Summary
We study the dynamics of the 1D t-J model with nearest neighbor (n.n) interaction at finite doping using the hybrid-loop quantum Monte Carlo. On the basis of the spectral functions of the 1/r 2 t-J model the excitation content for the one- and two-particle spectral functions for the n.n. t-J model are obtained from the Bethe-Ansatz solution and compared with the Monte Carlo results. We find that the procedure describes with extremely hight accuracy the excitation of the n.n. t-J model. We furthermore use quantum Monte Carlo simulations to analyze the phases of ultra-cold bosonic atom gases in optical lattices, in particular in the presence of frustrated and random interaction strength. We find that such systems display interesting quantum phases, such as supersolid and Bose-glass phases, and discuss possible experimental setups to examine such phenomena.
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References
P. Fulde, J. Keller and G. Zwicknagl, Solid State Physics — Advances in Research and Applications 41, 1 (1988).
For a recent review see e.g. P.A. Lee, N. Nagaosa, and X.-G. Wen, Rev. Mod Phys 78, 269 (2006).
U. Schollwöck, J. Richter, D. J. J. Farnell and R. F. Bishop (Eds.), Quantum Magnetism, Lecture Notes in Physics 645, Springer, Berlin (2004).
B. Paredes et al., Nature 429, 277 (2004).
M. Greiner et al., Nature 415, 39 (2002).
A. Foussats, A. Greco, M. Bejas, and A. Muramatsu, Phys. Rev. B 72, 020504(R) (2005).
S.R. Manmana, A. Muramatsu, and R.M. Noack, AIP Conf. Proc. 789, 269 (2005); ibid 816, 198 (2006).
E. Dagotto and T. M. Rice, Science 271, 618 (1996).
P. A. Bares and G. Blatter and M. Ogata, Phys. Rev. B 44, 130 (1991).
K. Penc, K. Hallberg, F. Mila, and H. Shiba, Phys. Rev. Lett. 77, 1390 (1996).
E. Dagotto, Rev. Mod. Phys. 66, 763 (1994).
H. Benthien, F. Gebhard and E. Jeckelmann, Phy. Rev. Lett. 92, 256401 (2004).
C. Lavalle, M. Arikawa, S. Capponi, F. Assaad, and A. Muramatsu, Phys. Rev. Lett. 90, 216401 (2003).
H. J. M. van Bemmel, et al., Phys. Rev. Lett. 72, 2442 (1994).
D. F. B. ten Haaf, H. J. M. van Bemmel, J. M. J. van Leeuwen, W. van Saarloos and D. M. Ceperley Phys. Rev. B 51, 13039 (1995).
S. Sorella and L. Capriotti, Phys. Rev. B. 61, 2599 (1999).
G. Khaliullin, JETP Lett. 52, 389 (1990).
A. Angelucci, Phys. Rev. B 51, 11580 (1995).
H. G. Evertz, Adv. Phys. 52, 1 (2003).
A. Muramatsu, in Quantum Monte Carlo Methods in Physics and Chemistry, edited by M. Nightingale and C. Umrigar (NATO Science Series, Kluwer, Dordrecht, 1999).
K. S. D. Beach, cond-mat/0403055.
M. Ogata, et al., Phys. Rev. Lett 66, 2388 (1991).
M. Nakamura, K. Nomura and A. Kitazawa, Phys. Rev. Lett. 79, 3214 (1997).
V. Inozemtsev, J. Stat. Phys. 59, 1143 (1990).
C. Lavalle, M. Arikawa and A. Muramatsu, in preparation.
S. Sorella and A. Parola, Phys. Rev. B 57, 6444 (1998).
M. H. Anderson et al., Science 269, 198 (1995).
C. C. Bardley et al., Phys. Rev. Lett. 75, 1687 (1995).
K. B. Davis et al., Phys. Rev. Lett. 75, 3969 (1995).
J. Stenger et al., Nature 396, 345 (1999).
A. Griesmaier et al., Phys. Rev. Lett. 94, 160401 (2005).
B. DeMarco and D. S. Jin, Science 285, 1703 (1999).
J. Jaksch et al., Phys. Rev. Lett. 81, 3108 (1998).
M. P. A. Fisher et al., Phys. Rev. B 40, 546 (1989).
T. Stöferle et al., Phys. Rev. Lett. 91 130403 (2004).
M. Rigol A. Muramatsu, G.G. Batrouni, and R.T. Scalettar, Phys. Rev. Lett. 91, 130403 (2003).
M. Rigol, A. Muramatsu, Phys. Rev. A 69, 053612 (2004).
M. Rigol and A. Muramatsu, Opt. Commun. 243, 33 (2004).
M. Rigol and A. Muramatsu, Phys. Rev. A 70, 031603(R) (2004).
M. Rigol and A. Muramatsu, Phys. Rev. A 70, 043627 (2004).
M. Rigol and A. Muramatsu, Phys. Rev. Lett. 93, 230404 (2004).
M. Rigol and A. Muramatsu, Phys. Rev. Lett. 94, 240403 (2005).
M. Rigol and A. Muramatsu, Phys. Rev. A 72, 013604 (2005).
M. Rigol and A. Muramatsu, Mod. Phys. Lett. B bf 19, 861 (2005).
M. Rigol et al., Phys. Rev. Lett. 95, 218901 (2005).
A. W. Sandvik and J. Kurkijärvi, Phys. Rev. B 43, 5950 (1991).
A. W. Sandvik, Phys. Rev. B 59, R14157 (1999).
O. F. Syljuåsen and A. W. Sandvik, Phys. Rev. E 66, 046701 (2002).
F. Alet, S. Wessel, and M. Troyer, Phys. Rev. E 71, 036706 (2005).
F. Alet et al., J. Phys. Soc. Jpn. Suppl. 74, 30 (2005); source codes available at http://alps.comp-phys.org/.
S. Wessel, et al., Adv. Solid State Phys. 44, 265 (2004).
S. Wessel, et al., Phys. Rev. A 70, 053615 (2004).
S. Wessel, et al., J. Phys. Soc. Jpn. Suppl. 74, 10 (2005).
E. Kim and M. H. W. Chan, Nature 427, 225 (2004); Science 305, 1941 (2004).
O. Penrose and L. Onsager, Phys. Rev. 104, 576 (1956).
A. J. Leggett, Phys. Rev. Lett. 25, 1543 (1970).
A. Leggett, Science 305, 1921 (2004).
N. Prokof’ev and B. Svistunov, Phys. Rev. Lett. 94, 155302 (2005).
E. Burovski et al., Phys. Rev. Lett. 94, 165301 (2005).
K. Góral, L. Santos and M. Lewenstein, Phys. Rev. Lett. 88, 170406 (2002).
H. P. Büchler and G. Blatter, Phys. Rev. Lett. 91, 130404 (2003).
V. W. Scarola and S. Das Sarma, Phys. Rev. Lett. 95, 03303 (2005).
G. G. Batrouni and R. T. Scalettar, Phys. Rev. Lett. 84, 1599 (2000).
P. Sengupta et al., Phys. Rev. Lett. 94, 207202 (2005).
L. Santos et al., Phys. Rev. Lett. 93 030601 (2004).
S. Wessel and M. Troyer, Phys. Rev. Lett. 95, 127205 (2005).
J. Villain et al., J. Phys. 41, 1263 (1980).
G. H. Wannier, Phys. Rev. 79, 357 (1950).
G. Murthy, D. Arovas and A. Auerbach, Phys. Rev. B 55, 3104 (1997).
M. Boninsegni, J. Low Temp. Phys. 132, 39 (2003).
D. Heidarian and K. Damle, Phys. Rev. Lett. 95, 127206 (2005).
R. Melko et al., Phys. Rev. Lett. 95, 127207 (2005).
R. B. Dimer et al., Phys. Rev. A 64, 033416 (2001).
P. Horak, J.-Y. Courtois and G. Grynberg, Phys. Rev. A 58, 3953 (2000).
P. W. Anderson, Phys. Rev. B 109, 5 (1958).
E. Tiesinga et al., Phys. Rev. A 47, 4114 (1993).
S. Inouye et al., Nature 392, 151 (1998).
H. Gimperlein, S. Wessel, J. Schmiedmayer, and L. Santos, Phys. Rev. Lett. 95, 170401 (2005).
S. Wildermuth et al., Nature 435, 440 (2005).
J. K. Freericks and H. Monien, Phys. Rev. B 53, 2691 (1996).
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Lavalle, C., Manmana, S.R., Wessel, S., Muramatsu, A. (2007). Monte Carlo Simulations of Strongly Correlated and Frustrated Quantum Systems. In: Nagel, W.E., Jäger, W., Resch, M. (eds) High Performance Computing in Science and Engineering ’06. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-36183-1_11
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DOI: https://doi.org/10.1007/978-3-540-36183-1_11
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