Quantum phase transitions in the exactly solved spin-1/2 Heisenberg–Ising ladder

Verkholyak, Taras; Strečka, Jozef

doi:10.1088/1751-8113/45/30/305001

Cited by 18 publications

(34 citation statements)

References 70 publications

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“…Frustrated spin ladders accounting for the crossing (next-nearest-neighbor) interaction were also intensively studied, some recent rigorous results for a ground-state phase diagram of the spin-1/2 Ising-Heisenberg ladder of this type can be found in Refs. [17,18]. Exact ground states were also found for a frustrated spin-1/2 Ising-Heisenberg ladder with the Heisenberg inter-leg coupling, the Ising intra-leg and crossing couplings.…”

Section: Introductionmentioning

confidence: 86%

Thermal entanglement and sharp specific-heat peak in an exactly solved spin-1/2 Ising-Heisenberg ladder with alternating Ising and Heisenberg inter–leg couplings

Rojas

Strečka

Souza

2016

Solid State Communications

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The spin-1/2 Ising-Heisenberg two-leg ladder accounting for alternating Ising and Heisenberg inter-leg couplings in addition to the Ising intra-leg coupling is rigorously mapped onto to a mixed spin-(3/2,1/2) Ising-Heisenberg diamond chain with the nodal Ising spins S = 3/2 and the interstitial spin-1/2 Heisenberg dimers. The latter effective model with higher-order interactions between the nodal and interstitial spins is subsequently exactly solved within the transfer-matrix method. The model under investigation exhibits five different ground states: ferromagnetic, antiferromagnetic, superantiferromagnetic and two types of frustrated ground states with a non-zero residual entropy. A detailed study of thermodynamic properties reveals an anomalous specific-heat peak at low enough temperatures, which is strongly reminiscent because of its extraordinary height and sharpness to an anomaly accompanying a phase transition. It is convincingly evidenced, however, that the anomalous peak in the specific heat is finite and it comes from vigorous thermal excitations from a two-fold degenerate ground state towards a macroscopically degenerate excited state. Thermal entanglement between the nearest-neighbor Heisenberg spins is also comprehensively explored by taking advantage of the concurrence. The threshold temperature delimiting a boundary between the entangled and disentangled parameter space may show presence of a peculiar temperature reentrance.

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Section: Introductionmentioning

confidence: 86%

Thermal entanglement and sharp specific-heat peak in an exactly solved spin-1/2 Ising-Heisenberg ladder with alternating Ising and Heisenberg inter–leg couplings

Rojas

Strečka

Souza

2016

Solid State Communications

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“…which can be alternatively viewed as a special case of the frustrated spin-1/2 Heisenberg-Ising ladders exactly solved in the recent works [14][15][16]. Therefore, it is sufficient to closely follow the approach elaborated in Ref.…”

Section: Model and Its Solutionmentioning

confidence: 98%

Enhanced magnetoelectric effect near a field-driven zero-temperature quantum phase transition of the spin-1/2 Heisenberg-Ising ladder

Strečka¹,

Gálisová²,

Verkholyak³

2020

Phys. Rev. E

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Magnetoelectric effect of the spin-1/2 Heisenberg-Ising ladder in a presence of the external electric and magnetic fields is rigorously examined by taking into account Katsura-Nagaosa-Balatsky mechanism. It is shown that the applied electric field may control a quantum phase transition between the Néel (stripy) ordered phase and the disordered paramagnetic phase. The staggered magnetization vanishes according to a power law with the Ising-type critical exponent 1/8, the electric polarization exhibits a weak singularity and the dielectric susceptibility shows a logarithmic divergence at this particular quantum phase transition. The external electric field may alternatively invoke a discontinuous phase transition accompanied with abrupt jumps of the dielectric polarization and susceptibility on assumption that the external magnetic field becomes nonzero.

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“…It is quite apparent from this figure that the Heisenberg coupling is assigned to all common edges shared by neighboring tetrahedra, while all other edges schematically represent the Ising interaction. The Ising-Heisenberg tetrahedral chain can be alternatively viewed as a special case of the frustrated Ising-Heisenberg two-leg ladder [36,37] with the Heisenberg intra-rung interaction and uniform Ising coupling along legs and diagonals, respectively (see Fig. 1(b)).…”

Section: Ising-heisenberg Tetrahedral Chainmentioning

confidence: 99%

Magnetization process, bipartite entanglement, and enhanced magnetocaloric effect of the exactly solved spin-1/2 Ising-Heisenberg tetrahedral chain

et al. 2014

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The frustrated spin-1/2 Ising-Heisenberg ladder with Heisenberg intra-rung and Ising inter-rung interactions is exactly solved in a longitudinal magnetic field by taking advantage of the local conservation of the total spin on each rung and the transfer-matrix method. We have rigorously calculated the ground-state phase diagram, magnetization process, magnetocaloric effect and basic thermodynamic quantities for the model, which can be alternatively viewed as an Ising-Heisenberg tetrahedral chain. It is demonstrated that a stepwise magnetization curve with an intermediate plateau at a half of the saturation magnetization is also reflected in respective stepwise changes of the concurrence serving as a measure of bipartite entanglement. The ground-state phase diagram and zero-temperature magnetization curves of the Ising-Heisenberg tetrahedral chain are contrasted with the analogous results of the purely quantum Heisenberg tetrahedral chain, which have been obtained through density-matrix renormalization group (DMRG) calculations. While both groundstate phase diagrams fully coincide in the regime of weak inter-rung interaction, the purely quantum Heisenberg tetrahedral chain develops Luttinger spin-liquid and Haldane phases for strongly coupled rungs which are absent in the Ising-Heisenberg counterpart model.

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Quantum phase transitions in the exactly solved spin-1/2 Heisenberg–Ising ladder

Cited by 18 publications

References 70 publications

Thermal entanglement and sharp specific-heat peak in an exactly solved spin-1/2 Ising-Heisenberg ladder with alternating Ising and Heisenberg inter–leg couplings

Thermal entanglement and sharp specific-heat peak in an exactly solved spin-1/2 Ising-Heisenberg ladder with alternating Ising and Heisenberg inter–leg couplings

Enhanced magnetoelectric effect near a field-driven zero-temperature quantum phase transition of the spin-1/2 Heisenberg-Ising ladder

Magnetization process, bipartite entanglement, and enhanced magnetocaloric effect of the exactly solved spin-1/2 Ising-Heisenberg tetrahedral chain

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