We analyze several properties of the lattice solitons in the incommensurate phase of spin-Peierls systems using exact diagonalization and quantum Monte Carlo simulations. These systems are modeled by an antiferromagnetic Heisenberg chain with nearest- and next-nearest-neighbor interactions coupled to the lattice in the adiabatic approximation. Several relations among features of the solitons and magnetic properties of the system have been determined and compared with analytical predictions. We have studied in particular the relation between the soliton width and the spin-Peierls gap. Although this relation has the form predicted by bosonized field theories, we have found some important quantitative differences which could be relevant to describe experimental studies of spin-Peierls materials.
We investigate a nearest-neighbor Ising model on the kagome lattice coupled to elastic lattice distortions. By integrating out the lattice degrees of freedom, we derive an approximate spin-only description in terms of a kagome
J1-
J2-
J3 Ising model with interactions extending to third nearest-neighbors. Using tensor network methods complemented by classical Monte Carlo simulations, we revisit its zero-temperature phase diagram and characterize the ground states studied more than thirty years ago. We discover three phases with extensive zero-temperature entropy and algebraically decaying spin correlations. Importantly, these states are not confined to fine-tuned points or frontiers between phases, but occupy extended areas of parameter space. Their quasi long-range order is reflected in Bragg-like peaks in the structure factors; we relate this, and other properties, to diverse phases found in Ising and Heisenberg models. Finally, we trace the trajectories generated by the magnetoelastic coupling through the effective-model phase diagram, explaining the emergence of self-frustration for the unfrustrated magnetoelastic model with ferromagnetic interactions.
We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic (
J1F) and antiferromagnetic (
J1A) nearest-neighbor interactions and ferromagnetic next-nearest-neighbor interaction (
J2F). In this model frustration is induced by the non-zero
J2F and the effect of dimerization is realized by changing the strength of
J1A for a fixed value of
J1F. The model with site spin
s behaves like a Haldane spin chain with site spin 2
s in the limit of vanishing
J2F and large
J1F/J1A. We show that the exact ground state of the model can be found along a line in the parameter space. The phase diagram in the space of
J1A−J2F is determined using numerical techniques complemented by some analytical calculations. A number of quantities, including the ground state spin, energy gap, structure factor, entanglement entropy, and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and application-wise important feature of this model is that it exhibits a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.
We study a one-dimensional antiferromagnetic-elastic model with magnetic ions having spin
S=3/2. By extensive density matrix renormalization group (DMRG) computations and complementary analytical methods, we uncover a first-order transition from a homogeneous or weakly dimerized phase (a situation that could be similar to the well-known
S=1/2 spin-Peierls effect) to a highly distorted phase, driven by the spin-phonon coupling $\ensuremath{\lambda}$. The striking characteristic of the second phase, present at large $\ensuremath{\lambda}$, is the appearance of weakly ferromagnetic (FM) couplings alternating with strong antiferromagnetic (AFM) ones (we dub it the FM-AFM phase) with a ground state close to a direct-product state of singlet dimers sitting on the AFM bonds. The behavior of the spin gap in both phases is studied by DMRG computation and contrasted with bosonization predictions and perturbation theory around the direct product of dimers. In the FM-AFM phase, robust magnetization plateaus and metamagnetic jumps appear under magnetic fields. The novel phase could be realized in 5d oxides of current interest, with giant spin-phonon coupling. Potential applications of the transition would be associated with the possibility of tuning the transition by external parameters such as striction, magnetic or electric fields, or alloying.
We study the spin 1/2 J1-J2 antiferromagnetic Heisenberg model on square lattice by using a recently proposed cluster update method for tensor product states (TPSs). The ground state energies in the thermodynamic limit are in good agreement with the state of art exact diagonalization study, and the energy differences between these two studies are of the order of 10J1 per site. For small bond dimension D (D < 5), we find a paramagnetic ground state with mixed columnar and staggered dimer orders of a magnitude 10−2 in the range of 0.47 < J2/J1 < 0.6, which agrees with previous results. For large bond dimension D (D ≥ 5), we observe all these orders vanish, implying the emergence of a spin liquid phase.
We develop an analytical approach based on a unitary transformation to investigate S=1/2 antiferromagnetic Heisenberg chains coupled to phonons, and find a new quantum phase transition at zero temperature. Although the usual phase transition occurs depending on the strengths of the spin-spin and spin-phonon interactions, the phase transition in the present work is induced by a change in the geometrical structure of the spin-phonon interaction. The magnetic properties of the phase transition can be understood in relation to a phase transition that has already been found in the frustrated J1-J2 model.