arXiv:1110.2404 · Journal of Physics A Mathematical and Theoretical

Finite size emptiness formation probability of the XXZ spin chain at $\Delta =-\frac{1}{2}$

Luigi Cantini A

Published Mar 20, 2012• 19 citations

Abstract

In this paper, we compute the emptiness formation probability of a (twisted-) periodic XXZ spin chain of finite length at , thus proving the formulas conjectured by Razumov and Stroganov (2001 J. Phys. A: Math. Gen. 34 3185 and 5335–40). The result is obtained by exploiting the fact that the ground state of the inhomogeneous XXZ spin chain at satisfies a set of qKZ equations associated with .

DOI: 10.1088/1751-8113/45/13/135207

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arXiv:1110.2404 · Journal of Physics A Mathematical and Theoretical

Finite size emptiness formation probability of the XXZ spin chain at $\Delta =-\frac{1}{2}$ Finite size emptiness formation probability of the XXZ spin chain at $\Delta =-\frac{1}{2}$

Luigi Cantini A

Published Mar 20, 2012• 19 citations

arXiv HTML PDF

Abstract

DOI: 10.1088/1751-8113/45/13/135207

Related papers

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Finite size emptiness formation probability of the XXZ spin chain at

\Delta =-\frac{1}{2}

We study the one-dimensional

S=\frac{1}{2}

XXZ

model on a finite lattice at zero temperature, varying the exchange anisotropy $\ensuremath{\Delta}$ and the number of sites

N

of the lattice. Special emphasis is given to the model with $\ensuremath{\Delta}=\frac{1}{2}$ and

N

odd, whose ground state, the so-called Razumov-Stroganov state, has a peculiar structure and no finite-size corrections to the energy per site. We find that such model corresponds to a special point on the $\ensuremath{\Delta}$ axis which separates the region where adding spin-pairs increases the energy per site from that where the longer the chain the lower the energy. Entanglement properties do not hold surprises for $\ensuremath{\Delta}=\frac{1}{2}$ and

N

odd. Finite-size corrections to the energy per site non trivially vanish also in the ferromagnetic $\ensuremath{\Delta}\ensuremath{\rightarrow}\ensuremath{-}{1}^{+}$ isotropic limit, which is consequently addressed; in this case, peculiar features of some entanglement properties, due to the finite length of the chain and related with the change in the symmetry of the Hamiltonian, are evidenced and discussed. In both the above models the absence of finite-size corrections to the energy per site is related to a peculiar structure of the ground state, which has permitted us to provide new exact analytic expressions for some correlation functions.