Asymptotic form of two-point correlation function of the XXZ spin chain
نویسنده
چکیده
Correlation functions of the XXZ spin chain in the critical regime is studied at zerotemperature. They are exactly represented in the Fredholm determinant form and are related with an operator-valued Riemann–Hilbert problem. Analyzing this problem we prove that a two-point correlation function consisting of sufficiently separated spin operators is expressed by power-functions of the distance between those operators.
منابع مشابه
String correlation functions of the spin-1/2 Heisenberg XXZ chain
We calculate certain string correlation functions, originally introduced as order parameters in integer spin chains, for the spin-1/2 XXZ Heisenberg chain at zero temperature and in the thermodynamic limit. For small distances, we obtain exact results from Bethe Ansatz and exact diagonalization, whereas in the large-distance limit, field-theoretical arguments yield an asymptotic algebraic decay...
متن کاملDensity matrix elements and entanglement entropy for the spin - 1 / 2 XXZ chain at ∆ = 1 / 2
We have analytically obtained all the density matrix elements up to six lattice sites for the spin-1/2 Heisenberg XXZ chain at ∆ = 1/2. We use the multiple integral formula of the correlation function for the massless XXZ chain derived by Jimbo and Miwa. As for the spin-spin correlation functions, we have newly obtained the fourthand fifth-neighbour transverse correlation functions. We have cal...
متن کاملCorrelation amplitude for the XXZ spin chain in the disordered regime
We proposed an analytical expression for the amplitude defining the long distance asymptotic of the correlation function 〈 σ kσ k+n 〉.
متن کاملThird-neighbor and other four-point correlation functions of spin-1/2 XXZ chain
The correlation functions of the spin-1/2 XXZ chain in the ground state were ex-pressed in the form of multiple integrals for −1 < ∆ ≤ 1 and 1 < ∆. In particular,adjacent four-point correlation functions were given as certain four-dimensional inte-grals. We show that these integrals can be reduced to polynomials with respect tospecific one-dimensional integrals. The results ...
متن کاملDensity matrix for the kink ground state of the ferromagnetic XXZ chain.
The exact expression for the density matrix of the kink ground state of the ferromagnetic XXZ chain is obtained. Utilizing this, we exactly calculate various correlation functions such as the longitudinal and transverse spin-spin correlation functions, and the ferromagnetic and antiferromagnetic string formation probabilities. The asymptotic behaviors of these correlation functions are also ana...
متن کامل