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Springer series in solid-state sciences

Dispersive Single-Particle Excitations in Strongly Correlated Two-Dimensional Systems

Yoshio Kuramoto, HELMUT J. SCHMIDT

Published Jan 1, 1989• 1 citation
Publisher
DOI
10.1007/978-3-642-83836-1_9

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We investigate the effects of suppression of single-particle dispersion near the Fermi level on the spin gap and the singlet-pairing correlation by using the exact diagonalization method for finite-size systems. We consider strongly correlated one-dimensional models, which have flat band dispersions near wave number k=π/2, if the interactions are switched off. Our results for strongly correlated models show that the spin gap region expands as the single-particle dispersion becomes flatter. The region where the singlet-pairing correlation is the most dominant also expands in models with flatter band dispersions. Based on our numerical results, we propose a pairing mechanism induced by the flat-band dispersion.
The pseudogap is a ubiquitous phenomenon in strongly correlated systems, such as high-T c superconductors, ultracold atoms, and nuclear physics.Whereas pairing fluctuations inducing the pseudogap are known to be enhanced in low-dimensional systems, such effects have not been explored well in one of the most fundamental one-dimensional models, that is, Gaudin-Yang model.In this paper, we show how the pseudogap effect emerges in the single-particle excitation in this system using a diagrammatic approach.Fermionic single-particle spectra exhibit a unique crossover from the double-particle dispersion to the pseudogap state with increasing the attractive interaction and the number density at finite temperature.Surprisingly, our results of thermodynamic quantities in unpolarized and polarized gases show an excellent agreement with the recent quantum Monte Carlo and complex Langevin results, indicating the validity of our approach even in the region where the pseudogap appears.
We extend the single mode approximation (SMA) into quantum Monte Carlo simulations to provides an efficient and fast method to obtain the dynamical dispersion of quantum many-body systems. Based on stochastic series expansion (SSE) and its projector algorithms, the SMA+SSE\mathrm{SMA}+\mathrm{SSE}SMA+SSE method can simply extract the dispersion of the dynamical dispersion in the long-wavelength limit and the upper bound of the dispersion elsewhere, without external calculations and high technique barriers. Meanwhile, numerical analytic continuation methods require the fine data of imaginary time correlations and complex programming. Therefore, our method can approach the excitation dispersion of large systems, e.g., we take the two-dimensional Heisenberg model on a $512\ifmmode\times\else\texttimes\fi{}512$ square lattice. We demonstrate the effectiveness and efficiency of our method with high precision via additional examples. We also demonstrate that SMA combined with SSE goes beyond spin-wave theory with numerical results. We further illustrate that SMA is able to extract useful information in strongly correlated systems with competing states.