A note on the spin-1/2 XXZ chain concerning its relation to the Bose gas

Abstract

By considering the one-particle and two-particle scattering data of the spin-1/2 Heisenberg chain at T=0 we derive a continuum limit relating the spin chain to the 1D Bose gas. Applying this limit to the quantum transfer matrix approach of the Heisenberg chain we obtain expressions for the correlation functions of the Bose gas at arbitrary temperatures.

arXiv commentcontinued in 0710.1814 math-ph

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Cited by in corpus (24)

• Form factor expansion for thermal correlators
• Local correlations in the 1D Bose gas from a scaling limit of the XXZ chain
• Néel-XXZ state overlaps: odd particle numbers and Lieb-Liniger scaling limit
• Overlaps of $q$-raised Néel states with XXZ Bethe states and their relation to the Lieb-Liniger Bose gas
• From the sinh-Gordon field theory to the one-dimensional Bose gas: exact local correlations and full counting statistics
• Ground-state energy and excitation spectrum of the Lieb-Liniger model : accurate analytical results and conjectures about the exact solution
• Form factors in SU(3)-invariant integrable models
• Frustrated spin chains in strong magnetic field: dilute two-component Bose gas regime
• Long-distance behavior of temperature correlation functions in the one-dimensional Bose gas
• Exact description of the magnetoelectric effect in the spin-1/2 XXZ-chain with Dzyaloshinskii-Moriya interaction
• The algebraic Bethe ansatz for scalar products in SU(3)-invariant integrable models
• Exact formulas for the form factors of local operators in the Lieb-Liniger model
• Scalar products of Bethe vectors in models with $\mathfrak{gl}(2|1)$ symmetry 2. Determinant representation
• Correlation functions of one-dimensional bosons at low temperature
• Correlation lengths of the repulsive one-dimensional Bose gas
• Delta-Bose gas on a half-line and the KPZ equation: boundary bound states and unbinding transitions
• Correlation functions of the integrable isotropic spin-1 chain at finite temperature
• Correlation functions of the integrable isotropic spin-1 chain: algebraic expressions for arbitrary temperature
• Efficient Thermodynamic Description of Multi-Component One-Dimensional Bose Gases
• Thermodynamics, density profiles and correlation functions of the inhomogeneous one-dimensional spinor Bose gas
• Quantum corrections to the classical field approximation for one-dimensional quantum many-body systems in equilibrium
• Momentum reconstruction and contact of the one-dimensional Bose-Fermi mixture
• The LeClair-Mussardo series and nested Bethe Ansatz
• Correlation functions of an interacting spinless fermion model at finite temperature