Bulletin of the American Physical Society
2006 APS March Meeting
Monday–Friday, March 13–17, 2006; Baltimore, MD
Session Y6: Is the Hubbard/t-J Model a High Temperature Superconductor? |
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Sponsoring Units: DCOMP Chair: Steven Kivelson, University of California, Los Angeles Room: Baltimore Convention Center 310 |
Friday, March 17, 2006 8:00AM - 8:36AM |
Y6.00001: High-$T_c$ and $t$-$J$ model: passions and disappointments Invited Speaker: I will discuss the high-temperature phase diagram of the
two-dimensional $t$-$J$ and related models. Among the many numerical
and analytical techniques which have been used to search for
superconductivity in these models, only a few provide unbiased
results. Particularly, the high-temperature series constructed for a
number of thermodynamical correlation functions indicate that in the
accessible range of temperatures, $T\ge J/2$, the superconducting
fluctuations are only pronounced in the unphysical regime, $J>t$,
while they are strongly suppressed in the physical regime, $J |
Friday, March 17, 2006 8:36AM - 9:12AM |
Y6.00002: Enhanced d-wave Superconducting Fluctuations in the 2D t-J model Invited Speaker: I have calculated high temperature series to 12th order in inverse temperature for singlet superconducting correlation functions of the 2D $t$-$J$ model with $s$-, $d_{x^2-y^2}$ and $d_{xy}$-symmetry pairs. The strengths of the different symmetry correlations are measured using ${\bf q}=0$ correlation lengths. I find that for $J/t=0.4$ the correlation length for $d_{x^2-y^2}$ pairing grows strongly with decreasing temperature, developing a broad peak around doping $\delta=0.25$ when the temperature is reduced to $T/J=0.25$. The correlation lengths for $s$ and $d_{xy}$ pairs remain small and do not display peaks as a function of doping. The temperature scale for growth in the $d_{x^2-y^2}$ correlation length agrees with the temperature scale where the temperature derivative of the momentum distribution function $dn_{\bf k}/dT$ and the gradient of the momentum distribution function $|\nabla_{\bf k}n_{\bf k}|$ develop peaks on the Brillouin zone diagonal. This indicates that the low energy excitations in the 2D $t$-$J$ model are concentrated near the zone diagonal, as would be expected for superconducting order with $d_{x^2-y^2}$-symmetry pairs. I will also discuss differences between my calculation and previous calculations for superconducting correlations in the 2D $t$-$J$ model. [Preview Abstract] |
Friday, March 17, 2006 9:12AM - 9:48AM |
Y6.00003: $d$-wave resonating valence bond states of ultracold fermionic atoms in optical lattices Invited Speaker: In view of the apparently exponential complexity of fermionic simulations in two and more dimensions, we consider a controlled quantum simulation to probe the ground state properties of the two-dimensional Hubbard model. We present a controlled experimental setup to adiabatically construct superfluid $d$-wave resonating valence bond (RVB) states of fermionic atoms confined in a 2D optical lattice. The key idea is to start from a pure initial state which is adiabatically transformed to $d$-wave RVB states at ultralow temperatures of a few percent of the Fermi temperature. We discuss hole doping techniques and describe a simple experimental measurement to study $d$-wave pairing.The proposed experiment can be used to effectively probe ground state properties of the repulsive Hubbard model on (coupled) plaquettes, ladders and the 2D square lattice. The proposal is within the capabilities of current technology, and shows how an adiabiatic quantum simulator could answer a question that cannot currently be reliably answered by classical computational methods. Reference: S. Trebst, U. Schollw\"ock, M. Troyer and P. Zoller, cond-mat/0506809. [Preview Abstract] |
Friday, March 17, 2006 9:48AM - 10:24AM |
Y6.00004: Superconducting correlations and thermodynamic properties in 2D square and triangular $t$-$J$ model Invited Speaker: Equal-time superconducting correlation functions of the two-dimensional $t$-$J$ model on the square lattice are studied using high-temperature expansion method.[1] The sum of the pairing correlation, its spatial dependence and correlation length are obtained down to $T \simeq 0.2t$. By comparison of single-particle contributions in the correlation functions, we find effective attractive interactions between quasi-particles in $d_{x^2-y^2}$-wave channel. It is shown that $d$-wave correlation grows rapidly at low temperatures for the doping $0.1 < \delta < 0.5$. The temperature for this growth is roughly scaled by $J/2$. This is in sharp contrast to the Hubbard model in a weak or intermediate coupling region, where there are few numerical evidences of superconductivity. We also study the possible $d$- and $f$-wave pairing in the triangular $t$-$J$ model.[2] When $t>0$ with hole doping, a rapid growth of effective $d$-wave paring interaction is found that indicates the resonating-valence-bond superconductivity. In contrast, when $t<0$, where the ferromagnetic- and antiferromagnetic correlation compete, correlation lengths of the $f$-wave triplet paring tends to diverge around $\delta=0.6$, although its effective interaction is small. This result is compared and discussed with the recently discovered superconductor, Na$_x$CoO$_2$$\cdot y$H$_2$O, where Co atoms form a triangular lattice. Specific heat in low temperatures are also obtained in the high-temperature expansion method. We will discuss that the doping dependence of the specific heat coefficient, $\gamma$, agrees with experimental data. \par\noindent [1] T. Koretsune and M. Ogata, J.\ Phys.\ Soc.\ Japan {\bf 74}, 1390 (2005). [2] T. Koretsune and M. Ogata, Phys.\ Rev.\ Lett.\ {\bf 89}, 116401 (2002), and Phys.\ Rev.\ B{\bf 72}, 134513 (2005). [Preview Abstract] |
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