Characterization of quantum correlations in low-dimensional molecular magnetic systems

Two different generalization schemes for the molecular field approximation are described. Both contain the possibility to incorporate generalized effective fields that induce correlations between the degrees of freedom at the boundary of a chosen cluster. Applications are presented for low-dimensional spin-1/2 systems. For the Ising models the critical couplings and critical exponents as well as the spontaneous magnetization curve are determined. An application of the method to the quantum $S$ = $\frac{1}{2}$ one-dimensional Heisenberg model is presented and reliable low-temperature estimates of the specific heat are evaluated. The data are combined with the quantum transfer matrix predictions for large system sizes and this leads to the following prediction for the low-temperature specific heat: ${C=AT}^{\ensuremath{\alpha}}$ with $\ensuremath{\alpha}=0.35\ifmmode\pm\else\textpm\fi{}0.07$.Two different generalization schemes for the molecular field approximation are described. Both contain the possibility to incorporate generalized effective fields that induce correlations between the degrees of freedom at the boundary of a chosen cluster. Applications are presented for low-dimensional spin-1/2 systems. For the Ising models the critical couplings and critical exponents as well as the spontaneous magnetization curve are determined. An application of the method to the quantum $S$=$\frac{1}{2}$ one-dimensional Heisenberg model is presented and reliable low-temperature estimates of the specific heat are evaluated. The data are combined with the quantum transfer matrix predictions for large system sizes and this leads to the following prediction for the low-temperature specific heat: ${C=AT}^{\ensuremath{\alpha}}$ with $\ensuremath{\alpha}=0.35\ifmmode\pm\else\textpm\fi{}0.07$.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsJul 1, 19977 citations

Novel quantum magnetic states in low dimensions

Peng Li

Jan 1, 20060 citations

Experimental observation of quantum entanglement in low-dimensional spin systems

Tatiana G. Rappoport, L. Ghivelder, J. C. Fernandes +2 more

We report macroscopic magnetic measurements carried out in order to detect and characterize field-induced quantum entanglement in low-dimensional spin systems. We analyze the pyroborate $\mathrm{Mg}\mathrm{Mn}{\mathrm{B}}_{2}{\mathrm{O}}_{5}$ and the warwickite $\mathrm{Mg}\mathrm{Ti}\mathrm{O}\mathrm{B}{\mathrm{O}}_{3}$ , systems with spin $5∕2$ and $1∕2$ , respectively. By using the magnetic susceptibility as an entanglement witness we are able to quantify entanglement as a function of temperature and magnetic field. In addition, we experimentally distinguish a system exhibiting a random singlet-phase state from one with the Griffiths phase. This analysis opens the possibility of a more detailed characterization of low-dimensional materials.We report macroscopic magnetic measurements carried out in order to detect and characterize field-induced quantum entanglement in low-dimensional spin systems. We analyze the pyroborate $\mathrm{Mg}\mathrm{Mn}{\mathrm{B}}_{2}{\mathrm{O}}_{5}$ and the warwickite $\mathrm{Mg}\mathrm{Ti}\mathrm{O}\mathrm{B}{\mathrm{O}}_{3}$, systems with spin $5∕2$ and $1∕2$, respectively. By using the magnetic susceptibility as an entanglement witness we are able to quantify entanglement as a function of temperature and magnetic field. In addition, we experimentally distinguish a system exhibiting a random singlet-phase state from one with the Griffiths phase. This analysis opens the possibility of a more detailed characterization of low-dimensional materials.

arXiv:cond-mat/0608403Physical Review BFeb 28, 200763 citations

S

\frac{1}{2}

one-dimensional Heisenberg model is presented and reliable low-temperature estimates of the specific heat are evaluated. The data are combined with the quantum transfer matrix predictions for large system sizes and this leads to the following prediction for the low-temperature specific heat: ${C=AT}^{\ensuremath{\alpha}}$ with $\ensuremath{\alpha}=0.35\ifmmode\pm\else\textpm\fi{}0.07$.

We report macroscopic magnetic measurements carried out in order to detect and characterize field-induced quantum entanglement in low-dimensional spin systems. We analyze the pyroborate

\mathrm{Mg}\mathrm{Mn}{\mathrm{B}}_{2}{\mathrm{O}}_{5}

and the warwickite

\mathrm{Mg}\mathrm{Ti}\mathrm{O}\mathrm{B}{\mathrm{O}}_{3}

, systems with spin

5∕2

and

1∕2

, respectively. By using the magnetic susceptibility as an entanglement witness we are able to quantify entanglement as a function of temperature and magnetic field. In addition, we experimentally distinguish a system exhibiting a random singlet-phase state from one with the Griffiths phase. This analysis opens the possibility of a more detailed characterization of low-dimensional materials.