Lanczos calculation for thes=1/2 antiferromagnetic Heisenberg chain up toN=28 spins

Abstract

Highly precise numerical calculations using a variation of the Lanczos method devised by Paige were performed for s = 2 antiferromagnetic Heisenberg finite chains up to sizes N=28. Several interesting physical quantities, including the ground-state energy, the mass gap, and the spin-wave velocity, were computed and fitted for logarithmic finite-size corrections, as suggested by conformal invariance and Bethe ansatz calculations. A crossover size for a maximum of the spin-wave velocity is predicted for N-50, well above the current available sizes in a typical Lanczos simulation. A list

Strongly Interacting Quantum Systems out of Equilibrium

“…However, states ͉f͘ and ͉i͘ with comparable energy will have a vanishing transition ma- ically for M 0 , the lower and upper bounds on the spectrum are determined by the ground state energies of the ferromagnetic and the antiferromagnetic Heisenberg models. Those are in the thermodynamic limit [33,192]. If one acts on a state |ψ ∈ M 0 of energy E with the operatorV = i[Ŝ ,Ĥ 0 t ] (cf.…”

Accurate calculation of ground-state energies in an analytic Lanczos expansion

“…In figure 1 we display log |δ LT n | versus the Lanczos step n for a system of size N = 64. We have taken the exact ground-state energy density for N = 64 from the finite-size correction formula of reference [15]. On top of the exact differences we have placed a best-fit straight line to indicate the extent of the deviations from this simple form.…”

Density Matrix Renormalization Group and Periodic Boundary Conditions: A Quantum Information Perspective

“…We thank M.A. Martin-Delgado for enlightening discussions about DMRG and G. Cabrera for sending the extended data of [17]. Work supported by the DFG (SFB 631), the european project and network Quprodis and Conquest, and the Kompetenznetzwerk der Bayerischen Staatsregierung Quanteninformation.…”