Duality between weak and strong interactions in quantum gases

Abstract

In one dimensional quantum gases there is a well known "duality" between hard core bosons and non-interacting fermions. However, at the field theory level, no exact duality connecting strongly interacting bosons to weakly interacting fermions is known. Here we propose a solution to this long standing problem. Our derivation relies on regularizing the only point-like interaction between fermions in 1D that induces a discontinuity in the wave function proportional to its derivative. In contrast to all known regularisations our potential is weak for small interaction strengths. Crucially, this allows one to apply standard methods of diagrammatic perturbation theory to strongly interacting bosons. As a first application we compute the finite temperature spectral function of the Cheon-Shigehara model, the fermionic model dual to the celebrated Lieb-Liniger model.

5 pages + supplemental material. Title changed and typos corrected

References in corpus (12)

• Pinning quantum phase transition for a Luttinger liquid of strongly interacting bosons
• Linear response theory for a pair of coupled one-dimensional condensates of interacting atoms
• Exact thermalization dynamics in the "Rule 54" Quantum Cellular Automaton
• Universal contact for a Tonks-Girardeau gas at finite temperature
• Phase diagram and momentum distribution of an interacting Bose gas in a bichromatic lattice
• Polarizability and dynamic structure factor of the one-dimensional Bose gas near the Tonks-Girardeau limit at finite temperatures
• Spatial nonlocal pair correlations in a repulsive 1D Bose gas
• Finite-temperature properties of hard-core bosons confined on one-dimensional optical lattices
• The Dynamic Structure Factor of the 1D Bose Gas near the Tonks-Girardeau Limit
• Systematic strong coupling expansion for out-of-equilibrium dynamics in the Lieb-Liniger model
• A Generalization of the One-Dimensional Boson-Fermion Duality Through the Path-Integral Formalism
• Ground-state properties of dilute spinless fermions in fractional dimensions

Cited by in corpus (8)

• Hydrodynamic gauge fixing and higher order hydrodynamic expansion
• BBGKY Hierarchy and Generalised Hydrodynamics
• Local Neumann semitransparent layers: resummation, pair production and duality
• Exact results of dynamical structure factor of Lieb-Liniger model
• Viscous Flow in a 1D Spin-Polarized Fermi Gas: the Role of Integrability on Viscosity
• Regularization of a strong-weak duality between pointlike interactions in one dimension
• Wavelet representation of hardcore bosons
• Regularization of energy-dependent pointlike interactions in 1D quantum mechanics