Short-distance thermal correlations in the XXZ chain

Abstract

Recent studies have revealed much of the mathematical structure of the static correlation functions of the XXZ chain. Here we use the results of those studies in order to work out explicit examples of short-distance correlation functions in the infinite chain. We compute two-point functions ranging over 2, 3 and 4 lattice sites as functions of the temperature and the magnetic field for various anisotropies in the massless regime $-1<\Delta <1$. It turns out that the new formulae are numerically efficient and allow us to obtain the correlations functions over the full parameter range with arbitrary precision.

25 pages, 5 colored figures, v2: some fonts changed and some typos corrected

References in corpus (11)

• The Kernel Polynomial Method
• Integral representations for correlation functions of the XXZ chain at finite temperature
• Hidden Grassmann structure in the XXZ model
• Integral representation of the density matrix of the XXZ chain at finite temperatures
• Factorization of the finite temperature correlation functions of the XXZ chain in a magnetic field
• Reduced qKZ equation and correlation functions of the XXZ model
• Factorization of multiple integrals representing the density matrix of a finite segment of the Heisenberg spin chain
• Third-neighbor and other four-point correlation functions of spin-1/2 XXZ chain
• Exact thermodynamic limit of short-range correlation functions of the antiferromagnetic $XXZ$-chain at finite temperatures
• High temperature expansion of emptiness formation probability for isotropic Heisenberg chain
• XX and Ising limits in integral formulae for finite temperature correlation functions of the XXZ chain

Cited by in corpus (35)

• Quench dynamics and relaxation in isolated integrable quantum spin chains
• Quantum correlations in spin chains at finite temperatures and quantum phase transitions
• Relaxation after quantum quenches in the spin-1/2 Heisenberg XXZ chain
• Exact steady states for quantum quenches in integrable Heisenberg spin chains
• Spotlighting quantum critical points via quantum correlations at finite temperatures
• Current operators in Bethe Ansatz and Generalized Hydrodynamics: An exact quantum/classical correspondence
• Overlaps of $q$-raised Néel states with XXZ Bethe states and their relation to the Lieb-Liniger Bose gas
• Thermal form factors of the XXZ chain and the large-distance asymptotics of its temperature dependent correlation functions
• Short-distance thermal correlations in the massive XXZ chain
• Low-temperature large-distance asymptotics of the transversal two-point functions of the XXZ chain
• Exact description of the magnetoelectric effect in the spin-1/2 XXZ-chain with Dzyaloshinskii-Moriya interaction
• Universal terms in the overlap of the ground state of the spin-1/2 XXZ chain with the Néel state
• Probabilistic quantum teleportation via thermal entanglement
• Finite temperature and quench dynamics in the Transverse Field Ising Model from form factor expansions
• On the physical part of the factorized correlation functions of the XXZ chain
• Equilibrium dynamics of the XX chain
• A systematic $1/c$-expansion of form factor sums for dynamical correlations in the Lieb-Liniger model
• Correlation functions of one-dimensional strongly interacting two-component gases
• Out-of-equilibrium dynamics of the XY spin chain from form factor expansion
• XXZ spin-1/2 representation of a finite-U Bose-Hubbard chain at half-integer filling
• Entanglement and magnetic order
• On the absorption of microwaves by the one-dimensional spin-1/2 Heisenberg-Ising magnet
• On the calculation of the correlation functions of the ${\mathfrak{sl}}_3$-model by means of the reduced qKZ equation
• On the theory of microwave absorption by the spin-1/2 Heisenberg-Ising magnet
• Accurate localization of Kosterlitz-Thouless-type quantum phase transitions for one-dimensional spinless fermions
• Divide and conquer the Hilbert space of translation-symmetric spin systems
• Detecting quantum critical points at finite temperature via quantum teleportation
• Detecting quantum critical points at finite temperature via quantum teleportation: further models
• Thermodynamics and short-range correlations of the XXZ chain close to its triple point
• Current mean values in the XYZ model
• Finite temperature detection of quantum critical points: a comparative study
• Anisotropic magnetic interactions and spin dynamics in the spin-chain compound Cu(py)${}_2$Br${}_2$: An experimental and theoretical study
• Finite temperature detection of quantum critical points via internal quantum teleportation
• Teleportation based detection of quantum critical points using small spin chains
• Fourth-neighbour two-point functions of the XXZ chain and the Fermionic basis approach