Magnetic Toys momentum-space

Rare Earth Neodymium Magnets 

Magnetic Toys momentum-space distribution rik a and  Magnet Toys
double occupancy d are needed. They may be evaluated

magnets

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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 =
n° , ) 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 — > 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 ©, 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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“El



Kc + ka \


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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, ,] — 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 n£ CT = 1)




Clearly Neodymium magnets for sale quasiparticle excitations are gapless, since
E k(T — > 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).

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