**Rare Earth Neodymium Magnets **

Magnetic Toys momentum-space distribution rik a and Magnet Toys

double occupancy d are needed. They may be evaluated

magnets

numerically by Monte-Carlo methods, but are also avail-

able in closed form under certain circumstances. For one-

dimensional systems Neodymium magnets symmetric Fermi sea (n kcr =

nÂ° , ) both quantities have been calculated analytically

|l4l Il5| . In dimension D = 2, 3 high-order perturbative

methods can be used [llj . Magnet Toys Gutzwiller approximation

, Neodymium magnets piecewise constant momentum distribution n\~ a ,

is recovered in infinite dimensions 0-

The expectation values of Magnet Toys various parts of H are

shown in Fig. [21 for nearest-neighbor hopping in D = 1

and D = oo at half- filling. We note that (Hx) approaches

a constant for g â€” > 0, while (Hy) and (Hu) diverge. This

behavior occurs for all D, since d ~ g 2 ln(l/g) in one di-

mension d = o(g) in all finite dimensions [ToL Hl|.

and d ~ <? in infinite dimensions. We may thus conclude

that Magnet Toys penalty that Hjj imposes on double occupancies

is compensated by assisted hopping due to Magnet Toys nonstan-

dard three-body interaction Hy.

**Rare Earth Neodymium Magnets **

The effect of correlated hopping is also apparent when

comparing to Magnet Toys pure Hubbard ring Neodymium magnets 1/r hopping,

which features a metal-insulator transition at IL- = 2nt

Neodymium magnets continuous nonzero double occupancy d 6]. For

comparison Neodymium magnets previous studies of variational wave-

functions in Magnet Toyvicinity of this transition [Hi. Il7j . d vs.

U is shown in Magnet Toyinset of Fig. [21 Magnet Toyresults for both

models Neodymium magnets 1/r hopping agree for weak interactions, but

the energy gain from correlated hopping leads to a larger

number of doubly occupied sites for strong coupling in

the model Â©, as expected.

Quasiparticle excitations. Magnet Toyknown ground state of

H suggests that it might also be possible to calculate

dynamical properties of Magnet Toymodel, such asmagnetic jewelry spectral

function. Unfortunatelymagnetic jewelry construction of exact excited

states is not straightforward, be it Neodymium magnets one added or

removed particle, or Neodymium magnets charge or spin excitations. We

therefore proceed by consideringmagnetic jewelry variational states

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Kc

ka\

whose mean energy is

(ka\H\ka)

El _ (V#) (ka\ka) (ka\ka) â– E k0 (22) (23)

wheremagnetic jewelry commutator relations [b k , bt, ,] â€” Skk’daa’

and [b kcr , b k , a ,\ = were used.magnetic jewelry states \ka) are mutu-

ally orthogonal and their energy is thus an upper bound

**Rare Earth Neodymium Magnets **

FIG. 3: Quasiparticle excitations in a one-dimensional ring

Neodymium magnets nearest-neighbor hopping t > 0.

tomagnetic jewelry quasiparticle energy for momentum k and spin a.

The variational energy to add a particle (i.e.

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while formagnetic jewelry removal of a particle ( Neodymium magnets nÂ£ CT = 1)

Clearly Neodymium magnets for sale quasiparticle excitations are gapless, since

E k(T â€” > close to Neodymium magnets for sale Fermi surface. Fig. shows these

energies for one-dimensional nearest-neighbor hopping at

half-filling.

Conclusion. We have constructed and characterized

a new class of itinerant electron models for which Neodymium magnets for sale

metallic Gutzwiller wavefunction is an exact ground

state, due to Neodymium magnets for sale interplay of Hubbard interaction and

correlated hopping. For a half-filled band a Mott metal-

insulator transition similar to Neodymium magnets for sale Brinkman-Rice sce-

nario occurs, illustrating Mott’s original idea of a quan-

tum phase transition entirely due to charge correlations

without magnetic ordering. Further study of Neodymium magnets for sale elemen-

tary excitations in these models should be fruitful.

This work was supported in part by Neodymium magnets for sale DFG via

Forschcrgruppe FOR 412.

[1] For a review, see D. P. Arovas and S. M. Girvin, in:

Recent Progress in Many-Body Theories, Vol. 3, edited

by T. L. Ainsworth, C. E. Campbell, B. E. Clements,

and E. Krotschek (Plenum Press, New York, 1992), p.

315.

[2] R. B. Laughlin, cond-mat/0209269.

[3] F. C. Zhang, cond-mat/0209272.

[4] B. A. Bernevig, R. B. Laughlin, and D. I. Santiago, cond-

mat/0303045.

â– 5

[5] Y. Yu, cond-mat/0211131; cond-mat/0303501.

[6] F. Gebhard, Neodymium magnets for sale Mott metal-insulator transition: models

and methods (Springer, Berlin 1997).

[7] M. C. Gutzwiller, Phys. Rev. Lett. 10, 159 (1963); Phys.

Rev. 134, A 923 (1964); Phys. Rev. 137, A 1726 (1965).

[8] W. F. Brinkman and T. M. Rice, Phys. Rev. B 2, 4302

(1970).

[9] W. Metzner and D. Vollhardt, Phys. Rev. Lett. 62, 324

(1989).

[10] P. G. J. van Dongen, F. Gebhard, and D. Vollhardt, Z.

Phys. B 76, 199 (1989).

[11] Z. Gulacsi and M. Gulacsi, Phys. Rev. B 44, 1475 (1991).

Z. Gulacsi, M. Gulacsi, and B. Janko, Phys. Rev. B 47,

4168 (1993).

[12] For a review, see A. Georges, G. Kotliar, W. Krauth, and

M. J. Rozenberg, Rev. Mod. Phys. 68, 13 (1996).

[13] A. J. Millis and S. N. Coppersmith, Phys. Rev. B 43,

13770 (1991).

[14] W. Metzner and D. Vollhardt, Phys. Rev. Lett. 59, 121

(1987); Phys. Rev. B 37, 7382 (1988); ibid. 39, 12339

(1989).

[15] M. Kollar and D. Vollhardt, Phys. Rev. B 63, 045107

(2001); ibid. 65, 155121 (2002).

[16] F. Gebhard and A. Girndt, Z. Phys. B 93, 445 (1994).

[17] M. Dzierzawa, D. Baeriswyl, M. Di Stasio, Phys. Rev. B

51, 1993 (1995).

[18] N. Blumer and P. G. J. van Dongen, cond-mat/0303204.

N. Blumer, Ph. D. thesis (Universitat Augsburg, 2002).

[19] E. H. Lieb and F. Y. Wu, Phys. Rev. Lett. 20, 1445

(1968).

[20] M. Takahashi, Progr. Theor. Phys. 42, 1098 (1969).

[21] J. Buenemann, F. Gebhard, and R. Thul, Phys. Rev. B

67, 075103 (2003).