Variational method for 1D spin chains

Frustrated Ferromagnetic Spin Chains: A Variational Approach to Chirality Transitions

We study the energy per particle of a one-dimensional ferromagnetic/anti-ferromagnetic frustrated spin chain with nearest and next-to-nearest interactions close to the helimagnet/ferromagnet transition point as the number of particles diverges. We rigorously prove the emergence of chiral ground states and we compute, by performing the Γ-limits of proper renormalizations and scalings, the energy...

Hartley Series Direct Method for Variational Problems

The computational method based on using the operational matrix of anorthogonal function for solving variational problems is computeroriented. In this approach, a truncated Hartley series together withthe operational matrix of integration and integration of the crossproduct of two cas vectors are used for finding the solution ofvariational problems. Two illustrative...

SADDLE POINT VARIATIONAL METHOD FOR DIRAC CONFINEMENT

A saddle point variational (SPV ) method was applied to the Dirac equation as an example of a fully relativistic equation with both negative and positive energy solutions. The effect of the negative energy states was mitigated by maximizing the energy with respect to a relevant parameter while at the same time minimizing it with respect to another parameter in the wave function. The Cornell pot...

Comment on “ Equivalence of the variational matrix prod - uct method and the density matrix renormalization group applied to spin chains

Integrability test for spin chains

We examine a simple heuristic test of integrability for quantum chains. This test is applied to a variety of systems, including a generic isotropic spin-1 model with nearestneighbor interactions and a multiparameter family of spin-1/2 models generalizing the XYZ chain, with next-to-nearest neighbor interactions and bond alternation. Within the latter family we determine all the integrable model...