We show that spin S Heisenberg spin chains with an additional three-body interaction of the form (S i−1 · S i )(S i · S i+1 ) + h.c. possess fully dimerized ground states if the ratio of the three-body interaction to the bilinear one is equal to 1/(4S(S + 1) − 2). This result generalizes the MajumdarGhosh point of the J1 − J2 chain, to which the present model reduces for S = 1/2. For S = 1, we use the density matrix renormalization group method (DMRG) to show that the transition between the Haldane and the dimerized phases is continuous with central charge c = 3/2. Finally, we show that such a three-body interaction appears naturally in a strong-coupling expansion of the Hubbard model, and we discuss the consequences for the dimerization of actual antiferromagnetic chains. Introduction -Over the years, exact results have proved to be extremely useful in quantum and statistical physics [1,2]. In quantum magnetism, the Bethe ansatz solution of the spin-1/2 Heisenberg chain [3] has led to the first proof that the spectrum is gapless [4], and its extensions, e.g., to the S = 1 chain with bilinear and biquadratic interactions (BLBQ) with equal [5][6][7] or opposite [8,9] amplitudes has helped a lot to clarify the physics of that model. In quantum frustrated magnetism [10], cases where an exact expression for the ground state wave function can be obtained have also played a very important role. For instance, for the spin-1 Heisenberg chain, the exact ground state of the AKLT point [11] has been a milestone in the confirmation of Haldane's prediction that the spectrum of integer-S spin chains is gapped [12]. For spin-1/2 magnets, the first example of a gapped spectrum goes back to the Majumdar-Ghosh [13] (MG) point J 2 /J 1 = 1/2 of the J 1 − J 2 model defined by the Hamiltonian

Building on the generalization of the exactly dimerized Majumdar-Ghosh ground state to arbitrary spin S for the Heisenberg chain with a three-site term (Si−1 · Si)(Si · Si+1) + H.c., we use densitymatrix renormalization group simulations and exact diagonalizations to determine the nature of the dimerization transition for S = 1, 3/2 and 2. The resulting central charge and critical exponent are in good agreement with the SU (2) k=2S Wess-Zumino-Witten values c = 3k/(2 + k) and η = 3/(2 + k). Since the 3-site term that induces dimerization appears naturally if exchange interactions are calculated beyond second order, these results suggest that SU (2) k>1 Wess-Zumino-Witten models might finally be realized in actual spin chains.

Although community services support ageing-in-place, older adults often report feelings of loneliness and social isolation. Unmet emotional needs are associated with poorer health, reduced functional abilities and increased mortality in this population. Pet ownership is an avenue worth exploring to reduce these adverse outcomes. This scoping review maps main findings and identifies key gaps with respect to the pros and cons of pet ownership in community-dwelling older adults pertaining to psycho-social, physical and functional outcomes. Scientific and grey literature published from January 2000 to July 2018 was searched. Data selection and extraction were performed by the first author and a sub-sample was co-validated by two co-authors. A total of 62 sources were included for descriptive and thematic analysis. A variety of pros (increased physical activity, wellbeing) and cons (grief, risk of falls) pertaining to psycho-social and physical outcomes were identified. Not many functional outcomes (support for daily routines) were mentioned, and few studies explored the simultaneous balance between the pros and cons of pet care. Further research exploring both clinicians’ and older pet owners’ perspectives is needed to deepen our understanding of the importance of considering companion animals in older adults’ daily lives and to strike a balance between perceived risks and benefits.

We study the T = 0 magnetization of frustrated two-leg spin ladders with arbitrary value of the spin S. In the strong-rung limit, we use degenerate perturbation theory to prove that frustration leads to magnetization plateaus at fractional values of the magnetization for all spins S and to determine the critical ratios of parallel to diagonal inter-rung couplings for the appearance of these plateaus. These ratios depend both on the plateau and on the spin. To confirm these results and to investigate the properties of these ladders away from the strong-coupling limit, we have performed extensive density-matrix renormalization-group calculations for S Յ 2. For large enough inter-rung couplings, all plateaus simply disappear, leading to a magnetization curve typical of integer-spin chains in a magnetic field. The intermediate region turns out to be surprisingly rich however, with, upon increasing the inter-rung couplings, the development of magnetization jumps and, in some cases, the appearance of one or more phase transitions inside a given plateau.

We investigate the properties of antiferromagnetic spin-S ladders with the help of local Berry phases defined by imposing a twist on one or a few local bonds. In gapped systems with time-reversal symmetry, these Berry phases are quantized, hence able in principle to characterize different phases. In the case of a fully frustrated ladder where the total spin on a rung is a conserved quantity that changes abruptly upon increasing the rung coupling, we show that two Berry phases are relevant to detect such phase transitions: the rung Berry phase defined by imposing a twist on one rung coupling, and the twist Berry phase defined by twisting the boundary conditions along the legs. In the case of nonfrustrated ladders, we have followed the fate of both Berry phases when interpolating between standard ladders and dimerized spin chains, with the surprising conclusion that, at least far enough from dimerized chains, they define different domains in parameter space. A careful investigation of the spin gap and of edge states shows that a change of twist Berry phase is associated with a quantum phase transition at which the bulk gap closes, and at which, with appropriate boundary conditions, edge states appear or disappear, while a change of rung Berry phase is not necessarily associated with a quantum phase transition. The difference is particularly acute for regular ladders, in which the twist Berry phase does not change at all upon increasing the rung coupling from zero to infinity while the rung Berry phase changes 2S times. By analogy with the fully frustrated ladder, these changes are interpreted as crossovers between domains in which the rungs are in different states of total spin from 0 in the strong rung limit to 2S in the weak rung limit. This interpretation is further supported by the observation that these crossovers turn into real phase transitions as a function of rung coupling if one rung is strongly ferromagnetic, or equivalently if one rung is replaced by a spin 2S impurity.