Quantum spin chains in a magnetic field

Abstract

We demonstrate that the ``worm'' algorithm allows very effective and precise quantum Monte Carlo (QMC) simulations of spin systems in a magnetic field, and its auto-correlation time is rather insensitive to the value of H at low temperature. Magnetization curves for the $s=1/2$ and $s=1$ chains are presented and compared with existing Bethe ansatz and exact diagonalization results. From the Green function analysis we deduce the magnon spectra in the s=1 system, and directly establish the "relativistic" form E(p)=(\Delta ^2 +v^2 p^2)^{1/2} of the dispersion law.Comment: 6 pages, 8 figures; removed discussion of spin-2 case - will be published later in a separate pape

Finite-size spectrum, magnon interactions, and magnetization ofS=1Heisenberg spin chains

“…8. The agreement with the Monte Carlo data, 19 at the same length and temperature, L ϭ100, Tϭ1/100 is remarkable.…”

“…͑1.6͒ at low temperature T and large L in order to fit recent Monte Carlo results. 19 We obtain a consistent value of a of about Ϫ0.34 from all three fits, as mentioned above. However, using a product wave-function renormalization-group method to calculate the magnetization, Okunishi et al obtained a considerably larger value, aϷϪ0.54 , which is closer to the prediction of the NL M. From the viewpoint of the renormalization-group treatment of the onedimensional Bose condensation transition, 20 we may regard a as the leading irrelevant coupling constant.…”

Many-spin effects and tunneling splittings in Mn12 magnetic molecules

“…The general strategy to solve this problem is to truncate the full Hilbert space thus reducing consideration to a much smaller number of relevant energy levels. This idea, implemented in a rather sophisticated way, forms a basis of several approaches for the evaluation of tunneling phenomena, such as quantum Monte Carlo methods [9], stochastic diagonalization [10], and instanton calculations [8].…”

Continuous-Time Quantum Monte Carlo Algorithm for the Lattice Polaron

“…The main idea then is to regard the imaginary-time evolution of a particle or spin configuration as a continuoustime Poisson process with "events" being either a particle jump or a spin flip. In this way continuous-time QMC algorithms were developed for a particle in an external potential [2], Heisenberg model [3,4], t − J model [5], bosonic Hubbard model [6], and Fröhlich polaron [7].In this Letter I present a continuous-time path-integral QMC algorithm for the lattice polaron, i.e., an electron strongly interacting with phonons on a lattice. The method combines analytical integration of the phonon degrees of freedom with the advantages of the continuoustime formulation of the Monte Carlo process.…”

“…The main idea then is to regard the imaginary-time evolution of a particle or spin configuration as a continuoustime Poisson process with "events" being either a particle jump or a spin flip. In this way continuous-time QMC algorithms were developed for a particle in an external potential [2], Heisenberg model [3,4], t − J model [5], bosonic Hubbard model [6], and Fröhlich polaron [7].…”