Exact solution of a 1D many-body system with momentum dependent interactions

Abstract

We discuss a 1D many-body model of distinguishable particles with local, momentum dependent two-body interactions. We show that the restriction of this model to fermions corresponds to the non-relativistic limit of the massive Thirring model. This fermion model can be solved exactly by a mapping to the 1D boson gas with inverse coupling constant. We provide evidence that this mapping is the non-relativistic limit of the duality between the massive Thirring model and the quantum sine-Gordon model. We also investigate the question if the generalization of this model to distinguishable particles is exactly solvable by the coordinate Bethe ansatz and find that this is not the case.

12 pages; mistake corrected changing one of our conclusions: the generalized model with distinguishable particles is not exactly solvable by Bethe Ansatz

References in corpus (2)

• Atomic Scattering in Presence of an External Confinement and a Gas of Impenetrable Bosons
• Fermion-Boson Duality of One-dimensional Quantum Particles with Generalized Contact Interaction

Cited by in corpus (20)

• Bethe Ansatz study of one-dimensional Bose and Fermi gases with periodic and hard wall boundary conditions
• Polarizability and dynamic structure factor of the one-dimensional Bose gas near the Tonks-Girardeau limit at finite temperatures
• Non-divergent pseudo-potential treatment of spin-polarized fermions under 1D and 3D harmonic confinement
• Universal One-dimensional Atomic Gases Near Odd-wave Resonance
• Exponentially decaying correlations in a gas of strongly interacting spin-polarized 1D fermions with zero-range interactions
• Bose-Fermi Mapping and Multi-Branch Spin Chain Model for Strongly Interacting Quantum Gases in One-Dimension: Dynamics and Collective Excitations
• One-dimensional fermionic gases with attractive p-wave interaction in a hard-wall trap
• Finite-Temperature Fluid-Insulator Transition of Strongly Interacting 1D Disordered Bosons
• Strongly interacting one-dimensional quantum gas mixtures with weak p-wave interactions
• Momentum distribution and contacts of one-dimensional spinless Fermi gases with an attractive p-wave interaction
• Effective super Tonks-Girardeau gases as ground states of strongly attractive multi-component fermions
• Exact solutions of two complementary 1D quantum many-body systems on the half-line
• Non Relativistic Limit of Integrable QFT with fermionic excitations
• Local Neumann semitransparent layers: resummation, pair production and duality
• Duality between weak and strong interactions in quantum gases
• Analysis of a one-dimensional Hamiltonian with a singular double well consisting of two nonlocal ${\delta }^{\prime }$ interactions
• Generalized local interactions in 1D: solutions of quantum many-body systems describing distinguishable particles
• Many-body quantum boomerang effect
• Quantum quenches in the sinh-Gordon and Lieb-Liniger models
• Efficient determination of eigenenergies and eigenstates of $N$ ($N=3$--$4$) identical 1D bosons and fermions under external harmonic confinement