Effective mass of elementary excitations in Galilean-invariant integrable models

Matveev, K. A.; Pustilnik, M.

doi:10.1103/PhysRevB.94.115436

Title: Effective mass of elementary excitations in Galilean-invariant integrable models

Journal Article · Tue Sep 27 00:00:00 EDT 2016 · Physical Review B

DOI:https://doi.org/10.1103/PhysRevB.94.115436· OSTI ID:1352654

Matveev, K. A. ^[1]; Pustilnik, M. ^[2]

Argonne National Lab. (ANL), Argonne, IL (United States). Materials Science Division
Georgia Inst. of Technology, Atlanta, GA (United States). School of Physics

Here, we study low-energy excitations of one-dimensional Galilean-invariant models integrable by Bethe ansatz and characterized by nonsingular two-particle scattering phase shifts. We also prove that the curvature of the excitation spectra is described by the recently proposed phenomenological expression for the effective mass. These results apply to such models as the repulsive Lieb-Liniger model and the hyperbolic Calogero-Sutherland model.

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Research Organization:: Argonne National Laboratory (ANL), Argonne, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES); National Science Foundation (NSF)

Grant/Contract Number:: AC02-06CH11357

OSTI ID:: 1352654

Alternate ID(s):: OSTI ID: 1326870

Journal Information:: Physical Review B, Vol. 94, Issue 11; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 7 works

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References (27)

The quantum mechanical Toda lattice, II Gutzwiller, Martin C. Annals of Physics, Vol. 133, Issue 2 https://doi.org/10.1016/0003-4916(81)90253-0	journal	May 1981
Thermodynamics of a One‐Dimensional System of Bosons with Repulsive Delta‐Function Interaction Yang, C. N.; Yang, C. P. Journal of Mathematical Physics, Vol. 10, Issue 7 https://doi.org/10.1063/1.1664947	journal	July 1969
Dissipationless kinetics of one-dimensional interacting fermions Protopopov, I. V.; Gutman, D. B.; Oldenburg, M. Physical Review B, Vol. 89, Issue 16 https://doi.org/10.1103/PhysRevB.89.161104	journal	April 2014
Soliton operators for the quantized sine-Gordon equation Mandelstam, S. Physical Review D, Vol. 11, Issue 10 https://doi.org/10.1103/PhysRevD.11.3026	journal	May 1975
The quantum Toda chain Sklyanin, E. K. Non-Linear Equations in Classical and Quantum Field Theory https://doi.org/10.1007/3-540-15213-X_80	book	January 1985
Solitons in a one-dimensional Wigner crystal Pustilnik, M.; Matveev, K. A. Physical Review B, Vol. 91, Issue 16 https://doi.org/10.1103/PhysRevB.91.165416	journal	April 2015
Effective Harmonic-Fluid Approach to Low-Energy Properties of One-Dimensional Quantum Fluids Haldane, F. D. M. Physical Review Letters, Vol. 47, Issue 25 https://doi.org/10.1103/PhysRevLett.47.1840	journal	December 1981
New wave‐operator identity applied to the study of persistent currents in 1D Mattis, Daniel C. Journal of Mathematical Physics, Vol. 15, Issue 5 https://doi.org/10.1063/1.1666693	journal	May 1974
Fermionic quasiparticle representation of Tomonaga-Luttinger Hamiltonian Rozhkov, A. V. The European Physical Journal B, Vol. 47, Issue 2 https://doi.org/10.1140/epjb/e2005-00312-3	journal	September 2005
Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State Lieb, Elliott H.; Liniger, Werner Physical Review, Vol. 130, Issue 4 https://doi.org/10.1103/PhysRev.130.1605	journal	May 1963
Hydrodynamic Hamiltonian for a nonideal Bose gas Popov, V. N. Theoretical and Mathematical Physics, Vol. 11, Issue 2 https://doi.org/10.1007/BF01028563	journal	May 1972
Dynamical structure factor at small q for the XXZ spin-1/2 chain Pereira, R. G.; Sirker, J.; Caux, J-S Journal of Statistical Mechanics: Theory and Experiment, Vol. 2007, Issue 08 https://doi.org/10.1088/1742-5468/2007/08/P08022	journal	August 2007
Dynamical Spin Structure Factor for the Anisotropic Spin- $1 / 2$ Heisenberg Chain Pereira, R. G.; Sirker, J.; Caux, J. -S. Physical Review Letters, Vol. 96, Issue 25 https://doi.org/10.1103/PhysRevLett.96.257202	journal	June 2006
One-dimensional quantum liquids: Beyond the Luttinger liquid paradigm Imambekov, Adilet; Schmidt, Thomas L.; Glazman, Leonid I. Reviews of Modern Physics, Vol. 84, Issue 3 https://doi.org/10.1103/RevModPhys.84.1253	journal	September 2012
'Luttinger liquid theory' of one-dimensional quantum fluids. I. Properties of the Luttinger model and their extension to the general 1D interacting spinless Fermi gas Haldane, F. D. M. Journal of Physics C: Solid State Physics, Vol. 14, Issue 19 https://doi.org/10.1088/0022-3719/14/19/010	journal	July 1981
Excitation Spectrum of the Lieb-Liniger Model Ristivojevic, Zoran Physical Review Letters, Vol. 113, Issue 1 https://doi.org/10.1103/PhysRevLett.113.015301	journal	July 2014
Fate of classical solitons in one-dimensional quantum systems Pustilnik, M.; Matveev, K. A. Physical Review B, Vol. 92, Issue 19 https://doi.org/10.1103/PhysRevB.92.195146	journal	November 2015
Scattering of hole excitations in a one-dimensional spinless quantum liquid Matveev, K. A.; Andreev, A. V. Physical Review B, Vol. 86, Issue 4 https://doi.org/10.1103/PhysRevB.86.045136	journal	July 2012
Dynamic Response of One-Dimensional Interacting Fermions Pustilnik, M.; Khodas, M.; Kamenev, A. Physical Review Letters, Vol. 96, Issue 19 https://doi.org/10.1103/PhysRevLett.96.196405	journal	May 2006
On the theory of the superfluidity of two- and one-dimensional bose systems Popov, V. N. Theoretical and Mathematical Physics, Vol. 11, Issue 3 https://doi.org/10.1007/BF01028373	journal	June 1972
Quantization of the (sin?)2 interaction in terms of fermion variables Pogrebkov, A. K.; Sushko, V. N. Theoretical and Mathematical Physics, Vol. 24, Issue 3 https://doi.org/10.1007/BF01029883	journal	September 1975
Exact Analysis of an Interacting Bose Gas. II. The Excitation Spectrum Lieb, Elliott H. Physical Review, Vol. 130, Issue 4 https://doi.org/10.1103/PhysRev.130.1616	journal	May 1963
Single-particle states, Kohn anomaly, and pairing fluctuations in one dimension Luther, A.; Peschel, I. Physical Review B, Vol. 9, Issue 7 https://doi.org/10.1103/PhysRevB.9.2911	journal	April 1974
Beautiful Models: 70 Years of Exactly Solved Quantum Many-Body Problems Sutherland, Bill https://doi.org/10.1142/5552	book	June 2004
Dynamics of Excitations in a One-Dimensional Bose Liquid Khodas, M.; Pustilnik, M.; Kamenev, A. Physical Review Letters, Vol. 99, Issue 11 https://doi.org/10.1103/PhysRevLett.99.110405	journal	September 2007
Lieb's soliton-like excitations in harmonic traps Astrakharchik, G. E.; Pitaevskii, L. P. EPL (Europhysics Letters), Vol. 102, Issue 3 https://doi.org/10.1209/0295-5075/102/30004	journal	May 2013
Phenomenology of One-Dimensional Quantum Liquids Beyond the Low-Energy Limit Imambekov, Adilet; Glazman, Leonid I. Physical Review Letters, Vol. 102, Issue 12 https://doi.org/10.1103/PhysRevLett.102.126405	journal	March 2009

Cited By (2)

Ground-state energy and excitation spectrum of the Lieb-Liniger model : accurate analytical results and conjectures about the exact solution Lang, Guillaume; Hekking, Frank; Minguzzi, Anna SciPost Physics, Vol. 3, Issue 1 https://doi.org/10.21468/scipostphys.3.1.003	journal	January 2017
Ground-state energy and excitation spectrum of the Lieb-Liniger model : accurate analytical results and conjectures about the exact solution Lang, Guillaume; Hekking, Frank; Minguzzi, Anna arXiv https://doi.org/10.48550/arxiv.1609.08865	text	January 2016

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