scholarly journals Kohn-Luttinger instability of thet−t′Hubbard model in two dimensions: Variational approach

2003 ◽  
Vol 67 (17) ◽  
Author(s):  
J. Mráz ◽  
R. Hlubina
Keyword(s):  
Hubbard Model ◽  
Variational Approach ◽  
Two Dimensions

PHASE TRANSITION IN $g\varphi^4_2$ THEORY

1992 ◽  
Vol 07 (24) ◽  
pp. 2189-2197 ◽  
Author(s):  
G. V. EFIMOV ◽  
G. GANBOLD
Keyword(s):  
Phase Transition ◽  
Order Phase Transition ◽  
Effective Potential ◽  
Variational Approach ◽  
Two Dimensions ◽  
Second Order ◽  
Complete Agreement ◽  
Vacuum Stability ◽  
Second Order Phase Transition

The vacuum stability of a scalar gφ4 theory in two dimensions is studied. A variational approach is applied to estimate the effective potential in this model. We find that the second order phase transition takes place. It is in complete agreement with the Simon-Griffiths theorem.

Variational Approach for the Bose–Hubbard Model

2008 ◽  
Vol 25 (5) ◽  
pp. 1792-1794
Author(s):  
Yu De-Shui ◽  
Chen Jing-Biao
Keyword(s):  
Hubbard Model ◽  
Variational Approach

LUTTINGER-LIQUID BEHAVIOUR IN 2D: THE VARIATIONAL APPROACH

1993 ◽  
Vol 07 (03) ◽  
pp. 119-141 ◽  
Author(s):  
CLAUDIUS GROS ◽  
ROSER VALENTÍ
Keyword(s):  
Monte Carlo ◽  
Variational Formulation ◽  
Variational Approach ◽  
Order Parameter ◽  
Luttinger Liquid ◽  
Two Dimensions ◽  
Point Of View ◽  
Two Dimensional ◽  
Liquid Type ◽  
D Wave

We study a variational formulation of the Luttinger-liquid concept in two dimensions. We show that a Luttinger-liquid wavefunction with an algebraic singularity at the Fermiedge is given by a Jastrow-Gutzwiller type wavefunction, which we evaluate by variational Monte Carlo for lattices with up to 38 × 38 = 1444 sites. We therefore find that, from a variational point of view, the concept of a Luttinger liquid is well defined even in 2D. We also find that the Luttinger liquid state is energetically favoured by the projected kinetic energy in the context of the 2D t-J model. We study and find coexistence of d-wave superconductivity and Luttinger-liquid behaviour in two-dimensional projected wavefunctions. We then argue that generally, any two-dimensional d-wave superconductor should be unstable against Luttinger-liquid type correlations along the (quasi-1D) nodes of the d-wave order parameter, at temperatures small compared to the gap.

scholarly journals Superconducting instabilities of the non-half-filled Hubbard model in two dimensions

1996 ◽  
Vol 54 (13) ◽  
pp. 9509-9519 ◽  
Author(s):  
D. Zanchi ◽  
H. J. Schulz
Keyword(s):  
Hubbard Model ◽  
Two Dimensions
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