Quantum phase transitions between the magnetically ordered and disordered states are studied for the two-dimensional antiferromagnetic quantum spin systems with ladder, plaquette, and mixed-spin structures. Starting with properly chosen singlet-cluster configurations, we perform the series expansion for the staggered magnetic susceptibility. The phase boundary is determined by applying the Dlog and biased Padé approximants to the staggered susceptibility thus obtained. The resulting phase diagram allows us to discuss the quantum phase transitions quantitatively, which agrees fairly well with the quantum Monte Carlo results for several cases previously studied.Quantum phase transitions between the magnetically ordered and disordered states are studied for the two-dimensional antiferromagnetic quantum spin systems with ladder, plaquette, and mixed-spin structures. Starting with properly chosen singlet-cluster configurations, we perform the series expansion for the staggered magnetic susceptibility. The phase boundary is determined by applying the Dlog and biased Padé approximants to the staggered susceptibility thus obtained. The resulting phase diagram allows us to discuss the quantum phase transitions quantitatively, which agrees fairly well with the quantum Monte Carlo results for several cases previously studied.

arXiv:cond-mat/9906240Journal of the Physical Society of JapanJul 15, 199917 citations

Quantum phase transitions in magnetic systems

Omid Nohadani

Jan 1, 20140 citations

Entanglement detection in the mixed-spin Ising–X Ymodel

Hamid Arian Zad

In the present work, we initially verify anisotropy effect on the heat capacity of a mixed-three-spin (1/2,1,1/2) system (where spins (1/2,1/2) have XY interaction and spins (1,1/2) have Ising interaction together) at finite temperatures, then, the pairwise entanglement for spins (1/2,1/2), by means of negativity (as a measure of entanglement) as a function of the temperature T, homogeneous magnetic field B, and anisotropy parameter γ is investigated. In addition, we show that one can find magnetic phase transition points for the spins (1/2,1/2) at finite temperatures and understand properly their behavior with respect to the magnetic field and the anisotropy parameter, via the negativity function. An interval of the magnetic field from the negativity diagram of the spins (1/2,1/2) is presented in which quantum phase transition occurs for the tripartite mixed-three-spin system. Finally, some new interesting entanglement witnesses are introduced by using non-degenerate perturbation theory for the mixed-three-spin system.In the present work, we initially verify anisotropy effect on the heat capacity of a mixed-three-spin (1/2,1,1/2) system (where spins (1/2,1/2) have XY interaction and spins (1,1/2) have Ising interaction together) at finite temperatures, then, the pairwise entanglement for spins (1/2,1/2), by means of negativity (as a measure of entanglement) as a function of the temperature T, homogeneous magnetic field B, and anisotropy parameter γ is investigated. In addition, we show that one can find magnetic phase transition points for the spins (1/2,1/2) at finite temperatures and understand properly their behavior with respect to the magnetic field and the anisotropy parameter, via the negativity function. An interval of the magnetic field from the negativity diagram of the spins (1/2,1/2) is presented in which quantum phase transition occurs for the tripartite mixed-three-spin system. Finally, some new interesting entanglement witnesses are introduced by using non-degenerate perturbation theory for the mixed-three-spin system.

Chinese Physics BMar 1, 20164 citations

Quantum Phase Transitions in Spin-Lattice Systems

MANFRED L. RISTIG, Khaled Abu Qasem, DAMIAN J. J. FARNELL

Jan 1, 20010 citations

Quantum phase transitions for the Haldane system in higher dimensions: A mixed-spin cluster expansion approach

Akihisa Koga, Norio Kawakami

We present a mixed-spin cluster expansion method to discuss the quantum phase transitions for the Haldane system in two and three dimensions. By mapping the $s=1$ antiferromagnetic spin model on square and cubic lattices to the equivalent mixed-spin model, we study the competition among the Haldane, the dimer, and the magnetically ordered phases. The mixed-spin cluster expansion proposed here realizes the notion of the valence bond solid in a perturbation theory. This method allows us to directly deal with the Haldane phase, which may not be reached by standard series expansion methods. The zero-temperature phase diagram is thus determined rather precisely for the two- and three-dimensional Haldane systems.We present a mixed-spin cluster expansion method to discuss the quantum phase transitions for the Haldane system in two and three dimensions. By mapping the $s=1$ antiferromagnetic spin model on square and cubic lattices to the equivalent mixed-spin model, we study the competition among the Haldane, the dimer, and the magnetically ordered phases. The mixed-spin cluster expansion proposed here realizes the notion of the valence bond solid in a perturbation theory. This method allows us to directly deal with the Haldane phase, which may not be reached by standard series expansion methods. The zero-temperature phase diagram is thus determined rather precisely for the two- and three-dimensional Haldane systems.

Physical review. B, Condensed matterMar 1, 200031 citations

We present a mixed-spin cluster expansion method to discuss the quantum phase transitions for the Haldane system in two and three dimensions. By mapping the

s=1

antiferromagnetic spin model on square and cubic lattices to the equivalent mixed-spin model, we study the competition among the Haldane, the dimer, and the magnetically ordered phases. The mixed-spin cluster expansion proposed here realizes the notion of the valence bond solid in a perturbation theory. This method allows us to directly deal with the Haldane phase, which may not be reached by standard series expansion methods. The zero-temperature phase diagram is thus determined rather precisely for the two- and three-dimensional Haldane systems.