Ground-state alternation and excitation energy of S=(1/2) linear Heisenberg antiferromagnets

Soos, Z. G.; Kuwajima, Satoru; Mihalick, Jennifer E.

doi:10.1103/physrevb.32.3124

Cited by 65 publications

(28 citation statements)

References 24 publications

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“…We find good agreement with previous results obtained from the Heisenberg spin model that predict electronic correlation enhances the instability to bond ordering. 52,51 In addition, we can see from the simulations of the symmetric lattice that the system is alternating between the two degenerate states of bond-order (see Fig 9).…”

Section: Long Range Order As Inferred By Bond Order Correlation Fmentioning

confidence: 99%

“…In order to confirm the existence of the bond ordered state, we carried out calculations on dimerized lattices (t o ± δ) whose inversion symmetry is explicitly broken, and let δ become small. QMC allows us to work with large enough lattices so as to study systems with levels of dimerization much smaller than previously feasible [31][32][33][34]51 . We find good agreement with previous results obtained from the Heisenberg spin model that predict electronic correlation enhances the instability to bond ordering.…”

Section: Long Range Order As Inferred By Bond Order Correlation Fmentioning

confidence: 99%

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Quantum Monte Carlo study of the one-dimensional ionic Hubbard model

2001

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Quantum Monte Carlo methods are used to study a quantum phase transition in a 1D Hubbard model with a staggered ionic potential (∆). Using recently formulated methods, the electronic polarization and localization are determined directly from the correlated ground state wavefunction and compared to results of previous work using exact diagonalization and Hartree-Fock. We find that the model undergoes a thermodynamic transition from a band insulator (BI) to a broken-symmetry bond ordered (BO) phase as the ratio of U/∆ is increased. Since it is known that at ∆ = 0 the usual Hubbard model is a Mott insulator (MI) with no long-range order, we have searched for a second transition to this state by (i) increasing U at fixed ∆ and (ii) decreasing ∆ at fixed U. We find no transition from the BO to MI state, and we propose that the MI state in 1D is unstable to bond ordering under the addition of any finite ionic potential ∆. In real 1D systems the symmetric MI phase is never stable and the transition is from a symmetric BI phase to a dimerized BO phase, with a metallic point at the transition.

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Section: Long Range Order As Inferred By Bond Order Correlation Fmentioning

confidence: 99%

Section: Long Range Order As Inferred By Bond Order Correlation Fmentioning

confidence: 99%

Quantum Monte Carlo study of the one-dimensional ionic Hubbard model

2001

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“…It is obvious that H AO and H FO stand for the same (translational invariant) spin Hamiltonian, and H FO will have lower ground state energy when x > − S j · S j+1 AF ≃ 0.4431. The dimerised AF Heisenberg chain (3.13) related to spin-Peierls state cannot be solved trivially, with the exception of the free-dimer limit (y = −0.25) and the uniform Heisenberg limit (y = −∞) [82], One finds the ground state energy per site ε ∞ (δ) of a pure dimerised spin chain [83],…”

Section: Ising Orbital Interactions (∆ = 0)mentioning

confidence: 99%

Quantum entanglement in the one-dimensional spin-orbitalSU(2)⊗XXZmodel

2015

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We investigate the phase diagram and the spin-orbital entanglement of a one-dimensional SU(2)⊗XXZ model with SU(2) spin exchange and anisotropic XXZ orbital exchange interactions and negative exchange coupling. 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 SU(2)⊗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.

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“…Numerical confirmation of this exponent and evidence for a logarithmic correction was reported in [31]. The important point here is that 4/3 < 2, which implies the instability of the translation invariant configurations under period 2 perturbations, provided f has a finite second derivative.…”

Section: Resultsmentioning

confidence: 65%

Stability of the Peierls instability for ring-shaped molecules

Lieb

Nachtergaele

1995

Phys. Rev. B

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We investigate the conventional tight-binding model of L π-electrons on a ring-shaped molecule of L atoms with nearest neighbor hopping. The hopping amplitudes, t(w), depend on the atomic spacings, w, with an associated distortion energy V (w). A Hubbard type on-site interaction as well as nearest-neighbor repulsive potentials can also be included. We prove that when L = 4k +2 the minimum energy E occurs either for equal spacing or for alternating spacings (dimerization); nothing more chaotic can occur. In particular this statement is true for the Peierls-Hubbard Hamiltonian which is the case of linear t(w) and quadratic V (w), i.e., t(w) = t 0 − αw and V (w) = k(w − a) 2 , but our results hold for any choice of couplings or functions t(w) and V (w). When L = 4k we prove that more chaotic minima can occur, as we show in an explicit example, but the alternating state is always asymptotically exact in the limit L → ∞. Our analysis suggests three interesting conjectures about how dimerization stabilizes for large systems. We also treat the spin-Peierls problem and prove that nothing more chaotic than dimerization occurs for L = 4k + 2 and L = 4k. INTRODUCTIONTo derive the shape (and other properties) of molecules from first principles has been an actively pursued goal since the early days of quantum mechanics. Many of the insights into the structure of molecules like benzene and its relatives have, however, been obtained using drastically simplified models. The Schrödinger equation for all the nuclei and electrons in such a molecule involves many dozens or even hundreds of degrees of freedom and, therefore, simpler models with a reduced number of degrees of freedom are a necessity. In the case of benzene the introduction of the Hückel model [1] played an important role. This model is standard textbook material for organic chemistry students (see e.g. [2]). London [3] used the Hückel model to explain the large diamagnetic anisotropy of aromatic compounds and certain other materials quite successfully. A similar approach was used earlier by Jones in his work on bismuth and bismuth alloys [4].In this paper we are interested in ring-shaped molecules of the type (CH) L , for even L, the so-called annulenes (sometimes called cyclic polyenes). The Hückel model for [L]-annulene describes the L π−electrons (one for each carbon atom) as hopping from one carbon atom to the next (tight-binding approximation). The carbon atoms are located at the L sites of a ring-shaped geometry, so L + 1 ≡ 1. The Coulomb interaction between the electrons is ignored in the Hückel model but we will include the Hubbard [5] on-site interaction as in the work of Pariser-Parr [6] and Pople [7], in our study (a nearest neighbour repulsion can also be included).

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Ground-state alternation and excitation energy of S=(1/2) linear Heisenberg antiferromagnets

Cited by 65 publications

References 24 publications

Quantum Monte Carlo study of the one-dimensional ionic Hubbard model

Quantum Monte Carlo study of the one-dimensional ionic Hubbard model

Quantum entanglement in the one-dimensional spin-orbitalSU(2)⊗XXZmodel

Stability of the Peierls instability for ring-shaped molecules

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