Exact results for the \(\sigma^z\) two-point function of the \(XXZ\) chain at \(\Delta = 1/2\\). (English) Zbl 1459.82048
Summary: We propose a new multiple-integral representation for the correlation function \(\langle \sigma_1^z\sigma_{m+1}^z\rangle\) of the \(XXZ\) spin-\( \frac{1}{2}\) Heisenberg chain in the disordered regime. We show that for \(\Delta = 1/2\) the integrals can be separated and computed exactly. As an example we give the explicit results up to the lattice distance \(m = 8\). It turns out that the answer is given as integer numbers divided by \(2^{(m+1)^2}\).
MSC:
| 82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
Keywords:
correlation functions; integrable spin chains (vertex models); quantum integrability (Bethe ansatz)References:
| [1] | Heisenberg W 1928 Z. Physik49 619 · JFM 54.0979.02 · doi:10.1007/BF01328601 |
| [2] | Razumov A V and Stroganov Y G 2001 J. Phys. A: Math. Gen.34 3185 [cond-mat/0012141] · Zbl 0995.82505 |
| [3] | Kitanine N, Maillet J M, Slavnov N A and Terras V 2002 J. Phys. A: Math. Gen.35 L385 [hep-th/0201134] · Zbl 1043.82004 |
| [4] | Jimbo M, Miki K, Miwa T and Nakayashiki A 1992 Phys. Lett. A 168 256 · doi:10.1016/0375-9601(92)91128-E |
| [5] | Jimbo M and Miwa T 1996 J. Phys. A: Math. Gen.29 2923 · Zbl 0896.35114 |
| [6] | Kitanine N, Maillet J M and Terras V 2000 Nucl. Phys. B 567 554 [math-ph/9907019] · Zbl 0955.82010 · doi:10.1016/S0550-3213(99)00619-7 |
| [7] | Kitanine N, Maillet J M, Slavnov N A and Terras V 2002 Nucl. Phys. B 641 487 [hep-th/0201045] · Zbl 0998.82008 · doi:10.1016/S0550-3213(02)00583-7 |
| [8] | Izergin A G and Korepin V E 1985 Commun. Math. Phys.99 271 · Zbl 1094.82503 · doi:10.1007/BF01212283 |
| [9] | Shiroishi M, Takahashi M and Sakai K 2003 J. Phys. A: Math. Gen.36 L337 [cond-mat/0304475] |
| [10] | Shiroishi M, Takahashi M and Sakai K 2004 J. Phys. A: Math. Gen.37 5097 [cond-mat/0402625] · Zbl 1047.82005 |
| [11] | Lukyanov S 1999 Phys. Rev. B 59 11163 [hep-th/9809254] · doi:10.1103/PhysRevB.59.11163 |
| [12] | Boos H, Jimbo M, Miwa T, Smirnov F and Takeyama Y 2004 A recursion formula for the correlation functions of an inhomogeneous XXX model Preprint hep-th/0405044 · Zbl 1124.82002 |
| [13] | Boos H, Jimbo M, Miwa T, Smirnov F and Takeyama Y 2004 Reduced qKZ equation and correlation functions of the XXZ model Preprint hep-th/0412191 · Zbl 1107.82006 |
| [14] | Razumov A V and Stroganov Y G 2004 Theor. Math. Phys.138 333 [math.CO/0104216] · Zbl 1178.82020 · doi:10.1023/B:TAMP.0000018450.36514.d7 |
| [15] | de Gier J, Batchelor M T, Nienhuis B and Mitra S 2002 J. Math. Phys.43 4235 [math-ph/0110011] · Zbl 1060.82012 · doi:10.1063/1.1487445 |
| [16] | Mitra S, Nienhuis B, de Gier J and Batchelor M T 2004 J. Stat. Mech. P09010 [cond-mat/0401245] |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
