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arXiv:0706.2477 · physica status solidi (b)

Spin–orbital entanglement near quantum phase transitions

Andrzej M. Oleś, Peter Horsch, Giniyat Khaliullin

Published Apr 26, 2007• 11 citations
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Abstract

Abstract Spin–orbital entanglement in the ground state of a one‐dimensional SU(2) ⊗ SU(2) spin–orbital model is analyzed using exact diagonalization of finite chains. For S = 1/2 spins and T = 1/2 pseudospins one finds that the quantum entanglement is similar at the SU(4) symmetry point and in the spin–orbital valence bond state. We also show that quantum transitions in spin–orbital models turn out to be continuous under certain circumstances, in constrast to the discontinuous transitions in spin models with SU(2) symmetry. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

DOI
10.1002/pssb.200674619

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physica status solidi (b)•Oct 28, 2005•2 citations
Abstract Spin–orbital entanglement in the ground state of a one‐dimensional SU(2) ⊗ SU(2) spin–orbital model is analyzed using exact diagonalization of finite chains. For S = 1/2 spins and T = 1/2 pseudospins one finds that the quantum entanglement is similar at the SU(4) symmetry point and in the spin–orbital valence bond state. We also show that quantum transitions in spin–orbital models turn out to be continuous under certain circumstances, in constrast to the discontinuous transitions in spin models with SU(2) symmetry. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Spin-orbital entanglement in quantum spin-orbital systems is quantified by a specifically reduced von Neumann entropy and is calculated for the ground state of a coupled spin-orbital chain with $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ symmetry. By analyzing the discontinuity and local extreme of the reduced entropy, we deduce a rich phase diagram describing quantum phase transitions in this system with complex correlations between multiple degrees of freedom.
Abstract Spin‐entanglement of two electrons occupying two spatial regions – domains – is expressed in a compact form in terms of spin‐spin correlation functions. The power of the formalism is demonstrated on several examples ranging fromgeneration of entanglement by scattering of two electrons to the entanglement of a pair of qubits represented by a double quantum dot coupled to leads. In the latter case the collapse of entanglement due to the Kondo effect is analyzed (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
In this work we analyzed the ground-state symmetry for the cases of two particles in a linear Fibonacci chain, using the generalized Hubbard Hamiltonian and a previously developed real-space mapping method. The method is based on mapping the correlated many-body problem onto an equivalent site-and bond-impurity one-body problem in a higher dimensional space, where the problem can be solved exactly. For the case of two particles, it is obtained a ground-state when the correlated hopping interactions are included. The two particle problem is analyzed by looking at the phase diagram for the bound state. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Abstract A recently developed numerical method, based on the modification of exact diagonalization calculations, is used to study the ground‐state properties of the spinless Falicov–Kimball model on the triangular lattice. The phase diagram as well as the valence and metal–insulator transitions are analysed and compared with results of the conventional Falicov–Kimball model on the square lattice. It is shown that the different cluster geometry leads to various changes in basic characteristics of the model. In particular, the triangular lattice destroys the symmetry of the phase diagram as well as the valence transitions, and stabilizes the new types of spatial charge ordering – the axial stripes and the phase separated distributions of localized f ‐electrons. Studying the conducting properties of the Falicov–Kimball model on the triangular lattice, the Mott‐Hubbard transition has been observed. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
We investigate the phase diagram and the spin-orbital entanglement of a one-dimensional $\mathrm{SU}(2)\phantom{\rule{0.16em}{0ex}}\ensuremath{\bigotimes}\phantom{\rule{0.16em}{0ex}}\text{XXZ}$ model with SU(2) spin exchange and anisotropic XXZ\text{XXZ}XXZ orbital exchange interactions and negative exchange coupling constant. As a unique feature, the spin-orbital entanglement entropy in the entangled ground states increases here linearly with system size. In the case of Ising orbital interactions, we identify an emergent phase with long-range spin-singlet dimer correlations triggered by a quadrupling of correlations in the orbital sector. The peculiar translational-invariant spin-singlet dimer phase has finite von Neumann entanglement entropy and survives when orbital quantum fluctuations are included. It even persists in the isotropic $\mathrm{SU}(2)\phantom{\rule{0.16em}{0ex}}\ensuremath{\bigotimes}\phantom{\rule{0.16em}{0ex}}\text{SU}$(2) limit. Surprisingly, for finite transverse orbital coupling, the long-range spin-singlet correlations also coexist in the antiferromagnetic spin and alternating orbital phase making this phase also unconventional. Moreover, we also find a complementary orbital singlet phase that exists in the isotropic case but does not extend to the Ising limit. The nature of entanglement appears essentially different from that found in the frequently discussed model with positive coupling. Furthermore, we investigate the collective spin and orbital wave excitations of the disentangled ferromagnetic-spin/ferro-orbital ground state and explore the continuum of spin-orbital excitations. Interestingly, one finds among the latter excitations two modes of exciton bound states. Their spin-orbital correlations differ from the remaining continuum states and exhibit logarithmic scaling of the von Neumann entropy with increasing system size. We demonstrate that spin-orbital excitons can be experimentally explored using resonant inelastic x-ray scattering, where the strongly entangled exciton states can be easily distinguished from the spin-orbital continuum.
Abstract A spin‐½ XX chain with three‐spin and uniform long‐range interactions among the z components of the spins is constructed. Based upon the model, using the Jordan–Wigner transformation, the thermodynamic quantities and spin transports of the system are evaluated exactly. The phase diagram together with the key parameters characterizing quantum phase transitions is presented. It is noted that, similarly to classical first‐order phase transitions, there are also the metastable states “supercooled” and “superheated” in the first‐order quantum phase transitions. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)