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Indian Journal of Pure & Applied Physics

Quantum Monte-Carlo simulation study of attractive Hubbard chain

M.S. Khurana, Kamlesh Kumari, Ishwar S Singh

Published Aug 1, 2007• 0 citations
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Abstract

Quantum Monte-Carlo simulations of one-dimensional narrow band systems with attractive interactions (U < 0) have been reported. Using Hubbard model, local squared magnetic moments, probability of double occupancy, spin magnetic susceptibility and various spin pairing correlation functions as a function of Coulomb interactions for different band fillings have been studied.

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Quantum Monte-Carlo simulations of one-dimensional narrow band systems with attractive interactions (U < 0) have been reported. Using Hubbard model, local squared magnetic moments, probability of double occupancy, spin magnetic susceptibility and various spin pairing correlation functions as a function of Coulomb interactions for different band fillings have been studied.
Abstract The path‐integral formulation along with the quantum Monte Carlo method is used to study the physical properties of the one‐dimensional Hubbard model for various band fillings and values of interaction strength U. Results for singlet and triplet pairing correlations, local square magnetic moment, total energy, probability of double occupancy, and nearest‐neighbour charge‐density correlations are presented. These results are explored at β (inverse temperature) = 2.0, 1.0, and 0.5 for the linear chain N = 16. These results show that the effect of correlation on the physical quantities is small for low band‐filling and it becomes most evident for the half‐filled band at finite temperatures.
Many rare earth and actinide intermetallics, known as Heavy Fermion Systems, have recently been successfully described by the Periodic Anderson Model. We investigate, in this work, various electronic and magnetic properties of the one-dimensional Periodic Anderson model using path integral formulation along with the quantum Monte Carlo simulation technique. We have studied the singlet and triplet pairing correlation functions, nearest neighbor charge-density correlations, spin density correlations, local squared magnetic moment and probability of double occupancy of f-electrons, as a function of intra-atomic Coulomb interaction for various values of hybridization parameter and the temperatures.
The Hubbard model has been widely used to describe magnetism due to itinerant electrons. However, except for the one-dimensional case, no exact solution of the model exists. We have studied the two-dimensional Hubbard model on a square lattice using a Monte Carlo simulation technique. Simulations were performed on lattices of up to 8×8 in spatial size. We will discuss results for thermodynamic properties and correlation functions as a function of temperature and interaction strength. For the half-filled band case, our results indicate that the system exhibits long-range antiferromagnetic order in the ground state for any nonzero interaction, although substantially reduced from the classical Néel state due to both charge and spin fluctuations. For the non-half-filled band case, our results suggest that no long-range magnetic order exists. We also don’t find any indication of short-ranged ferromagnetic correlations in the parameter range studied. We have also studied the predictions of various approximate treatments for this model, particularly the static approximation and the coherent potential approximation (CPA). By comparison with the Monte Carlo results, we discuss the validity of these schemes. Finally, we discuss the effect of changing the band structure on the magnetic properties of the system.
We have studied the behavior of pairing correlations and susceptibilities in the repulsive Hubbard model on a two-dimensional square lattice by Monte Carlo simulations. Lattice sizes up to 8\ifmmode\times\else\texttimes\fi{}8, temperatures down to T=0.083 (in units where the bandwidth W=8), interaction strengths up to U=16, and several band fillings ranging from (1/2-filled to (1/4-filled were considered. Our results suggest that the model does not exhibit superconductivity. The implications with respect to possible mechanisms for high-Tc{T}_{c}Tc​ superconductivity in oxides are discussed.
We report the results of zero-temperature quantum Monte Carlo simulations and zero-temperature mean-field calculations of the attractive Hubbard model on chains, ladders, and square lattices. We investigated the predictability of the BCS approximation, the dimensional crossover of the pairing correlation function from one to two dimensions as a function of the ladder width, and the scaling of these correlations to the thermodynamic limit of the two-dimensional model. We found that the BCS wave function is quantitatively correct only for small values of U/t.U/t.U/t. For the system sizes, electron fillings, and interaction strengths studied, we never saw the dimensional crossover. In general, our ability to achieve the dimensional crossover and accurate scaling to the thermodynamic limit was limited by the size of the systems we could simulate. For these sizes, although we saw the necessary signature of off-diagonal long-range order, the properties of the model did not vary monotonically with increasing system size because of shell effects. We contrast this situation with the dimensional crossover and scaling to the thermodynamic limit of the Ising model.
The one-dimensional Hubbard model is studied at and close to half-filling using a generalization of Handscomb's quantum Monte Carlo method. Results for spin-correlation functions and susceptibilities are presented for systems of up to 128 sites. The spin-correlation function at low temperature is well described by a recently introduced formula relating the correlation function of a finite periodic system to the corresponding T=0 correlation function of the infinite system. For the T\ensuremath{\rightarrow}0 divergence of the q=2kF{\mathit{k}}_{\mathit{F}}kF​ spin susceptibility, our results are consistent with the form \ensuremath{\chi}(2kF{\mathit{k}}_{\mathit{F}}kF​)\ensuremath{\sim}\ensuremath{\Vert}ln(T)${\mathrm{\ensuremath{\Vert}}}^{\mathrm{\ensuremath{\sigma}}}$${\mathit{T}}_{\mathrm{\ensuremath{\rho}}}^{\mathit{K}}$-1, with \ensuremath{\sigma}=1/2.