We start this article by recalling the main exact results previously obtained for describing the static magnetic properties of 2d square lattices composed of classical spins isotropically coupled between first-nearest neighbors (i.e., showing Heisenberg couplings) [4c]. Near the critical temperature TC= 0 K we give criterions allowing to directly determine the magnetic phases characterizing 2d magnetic compounds described by our microscopic model. We show that there are three distinct regimes: The Renormalized Classical Regime (RCR), the Quantum Disordered Regime (QDR) and the Quantum Critical Regime (QCR). The static properties give a good image of the spin arrangement and thus remain a good starting point for the study of dynamic properties. As a result, inside each of the three regimes, we may derive the corresponding dynamic behaviors. For practical reasons that we shall detail, we restrict our study to the RCR and QCR cases. An experimental test is given for illustrating this theoretical work. We notably show that it allows one to derive the static correlation length which is an important tool for understanding both static and dynamic properties.
Magnetic molecules are prototypical systems to investigate peculiar quantum mechanical phenomena. As such, simulating their static and dynamical behavior is intrinsically difficult for a classical computer, due to the exponential increase of required resources with the system size. Quantum computers solve this issue by providing an inherently quantum platform, suited to describe these magnetic systems. Here, we show that both the ground state properties and the spin dynamics of magnetic molecules can be simulated on prototype quantum computers, based on superconducting qubits. In particular, we study small-size anti-ferromagnetic spin chains and rings, which are ideal test-beds for these pioneering devices. We use the variational quantum eigensolver algorithm to determine the ground state wave-function with targeted ansatzes fulfilling the spin symmetries of the investigated models. The coherent spin dynamics are simulated by computing dynamical correlation functions, an essential ingredient to extract many experimentally accessible properties, such as the inelastic neutron cross-section.
The static and dynamic properties of the anisotropic
XY model
(s=1∕2) on the inhomogeneous periodic chain, composed of
N cells with
n different exchange interactions and magnetic moments, in a transverse field
h, are determined exactly at arbitrary temperatures. The properties are obtained by introducing the Jordan-Wigner fermionization and by reducing the problem to a diagonalization of a finite matrix of
nth order. The quantum transitions are determined exactly by analyzing, as a function of the field, the induced magnetization $1∕n{\ensuremath{\sum}}_{m=1}^{n}{\ensuremath{\mu}}_{m}⟨{S}_{j,m}^{z}⟩$ (
j denotes the cell,
m the site within the cell, ${\ensuremath{\mu}}_{m}$ the magnetic moment at site
m within the cell) and the spontaneous magnetization $1∕n{\ensuremath{\sum}}_{m=1}^{n}⟨{S}_{j,{m}^{\ensuremath{'}}}^{x}⟩$ which is obtained from the correlations
⟨Sj,mxSj+r,mx⟩ for large spin separations. These results, which are obtained for infinite chains, correspond to an extension of the ones obtained by Tong and Zhong [Physica B 304, 91 (2001)]. The dynamic correlations, $⟨{S}_{j,m}^{z}(t){S}_{{j}^{\ensuremath{'}},{m}^{\ensuremath{'}}}^{z}(0)⟩$, and the dynamic susceptibility, ${\ensuremath{\chi}}_{q}^{zz}(\ensuremath{\omega})$, are also obtained at arbitrary temperatures. Explicit results are presented in the limit
T=0, where the critical behavior occurs, for the static susceptibility ${\ensuremath{\chi}}_{q}^{zz}(0)$ as a function of the transverse field
h, and for the frequency dependency of dynamic susceptibility ${\ensuremath{\chi}}_{q}^{zz}(\ensuremath{\omega})$.