11-01-00440, RFBR-11-01-12037-ofi-m, SS-4612.2012.1. When this work was being carried out, KKK was supported by the EU Marie-Curie Excellence Grant MEXT-CT-2006-042695, DESY and IUPUI.
Поступила в редакцию: 25.06.2012 Принята в печать: 02.08.2012
Реферативные базы данных:
Тип публикации:
Статья
Язык публикации: английский
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/jsm5
Эта публикация цитируется в следующих 83 статьяx:
Frank Göhmann, Encyclopedia of Mathematical Physics, 2025, 38
Giuliano Niccoli, Véronique Terras, “On correlation functions for the open XXZ chain with non-longitudinal boundary fields: The case with a constraint”, SciPost Phys., 16:4 (2024)
N. A. Slavnov, “Algebraic Bethe ansatz approach to the correlation functions of the one-dimensional bosons with attraction”, JHEP, 2024 (2024), 61
Oleksandr Gamayun, Oleg Lychkovskiy, “One-dimensional Fermi polaron after a kick: Two-sided singularity of the momentum distribution, Bragg reflection and other exact results”, SciPost Phys., 17:2 (2024)
F. H. L. Essler, A. J. J. M. de Klerk, “Statistics of Matrix Elements of Local Operators in Integrable Models”, Phys. Rev. X, 14:3 (2024)
Ovidiu I. Pâţu, Andreas Klümper, Angela Foerster, “Exact spectral function and nonequilibrium dynamics of the strongly interacting Hubbard model”, Phys. Rev. B, 110:20 (2024)
Frank Göhmann, Karol K Kozlowski, Mikhail D Minin, “Thermal form-factor expansion of the dynamical two-point functions of local operators in integrable quantum chains”, J. Phys. A: Math. Theor., 56:47 (2023), 475003
Г. В. Кулкарни, Н. А. Славнов, “Действие элементов матрицы монодромии в обобщенном алгебраическом анзаце Бете”, ТМФ, 217:3 (2023), 555–576; G. Kulkarni, N. A. Slavnov, “Action of the monodromy matrix elements in the generalized algebraic Bethe ansatz”, Theoret. and Math. Phys., 217:3 (2023), 1889–1906
Г. В. Кулкарни, Н. А. Славнов, “Скалярные произведения векторов Бете в обобщенном алгебраическом анзаце Бете”, ТМФ, 217:1 (2023), 179–203; G. Kulkarni, N. A. Slavnov, “Scalar products of Bethe vectors in the generalized algebraic
Bethe ansatz”, Theoret. and Math. Phys., 217:1 (2023), 1574–1594
Ovidiu I. Pâţu, “Exact spectral function of the Tonks-Girardeau gas at finite temperature”, Phys. Rev. A, 106:5 (2022)
Daniel Chernowitz, Oleksandr Gamayun, “On the dynamics of free-fermionic tau-functions at finite temperature”, SciPost Phys. Core, 5:1 (2022)
Frank Göhmann, Karol Kozlowski, Jesko Sirker, Junji Suzuki, “Spin conductivity of the XXZ chain in the antiferromagnetic massive regime”, SciPost Phys., 12:5 (2022)
Aleksandra Petković, “Local spectral density of an interacting one-dimensional Bose gas with an impurity”, Phys. Rev. A, 105:4 (2022)
Hao Pei, Véronique Terras, “On scalar products and form factors by separation of variables: the antiperiodic XXZ model”, J. Phys. A: Math. Theor., 55:1 (2022), 015205
G Niccoli, V Terras, “Correlation functions for open XXZ spin 1/2 quantum chains with unparallel boundary magnetic fields”, J. Phys. A: Math. Theor., 55:40 (2022), 405203
Etienne Granet, Henrik Dreyer, Fabian Essler, “Out-of-equilibrium dynamics of the XY spin chain from form factor expansion”, SciPost Phys., 12:1 (2022)
Jacopo De Nardis, Benjamin Doyon, Marko Medenjak, Miłosz Panfil, “Correlation functions and transport coefficients in generalised hydrodynamics”, J. Stat. Mech., 2022:1 (2022), 014002
A. A. Ovchinnikov, “Threshold singularities in the XXZ-spin chain”, Mod. Phys. Lett. B, 35:02 (2021), 2150044
Constantin Babenko, Frank Göhmann, Karol K. Kozlowski, Jesko Sirker, Junji Suzuki, “Exact Real-Time Longitudinal Correlation Functions of the Massive
XXZ
Chain”, Phys. Rev. Lett., 126:21 (2021)
Oleksandr Gamayun, Nikolai Iorgov, Yu. Zhuravlev, “Effective free-fermionic form factors and the XY spin chain”, SciPost Phys., 10:3 (2021)
Обратная связь: