Correlation functions of the XXZ spin-1/2 chain: recent progress

More documents

Recommendations

Info

J. M. Maillet Correlation functionsMatrix elements of local operatorsFor example :〈0|N∏N∏C(µ j ) σ z nB(λ k ) |0〉 =j=1k=1= 〈0|N∏C(µ j )n−1∏t(ξ k ) · (A− D ) (ξ j ) ·n∏t −1 (ξ k )N∏B(λ k ) |0〉j=1k=1k=1k=1Here the sets {λ k } and {µ j } are both solutions of Bethe equations −→〈0|N∏N∏C(µ j ) σ z nB(λ k ) |0〉 = Φ n 〈0|j=1k=1N∏C(µ j ) ( A − D ) N∏(ξ j ) B(λ k ) |0〉j=1k=1Hence it leads to determinant representations of these matrix elements (using thescalar product formula)– Typeset by FoilTEX – Florence 2003 7
J. M. Maillet Correlation functionsCorrelation functions : elementary blocksj=1F m ({ɛ j , ɛ ′ j }) = 〈ψ g | m ∏E ɛ′ j ,ɛ jj|ψ g 〉〈ψ g |ψ g 〉E ɛ′ ,ɛlk= δ l,ɛ ′δ k,ɛSolution of the quantum inverse scattering problem + Yang-Baxter algebra of operatorsT (λ) −→ Multiple integral formula for the correlation functionsmF m ({ɛ j , ɛ ′ j }) = ( ∏∫k=1C h kdλ k ) Ω m ({λ k }, {ɛ j , ɛ ′ j }) S h({λ k })where Ω m ({λ k }, {ɛ j , ɛ ′ j }) is purely algebraic and S h({λ k }), C h kregime and the magnetic field h.are depending on the−→ Proof of the results and conjectures of Jimbo, Miwa et al. and extension to the nonzero magnetic field h (a case where the quantum affine symmetry is broken)– Typeset by FoilTEX – Florence 2003 8
Page 1 and 2: Correlation functions of the XXZspi
Page 3 and 4: J. M. Maillet Correlation functions
Page 7: J. M. Maillet Correlation functions

Correlation functions of the XXZ spin-1/2 chain: recent progress

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?