Incommensurability Effects in Odd Length J_1-J_2 Quantum Spin Chains: On-site magnetization and Entanglement

For the antiferromagnetic J_1-J_2 quantum spin chain with an even number of sites, the point J_2^d=1/2 J_1 is a disorder point. It marks the onset of incommensurate real space correlations for J_2>J_2^d. At a distinct larger value of J_2^L=0.52036(6)J_1, the Lifshitz point, the peak in the static structure factor begins to move away from k=\pi. Here, we focus on chains with an odd number of sites. In this case the disorder point is also at J_2^d=1/2 J_1, but the behavior close to the Lifshitz point, J_2^L approx. 0.538 J_1, is quite different: starting at J_2^L, the ground-state goes through a sequence of level crossings as its momentum changes away from k=\pi/2. An even length chain, on the other hand, is gapped for any J_2>0.24J_1 and has the ground-state momentum k=0. This gradual change in the ground-state wave function for chains with an odd number of sites is reflected in a dramatic manner directly in the ground-state on-site magnetization as well as in the bi-partite von Neumann entanglement entropy. Our results are based on DMRG calculations and variational calculations performed in a restricted Hilbert space defined in the valence bond picture. In the vicinity of the point J_2=1/2 J_1, we expect the variational results to be very precise.Comment: Accepted for publication in Phys. Rev.

Kondo Screening Cloud Scaling: Impurity Entanglement and Magnetization

The screening of an impurity spin in the Kondo model occurs over a characteristic length scale $\xi_K$, that defines the size of the Kondo screening cloud or ``mist". The presence of such a length sc A consistent way to show the presence of the screening cloud is to demonstrate scaling in the spatial correlations depending on $r$, in terms of the single variable $r/\xi_K$ rather than depending on $r$ and $\xi_K$ separately. Here we study the paradigmatic one channel Kondo model using a spin chain representation, with an impurity spin at one end of the chain coupled with a strength $J_K'$. Using Fermi liquid theory combined with numerical results, we obtain new high precision estimates of the non-universal terms in the entanglement entropy which leads to a verification of the expected non-integer ground-state degeneracy, $g$. This then allows us to study the impurity contribution to the entanglement in detail. If the impurity coupling $J_K'$ is varied, a precise determination of $\xi_K$ can then be obtained. The length scale, $\xi_K$, is then shown to characterize the scaling of both the uniform and alternating part of a measure of the magnetization of part of an odd length chain with.Comment: 17 oages, 7 figure

Estimates of Effective Hubbard Model Parameters for C20 isomers

We report on an effective Hubbard Hamiltonian approach for the study of electronic correlations in C$_{20}$ isomers, cage, bowl and ring, with quantum Monte Carlo and exact diagonalization methods. The tight-binding hopping parameter, $t$, in the effective Hamiltonian is determined by a fit to density functional theory calculations, and the on-site Coulomb interaction, $U/t$, is determined by calculating the isomers' affinity energies, which are compared to experimental values. For the C$_{20}$ fullerene cage we estimate $t_{\rm cage}\simeq 0.68-1.36$ eV and $(U/t)_{\rm cage} \simeq 7.1-12.2$. The resulting effective Hamiltonian is then used to study the shift of spectral peaks in the density of states of neutral and one-electron-doped C$_{20}$ isomers. Energy gaps are also extracted for possible future comparison with experiments.Comment: 6 pages, 5 figure

Revealing divergent length scales using quantum Fisher information in the Kitaev honeycomb model

We compute the quantum Fisher information (QFI) associated with two different local operators in the Kitaev honeycomb model, and find divergent behaviour in the second derivatives of these quantities with respect to the driving parameter at the quantum phase transition between the gapped and gapless phases for both fully anti-ferromagnetic and fully ferromagnetic exchange couplings. The QFI associated with a local magnetization operator behaves differently from that associated with a local bond operator depending on whether the critical point is approached from the gapped or gapless side. We show how the behaviour of the second derivative of the QFI at the critical point can be understood in terms of diverging length scales in the correlators of the local generators

State Space Geometry of the Spin-1 Antiferromagnetic Heisenberg Chain

We study the phase diagram of the spin-1 antiferromagnetic Heisenberg chain with uniaxial anisotropy and applied magnetic field in terms of the genuine multipartite entanglement as witnessed by the mean quantum Fisher information density. By generalizing the manifold studied in [1, 2] to the many body case for spin 1, we connect the state space curvature in the vicinity of the ground state of the Heisenberg chain to the genuine multipartite entanglement. Our analysis demonstrates that the quantum critical points and symmetry protected topological (SPT) phase exhibit large state space curvature, while the separable phases are completely flat, offering insight into the physical interpretation of state space curvature. We further show that the entanglement in the SPT phase is enhanced by the presence of uniaxial anisotropy, and undiminished in the presence of uniform magnetic fields. The magnon condensate phase induced by large fields is shown to emanate from the Gaussian critical point, and exhibits massive multipartite entanglement over a robust region of the parameter space

The Generic, Incommensurate Transition in the two-dimensional Boson Hubbard Model

The generic transition in the boson Hubbard model, occurring at an incommensurate chemical potential, is studied in the link-current representation using the recently developed directed geometrical worm algorithm. We find clear evidence for a multi-peak structure in the energy distribution for finite lattices, usually indicative of a first order phase transition. However, this multi-peak structure is shown to disappear in the thermodynamic limit revealing that the true phase transition is second order. These findings cast doubts over the conclusion drawn in a number of previous works considering the relevance of disorder at this transition.Comment: 13 pages, 10 figure

Extended Hubbard model on a C20_{20} molecule

The electronic correlations on a C$_{20}$ molecule, as described by an extended Hubbard Hamiltonian with a nearest neighbor Coulomb interaction of strength $V$, are studied using quantum Monte Carlo and exact diagonalization methods. For electron doped C$_{20}$, it is known that pair-binding arising from a purely electronic mechanism is absent within the standard Hubbard model (V=0). Here we show that this is also the case for hole doping for $0<U/t\leq 3$ and that, for both electron and hole doping, the effect of a non-zero $V$ is to work against pair-binding. We also study the magnetic properties of the neutral molecule, and find transitions between spin singlet and triplet ground states for either fixed $U$ or $V$ values. In addition, spin, charge and pairing correlation functions on C$_{20}$ are computed. The spin-spin and charge-charge correlations are very short-range, although a weak enhancement in the pairing correlation is observed for a distance equal to the molecular diameter.Comment: 9 pages, 8 figures, 4 table

Eleven Competing Phases in the Heisenberg-Gamma (JΓ\Gamma) Ladder

The spin-orbit generated $\Gamma$ interaction is known to induce strong frustration and to be significant in realistic models of materials. To gain an understanding of the possible phases that can arise from this interaction, it is of considerable interest to focus on a limited part of parameter space in a quasi one-dimensional model where high precision numerical results can be obtained. Here we study the Heisenberg-Gamma (J$\Gamma$) ladder, determining the complete zero temperature phase diagram by analyzing the entanglement spectrum (ES) and energy susceptibility. A total of 11 different phases can be identified. Two of the phases, the antiferromagnetic Gamma (A$\Gamma$) and ferromagnetic Gamma (F$\Gamma$) phases, have previously been observed in the Kitaev-Gamma ladder, demonstrating that the A$\Gamma$-phase is a symmetry protected topological phase (SPT) protected by $TR\times \mathcal{R}_{b}$ symmetry, the product of time-reversal ($TR$) and $\pi$ rotation around the $b$-axis ($\mathcal{R}_{b}$), while the F$\Gamma$-phase is related to a rung-singlet phase through a local unitary transformation. Three other phases, $\Upsilon$, $\Omega$ and $\delta$ show no conventional order, a doubling of the entanglement spectrum and for the $\Upsilon$ and $\Omega$-phases a gap is clearly present. The $\delta$-phase has a significantly smaller gap and displays incommensurate correlations, with a peak in the static structure factor, $S(k)$ continuously shifting from $k/\pi\mathord{=}2/3$ to $k\mathord{=}\pi$. In the $\Omega$-phase we find pronounced edge-states consistent with a SPT phase protected by the same $TR\times \mathcal{R}_{b}$ symmetry as the A$\Gamma$-phase. The precise nature of the $\Upsilon$ and $\delta$-phases is less clear.Comment: 25 pages, 13 figure