Algebraic properties of the 1+1 dimensional Heisenberg spin field model

Roeland Wiersema, Efekan Kökcü, Alexander F. Kemper +1 more

Much is understood about 1-dimensional spin chains in terms of entanglement properties, physical phases, and integrability. However, the Lie algebraic properties of the Hamiltonians describing these systems remain largely unexplored. In this work, we provide a classification of all Lie algebras generated by the terms of 2-local spin chain Hamiltonians, or so-called dynamical Lie algebras, on 1-dimensional linear and circular lattice structures. We find 17 unique dynamical Lie algebras. Our classification includes some well-known models such as the transverse-field Ising model and the Heisenberg chain, and we also find more exotic classes of Hamiltonians that appear new. In addition to the closed and open spin chains, we consider systems with a fully connected topology, which may be relevant for quantum machine learning approaches. We discuss the practical implications of our work in the context of variational quantum computing, quantum control and the spin chain literature.

Alf Sjölander

Taku Matsui

Hajime Yoshino, Hajime Takayama

Slow dynamics in the 3-dimensional isotropic Heisenberg spin glass (SG) model is investigated by Monte Carlo simulations. The spin autocorrelation function exhibits an exponential decay multiplied by an algebraic factor. The relaxation time of the exponential decay obeys the conventional dynamical scaling with T = 0 transition. However, the behaviour of the algebraic prefactor is rather peculiar, which may be regarded as one of the SG properties inherent in the model.

康広 藤井

Shuo Jin, Bing-Hao Xie, (1)北京航空航天大学物理系，北京 100083; (2)北京信息工程学院，北京 100101

On the linear spin-wave frame, the XYZ antiferromagnetic Heisenberg model in an external magnetic field is proposed to have an so(3,2) algebraic structure. The energy eigenvalues and the squeezed state solutions are obtained by making use of algebraic diagonalization. Some properties of the energy eigenvalues are investigated. The connection with the model of the special two-mode harmonic oscillators is also established.