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Journal of Physics Condensed Matter

Ground-state phase diagram, fermionic entanglement and kinetically-induced frustration in a hybrid ladder with localized spins and mobile electrons

R.C.P. Carvalho, Maria S. S. Pereira, I. N. de Oliveira, Jozef Strečka, M. L. Lyra

Published Jul 4, 2017• 8 citations
Publisher

Abstract

We introduce an exactly solvable hybrid spin-ladder model containing localized nodal Ising spins and interstitial mobile electrons, which are allowed to perform a quantum-mechanical hopping between the ladder's legs. The quantum-mechanical hopping process induces an antiferromagnetic coupling between the ladder's legs that competes with a direct exchange coupling of the nodal spins. The model is exactly mapped onto the Ising spin ladder with temperature-dependent two- and four-spin interactions, which is subsequently solved using the transfer-matrix technique. We report the ground-state phase diagram and compute the fermionic concurrence to characterize the quantum entanglement between the pair of interstitial mobile electrons. We further provide a detailed analysis of the local spin ordering including the pair and four-spin correlation functions around an elementary plaquette, as well as, the local ordering diagrams. It is shown that a complex sequence of distinct local orderings and frustrated correlations takes place when the model parameters drive the investigated system close to a zero-temperature triple coexistence point.

DOI
10.1088/1361-648x/aa7d61

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We introduce an exactly solvable hybrid spin-ladder model containing localized nodal Ising spins and interstitial mobile electrons, which are allowed to perform a quantum-mechanical hopping between the ladder's legs. The quantum-mechanical hopping process induces an antiferromagnetic coupling between the ladder's legs that competes with a direct exchange coupling of the nodal spins. The model is exactly mapped onto the Ising spin ladder with temperature-dependent two- and four-spin interactions, which is subsequently solved using the transfer-matrix technique. We report the ground-state phase diagram and compute the fermionic concurrence to characterize the quantum entanglement between the pair of interstitial mobile electrons. We further provide a detailed analysis of the local spin ordering including the pair and four-spin correlation functions around an elementary plaquette, as well as, the local ordering diagrams. It is shown that a complex sequence of distinct local orderings and frustrated correlations takes place when the model parameters drive the investigated system close to a zero-temperature triple coexistence point.
The strongly correlated spin-electron system on a diamond chain containing localized Ising spins on its nodal lattice sites and mobile electrons on its interstitial sites is exactly solved in a magnetic field using the transfer-matrix method. We have investigated in detail all available ground states, the magnetization processes, the spin-spin correlation functions around an elementary plaquette, fermionic quantum concurrence, and spin frustration. It is shown that the fermionic entanglement between mobile electrons hopping on interstitial sites and the kinetically induced spin frustration are closely related yet independent phenomena. In the ground state, quantum entanglement only appears within a frustrated unsaturated paramagnetic phase, while thermal fluctuations can promote some degree of quantum entanglement above the nonfrustrated ground states with saturated paramagnetic or classical ferrimagnetic spin arrangements.
We introduce a spin ladder model incorporating localized and delocalized spins, which is exactly solvable using the decoration-iteration and transfer-matrix techniques.Quantum correlations between delocalized spins induce an antiferromagnetic coupling between the spin chains that competes with a direct ferromagnetic exchange coupling.A resulting kinetically-driven frustration is predominant in the regime of low temperatures and large hopping amplitudes.We provide the full ground-state phase diagram, as well as the frustration diagram on distinct coupling regimes.
The degree of fermionic entanglement is examined in an exactly solvable Ising-Hubbard ladder, which involves interacting electrons on the ladder's rungs described by Hubbard dimers at half-filling on each rung, accounting for intrarung hopping and Coulomb terms. The coupling between neighboring Hubbard dimers is assumed to have an Ising-like nature. The ground-state phase diagram consists of four distinct regions corresponding to the saturated paramagnetic, the classical antiferromagnetic, the quantum antiferromagnetic, and the mixed classical-quantum phase. We have exactly computed the fermionic concurrence, which measures the degree of quantum entanglement between the pair of electrons on the ladder rungs. The effects of the hopping amplitude, the Coulomb term, temperature, and magnetic fields on the fermionic entanglement are explored in detail. It is shown that the fermionic concurrence displays a re-entrant behavior when quantum entanglement is being generated at moderate temperatures above the classical saturated paramagnetic ground state.
We study a mixed spin-(3/2, 1) ladder system with antiferromagnetic rung coupling and next-nearest-neighbor interaction. The exactly solved Ising-chain model is employed to investigate the ground-state properties and thermodynamics of the low-dimensional ladder system. Our results show that the competition between different exchange couplings brings in a large variety of ground states characterized by various values of normalized magnetization equal to 0, 1/5, 2/5, 3/5, 1. Moreover, an interesting double-peak structure is also detected in the thermal dependence of magnetic susceptibility and specific heat when the frustration comes into play. It is shown that the double-peak phenomenon at zero-field for the case of AF 2 ground-state arises from the very strong antiferromagnetic rung coupling, while other cases are attributed to the excitations induced by temperature and external field around the phase boundary.
We study a frustrated two-leg spin ladder with alternate isotropic Heisenberg and Ising rung exchange interactions, whereas, interactions along legs and diagonals are Ising-type. All the interactions in the ladder are anti-ferromagnetic in nature and induce frustration in the system. This model shows four interesting quantum phases: (i) stripe rung ferromagnetic (SRFM), (ii) stripe rung ferromagnetic with edge singlet (SRFM-E), (iii) anisotropic antiferromagnetic (AAFM), and (iv) stripe leg ferromagnetic (SLFM) phase. We construct a quantum phase diagram for this model and show that in stripe rung ferromagnet (SRFM), the same type of sublattice spins (either SSS or σσσ-type spins) are aligned in the same direction. Whereas, in anisotropic antiferromagnetic phase, both SSS and σσσ-type of spins are anti-ferromagnetically aligned with each other, two nearest SSS spins along the rung form an anisotropic singlet bond whereas two nearest σσσ spins form an Ising bond. In large Heisenberg rung exchange interaction limit, spins on each leg are ferromagnetically aligned, but spins on different legs are anti-ferromagnetically aligned. The thermodynamic quantities like Cv(T)Cv(T)Cv(T), χ(T)χ(T)χ(T) and S(T)S(T)S(T) are also calculated using the transfer matrix method for different phase. The magnetic gap in the SRFM and the SLFM can be notice from χ(T)χ(T)χ(T) and Cv(T)Cv(T)Cv(T) curves.
Ground states of the frustrated spin-1 Ising-Heisenberg two-leg ladder with Heisenberg intra-rung coupling and only Ising interaction along legs and diagonals are rigorously found by taking advantage of local conservation of the total spin on each rung.The constructed ground-state phase diagram of the frustrated spin-1 Ising-Heisenberg ladder is then compared with the analogous phase diagram of the fully quantum spin-1 Heisenberg two-leg ladder obtained by density matrix renormalization group (DMRG) calculations.Both investigated spin models exhibit quite similar magnetization scenarios, which involve intermediate plateaux at one-quarter, one-half and threequarters of the saturation magnetization.