Next Nearest-Neighbor Correlation Functions of the Spin-1/2 XXZ Chain at Critical Region

Abstract

The correlation functions of the spin-1/2 XXZ spin chain in the ground state are expressed in the form of the multiple integrals. For -1< Delta <1, they were obtained by Jimbo and Miwa in 1996. Especially the next nearest-neighbour correlation functions are given as certain three-dimensional integrals. We shall show these integrals can be reduced to one-dimensional ones and thereby evaluate the values of the next nearest-neighbor correlation functions. We have also found that the remaining one-dimensinal integrals can be evaluated analytically, when nu = arccos(Delta)/pi is a rational number.

10 pages, 2 figures

References in corpus (4)

• Long-distance asymptotics of spin-spin correlation functions for the XXZ spin chain
• Emptiness Formation Probability and Quantum Knizhnik-Zamolodchikov Equation
• Large distance asymptotic behavior of the emptiness formation probability of the XXZ spin-1/2 Heisenberg chain
• On the probability of ferromagnetic strings in antiferromagnetic spin chains

Cited by in corpus (27)

• Quantum discord and quantum phase transition in spin chains
• Computation of dynamical correlation functions of Heisenberg chains: the gapless anisotropic regime
• Algebraic representation of correlation functions in integrable spin chains
• Correlation and nonlocality measures as indicators of quantum phase transitions in several critical systems
• 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
• Weakly anisotropic frustrated zigzag spin chain
• Solving condensed-matter ground-state problems by semidefinite relaxations
• Third-neighbor and other four-point correlation functions of spin-1/2 XXZ chain
• Permutation operators, entanglement entropy, and the XXZ spin chain in the limit Δ-> -1
• Short-distance thermal correlations in the XXZ chain
• Correlation functions of the spin-1/2 anti-ferromagnetic Heisenberg chain: exact calculation via the generating function
• Analytical Bethe Ansatz for closed and open gl(n)-spin chains in any representation
• Exact thermodynamic limit of short-range correlation functions of the antiferromagnetic $XXZ$-chain at finite temperatures
• First principle approach to correlation functions of spin-1/2 Heisenberg chain : fourth-neighbor correlators
• A Q-Operator Identity for the Correlation Functions of the Infinite XXZ Spin-Chain
• Next Nearest-Neighbor Correlation Functions of the Spin-1/2 XXZ Chain at Massive Region
• Exact evaluation of density matrix elements for the Heisenberg chain
• Density matrix elements and entanglement entropy for the spin-1/2 XXZ chain at $\Delta$=1/2
• Intrinsic Jump Character of the First-Order Quantum Phase Transitions
• Finite temperature density matrix and two-point correlations in the antiferromagnetic XXZ chain
• XX and Ising limits in integral formulae for finite temperature correlation functions of the XXZ chain
• Exact results for the sigma^z two-point function of the XXZ chain at Delta=1/2
• The action of the Virasoro algebra in quantum spin chains. I. The non-rational case
• Quantum Statistical Complexity Measure as a Signalling of Correlation Transitions
• Time dynamics of Bethe ansatz solvable models
• High accuracy energy formulas for the attractive two-site Bose-Hubbard model