Real-space renormalization group study of the Hubbard model on a non-bipartite lattice (original) (raw)
Real-space renormalization-group study of the Hubbard model: A modified scheme
Physical Review B, 1998
We present the real-space block renormalization group equations for fermion systems described by a Hubbard Hamiltonian on a triangular lattice with hexagonal blocks. The conditions that keep the equations from proliferation of the couplings are derived. Computational results are presented including the occurrence of a first-order metal-insulator transition at the critical value of U/t ≈ 12.5.
Journal of Physics: Condensed Matter, 1999
We have studied the Hubbard model with bond-charge interaction on a triangular lattice for a half-filled band. At the point of particle-hole symmetry the model could be analyzed in detail in two opposite regimes of the parameter space. Using a real space renormalization group we calculate the ground state energy and the local moment over the whole parameter space. The RG results obey the exact results in the respective limits. In the intermediate region of the parameter space the RG results clearly show the effects of the non-bipartite geometry of the lattice as well as the absence of symmetry in the reversal of the sign of the hopping matrix element.
Phases of the Infinite U Hubbard Model on Square Lattices
We apply the density matrix renormalization group (DMRG) to study the phase diagram of the infinite U Hubbard model on 2-, 4-, and 6-leg ladders. Where the results are largely insensitive to the ladder width, we consider the results representative of the 2D square lattice model. We find a fully polarized ferromagnetic Fermi liquid phase when n, the density of electrons per site, is in the range 1 > n > nF ≈ 4/5. For n = 3/4 we find an unexpected commensurate insulating "checkerboard" phase with coexisting bond density order with 4 sites per unit cell and block spin antiferromagnetic order with 8 sites per unit cell. For 3/4 > n, the wider ladders have unpolarized groundstates, which is suggestive that the same is true in 2D.
Physical Review B, 2008
We investigate the Hubbard model on the triangular lattice at half-filling using the dynamical cluster approximation (DCA) and dual fermion (DF) methods in combination with continuous-time quantum Monte carlo (CT QMC) and semiclassical approximation (SCA) methods. We study the one-particle properties and nearest-neighbor spin correlations using the DCA method. We calculate the spectral functions using the CT QMC and SCA methods. The spectral function in the SCA and obtained by analytic continuation of the Pade approximation in CT QMC are in good agreement. We determine the metal-insulator transition (MIT) and the hysteresis associated with a first-order transition in the double occupancy and nearest-neighbor spin correlation functions as a function of temperature. As a further check, we employ the DF method and discuss the advantages and limitation of the dynamical mean field theory (DMFT), DCA and recently developed DF methods by comparing Green's functions. We find an enhancement of antiferromagnetic (AF) correlations and provide evidence for magnetically ordered phases by calculating the spin susceptibility.
Mott metal-insulator transition in the half-filled Hubbard model on the triangular lattice
Physical Review B, 2001
We investigate the metal-insulator transition in the half-filled Hubbard model on a two-dimensional triangular lattice using both the Kotliar-Ruckenstein slave-boson technique, and exact numerical diagonalization of finite clusters. Contrary to the case of the square lattice, where the perfect nesting of the Fermi surface leads to a metal-insulator transition at arbitrarily small values of U , always accompanied by antiferromagnetic ordering, on the triangular lattice, due to the lack of perfect nesting, the transition takes place at a finite value of U , and frustration induces a nontrivial competition among different magnetic phases. Indeed, within the mean-field approximation in the slave-boson approach, as the interaction grows the paramagnetic metal turns into a metallic phase with incommensurate spiral ordering. Increasing further the interaction, a linear spin-densitywave is stabilized, and finally for strong coupling the latter phase undergoes a first-order transition towards an antiferromagnetic insulator. No trace of the intermediate phases is instead seen in the exact diagonalization results, indicating a transition between a paramagnetic metal and an antiferromagnetic insulator. 71.10.Fd, 71.30.+h, 75.10.Lp
Equation of State of the Fermionic 2D Hubbard Model
2013
We present results for the equation of state of the two-dimensional Hubbard model on an isotropic square lattice as obtained from a controlled and numerically exact large-cluster dynamical mean field simulation. Our results are obtained for large but finite systems and are extrapolated to infinite system size using a known finite size scaling relation. We present the energy, entropy, double occupancy and nearest-neighbour spin correlations extrapolated to the thermodynamic limit and discuss the implications of these calculations on pseudogap physics of the 2D-Hubbard model away from half filling. We find a strong behavioural shift in energy below a temperature T * which becomes more pronounced for larger clusters. Finally, we provide reference calculations and tables for the equation of state for values of doping away from half filling which are of interest to cold atom experiments.
Role of the attractive intersite interaction in the extended Hubbard model
The European Physical Journal B, 2008
We consider the extended Hubbard model in the atomic limit on a Bethe lattice with coordination number z. By using the equations of motion formalism, the model is exactly solved for both attractive and repulsive intersite potential V. By focusing on the case of negative V , i.e., attractive intersite interaction, we study the phase diagram at finite temperature and find, for various values of the filling and of the on-site coupling U , a phase transition towards a state with phase separation. We determine the critical temperature as a function of the relevant parameters, U/|V |, n and z and we find a reentrant behavior in the plane (U/|V |,T). Finally, several thermodynamic properties are investigated near criticality.
The two orbital Hubbard model in a square lattice: a DMFT + DMRG approach
Journal of Physics: Conference Series, 2014
We develop a precise and reliable numerical method for the calculation of electronic properties of the two orbital Hubbard model in a square lattice at half filling, based on the Dynamical Mean Field Theory (DMFT). We use the Density Matrix Renormalization Group (DMRG) as the impurity solver for the DMFT 's selfconsistent equations to obtain accurate values for the Green's functions on the real axis. This way, reliable densities of states are obtained that do not need to resort to analytical continuation methods as those using quantum Monte Carlo techniques. Large system sizes can be achieved with increasing accuracy.
Physical Review B, 2007
We analyze the particle-hole symmetric two-dimensional Hubbard model on a square lattice starting from weak-to-moderate couplings by means of the field-theoretical renormalization group (RG) approach up to two-loop order. This method is essential in order to evaluate the effect of the momentum-resolved anomalous dimension eta(textbfp)\eta(\textbf{p})eta(textbfp) which arises in the normal phase of this model on the corresponding low-energy single-particle excitations. As a result, we find important indications pointing to the existence of a non-Fermi liquid (NFL) regime at temperature Tto0T\to 0Tto0 displaying a truncated Fermi surface (FS) for a doping range exactly in between the well-known antiferromagnetic insulating and the dx2−y2d_{x^2-y^2}dx2−y2-wave singlet superconducting phases. This NFL evolves as a function of doping into a correlated metal with a large FS before the dx2−y2d_{x^2-y^2}dx2−y2-wave pairing susceptibility finally produces the dominant instability in the low-energy limit.
Numerical study of the two-dimensional Hubbard model
Physical review. B, Condensed matter, 1989
We report on a numerical study of the two-dimensional Hubbard model and describe two new al- gorithms for the simulation of many-electron systems. These algorithms allow one to carry out simulations within the grand canonical ensemble at significantly lower temperatures than had previ- ously been obtained and to calculate ground-state properties with fixed numbers of electrons. We present results for the two-dimerisional Hubbard model with half-and quarter-filled bands. Our re- sults support the existence of long-range antiferromagnetic order in the ground state at half-filling and its absence at quarter-filling. Results for the magnetic susceptibility and the momentum occu- pation along with an upper bound to the spin-wave spectrum are given. We find evidence for an at- tractive effective d-wave pairing interaction near half-filling but have not found evidence for a phase transition to a superconducting state.