By John B. Parkinson

The subject of lattice quantum spin structures is an engaging and through now well-established department of theoretical physics. despite the fact that, many vital questions stay to be responded. Their intrinsically quantum mechanical nature and the big (usually successfully limitless) variety of spins in macroscopic fabrics usually results in unforeseen or counter-intuitive effects and insights. Spin platforms are usually not basically the elemental types for an entire host of magnetic fabrics yet also they are vital as prototypical types of quantum structures. Low dimensional platforms (as taken care of during this primer), in 2nd and particularly 1D, were rather fruitful simply because their simplicity has enabled detailed strategies to be made up our minds in lots of situations. those specific ideas include many hugely nontrivial positive factors. This e-book was once encouraged by means of a collection of lectures on quantum spin platforms and it really is set at a degree of useful aspect that's lacking in different textbooks within the quarter. it is going to advisor the reader during the foundations of the sector. specifically, the recommendations of the Heisenberg and XY types at 0 temperature utilizing the Bethe Ansatz and the Jordan-Wigner transformation are coated in a few aspect. using approximate tools, either theoretical and numerical, to take on extra complicated themes is taken into account. the ultimate bankruptcy describes a few very fresh purposes of approximate tools which will express a number of the instructions during which the learn of those platforms is presently developing.

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Phys. Rev. : Phys. Rev. : Prog. Theor. Phys. : Phys. Rev. Lett. : Europhys. Lett. 9, 815–820 (1989) 46 47 Chapter 5 Antiferromagnetic Spin Waves Abstract The ground state of the antiferromagnetic spin-1/2 linear chain is a made up of a linear combination of basis states with exactly half (N /2) the spins reversed. The elementary excitations from the ground state have N /2 ± 1 spins reversed. To calculate the energies of these states, des Cloiseaux and Pearson used a modified version of the same method that Hulthén had used for the ground state energy.

10) this implies eik1 N eik2 N = 1 so (k1 + k2 )N = λ2π and therefore where λ is an integer, k1 + k2 = λ 2π . 17) k1 + k1 is the total wavevector, and the fact that this has to be an integer multiple of 2π/N merely reflects the translational symmetry. More interestingly, however, we also have f 2 , 1 +N = f 1, 2 since the ( 1 + N )’th site is the same as the 1 ’th site and our convention is that the second subscript is always greater than the first. 12) gives eik1 2 eik2 ( 1 +N ) eiφ/2 +eik2 2 eik1 ( 1 +N ) e−iφ/2 = eik1 1 eik2 2 eiφ/2 +eik2 1 eik1 2 e−iφ/2 .

Theor. Phys. : Phys. Rev. Lett. : Europhys. Lett. 9, 815–820 (1989) 46 47 Chapter 5 Antiferromagnetic Spin Waves Abstract The ground state of the antiferromagnetic spin-1/2 linear chain is a made up of a linear combination of basis states with exactly half (N /2) the spins reversed. The elementary excitations from the ground state have N /2 ± 1 spins reversed. To calculate the energies of these states, des Cloiseaux and Pearson used a modified version of the same method that Hulthén had used for the ground state energy.