Computational Physics

Table 12.2. Meaning of several physical quantities in different interpretations of the path integral. Quantum mechanics Quantum ...

404 Quantum Monte Carlo methods time – there exist versions with real time, which are used to study the dynamics of quantum syst ...

12.4 Path-integral Monte Carlo 405 Note that the numerator differs from the path integral (which occurs in the denom- inator) in ...

406 Quantum Monte Carlo methods is that 1/βand〈K〉/(NM)are both large, but their difference is small. Hermanet al. [20]have propo ...

12.4 Path-integral Monte Carlo 407 to the time-evolution operator. The effect of averaging over all the continuous paths from(r, ...

408 Quantum Monte Carlo methods 0 0.5 1 1.5 2 2.5 3 3.5 4 V r Figure 12.5. The cumulant potential for τ=0.2 (diamonds) and the C ...

12.4 Path-integral Monte Carlo 409 within a cube (or a sphere). If we update the coordinateRm, keepingRm− 1 and Rm+ 1 fixed, the ...

410 Quantum Monte Carlo methods It will be clear that for a full boson simulation, moving particles is not sufficient: we must a ...

12.5 Quantum Monte Carlo on a lattice 411 Finally, this model may be formulated for interacting fermions. A famous model of this ...

412 Quantum Monte Carlo methods Figure 12.7. The checkerboard decomposition of the space-time lattice. Two world lines are shown ...

12.5 Quantum Monte Carlo on a lattice 413 for each plaquette (remember thesioccurring in this equations are the eigenvalues of t ...

414 Quantum Monte Carlo methods In the case where, instead of spin-1/2 degrees of freedom, we have (boson) numbers on the sites, ...

12.6 The Monte Carlo transfer matrix method 415 s' 0 s' 1 (= s 0 ) s' 2 (= s 1 ) s'L- 1 (= sL- 2 ) sL- 1 Figure 12.8. Helical bo ...

416 Quantum Monte Carlo methods Table 12.3.Largest eigenvalues of the transfer matrix of the Ising model on a strip with helical ...

Exercises 417 4.418 4.42 4.422 4.424 4.426 4.428 4.43 4.432 0.01 0.014 0.018 0.022 0.026 ln λ^0 1 /L^2 Figure 12.9. The logarith ...

418 Quantum Monte Carlo methods where the quantum statistical partition functionZis given by Z=Tre−βH. We take
≡1. (a) Show by u ...

Exercises 419 in the path-integral formalism, we should include all paths satisfying these boundary conditions. Using completene ...

420 Quantum Monte Carlo methods (a) Show that for a two-dimensional table containing values of a functionf(x,y)for integerxandy, ...

References 421 References [1] P. A. M. Dirac,The Principles of Quantum Mechanics. Oxford, Oxford University Press, 1958. [2] B. ...

422 Quantum Monte Carlo methods [26] M. Plischke and H. Bergersen,Equilibrium Statistical Physics. Englewood Cliffs, NJ, Prentic ...