Thermodynamics of the spin-1/2 chain: Limiting cases

Andreas Klümper, Christian Scheeren

Lu, Ping

The quasiparticle composition of the eigenstates of quantum spin chains with nearest-neighbor exchange coupling subject to strong axial anisotropy is the focus of this dissertation. Complementary sets of quasiparticles are generated from opposite ends of the spectrum for the systematic generation of all eigenstates. The exclusion statistics of all quasiparticles thus introduced are determined exactly and used, in selected cases, for the exact thermodynamic analysis of the underlying spin chain model. This project starts from the Ising model with spin s = 1/2 and then branches out to the spin s = 1/2 XXZ model in the axial regime and to the spin s = 1 Ising model. In the s = 1/2 Ising case, the two complementary sets of quasiparticles are antiferromagnetic domain walls (solitons) and ferromagnetic domains (strings). In the s = 1 Ising case, they are soliton pairs and nested strings, respectively. The string quasiparticles of the s = 1/2 Ising chains are identified as limiting cases of Bethe ansatz solutions of the axial XXZ model. The thermodynamics of the Ising chain for s 1/2 is shown to be equivalent to that of a system of two species of solitons and for s = 1 to that of a system of six species of soliton pairs. Solitons exist on single bonds but soliton pairs may be spread across many bonds. The thermodynamics of a system of domains spanning up to M lattice sites is amenable to exact analysis and shown to become equivalent, in the limit M → ∞, to the thermodynamics of the s = 1/2 Ising chain. A relation is presented between the solitons in the Ising limit and the spinons in the XX limit of the s = 1/2 XXZ chain. The exclusion statistics is semionic for both spinons and solitons but the spinon vacuum is unique whereas the soliton vacuum is twofold with broken symmetry.

Rob Klabbers

We study the thermodynamic behaviour of Inozemtsev's long-range elliptic spin chain using the Bethe ansatz equations describing the spectrum of the model in the infinite-length limit. We classify all solutions of these equations in that limit and argue which of these solutions determine the spectrum in the thermodynamic limit. Interestingly, some of the solutions are not selfconjugate, which puts the model in sharp contrast to one of the model's limiting cases, the Heisenberg xxx spin chain. Invoking the string hypothesis we derive the thermodynamic Bethe ansatz equations (TBA-equations) from which we determine the Helmholtz free energy in thermodynamic equilibrium and derive the associated Y-system. We corroborate our results by comparing numerical solutions of the TBA-equations to a direct computation of the free energy for the finite-length hamiltonian. In addition we confirm numerically the interesting conjecture put forward by Finkel and González-López that the original and supersymmetric versions of Inozemtsev's elliptic spin chain are equivalent in the thermodynamic limit.

Alessandro Cuccoli, V. Tognetti, Ruggero Vaia +1 more

Paul B. Slater

Kang Hao Lee, Vinitha Balachandran, Dario Poletti

Balachandran et al. [Phys. Rev. Lett. 120, 200603 (2018)PRLTAO0031-900710.1103/PhysRevLett.120.200603] presented a segmented XXZ spin chain with zero anisotropy in one half and a large anisotropy on the other half that gave rise to a spin current rectification which is perfect in the thermodynamic limit. Here we extend the previous study to segmented chains with interacting integrable as well as nonintegrable halves, considering even cases in which no ballistic transport can emerge in either half. We demonstrate that, also in this more general case, it is possible to obtain giant rectification when the two interacting half chains are sufficiently different. We also show that the mechanism causing this effect is the emergence of an energy gap in the excitation spectrum of the out-of-equilibrium insulating steady state in one of the two biases. Finally, we demonstrate that in the thermodynamic limit there is no perfect rectification when each of the two half chains is interacting.