Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1501.03587

The Hubbard model in the strong coupling theory at arbitrary filling

A. Sherman
View original source ↗Read source document ↗Export metadata ↓

Abstract

Equations for the electron Green's function of the two-dimensional Hubbard model, derived using the strong coupling diagram technique, are self-consistently solved for different electron concentrations $n$ and tight-binding dispersions. Comparison of spectral functions calculated for the ratio of Hubbard repulsion to the nearest neighbor hopping $U/t=8$ with Monte Carlo data shows not only qualitative, but in some cases quantitative agreement in position of maxima. General spectral shapes, their evolution with momentum and filling in the wide range $0.7\lesssim n\leq 1$ are also similar. At half-filling and for the next nearest neighbor hopping constant $t'=-0.3t$ the Mott transition occurs at $U_c\approx 7Δ/8$, where $Δ$ is the initial bandwidth. This value is close to those obtained in the cases of the semi-elliptical density of states and for $t'=0$. In the case $U=8t$ and $t'=-0.3t$ the Mott gap reaches maximum width at $n=1.04$, and it is larger than that at $t'=0$ for half-filling. In all considered cases positions of spectral maxima are close to those in the Hubbard-I approximation.

Explore related subjects

cond-mat.str-el

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

A. Sherman. 2015-01-15. The Hubbard model in the strong coupling theory at arbitrary filling. https://doi.org/10.1002/pssb.201552026

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Autoregressive Neural Network Extrapolation of Quantum Spin Dynamics Across Time and Space

Understanding the long-time dynamics of strongly correlated quantum matter remains a major challenge: as quantum entanglement grows during time evolution, conventional numerical methods become increasingly costly, limiting access to the long-range correlations and low-energy excitations that govern gapless systems. Here we show that these dynamical correlations can be extended beyond the accessible numerical window without explicitly evolving the underlying many-body wavefunction. We introduce an autoregressive machine-learning framework that enables the extrapolation of dynamical spin correlations in both time and space beyond the reach of conventional numerical methods. Trained on time-dependent density matrix renormalization group simulations of the gapless XXZ model, our approach is benchmarked against exact solutions available for this analytically solvable system. Combined with physics-informed spatial extension, a multi-layer perceptron model using ReLU activation functions has been shown to be superior to convolutional neural networks and linear regressions for longer time extrapolation. A study of error accumulation further demonstrates that our autoregressive neural network extrapolations are highly robust to perturbations, suggesting stable and reliable predictions. This work offers a complementary route to studying the dynamics of gapless quantum many-body systems, in which machine learning extends and complements the capabilities of state-of-the-art numerical approaches.

cond-mat.str-el↗
arXiv2026

Symbolic recursion method for strongly correlated fermions in two and three dimensions

We present a symbolic implementation of the recursion method for dynamical correlations and transport in fermionic systems on one-, two-, and three-dimensional lattices. The implementation is applicable in the strongly correlated regime, yields results directly in the thermodynamic limit, and covers all time scales, from short times through the thermalization time to the late-time asymptotics. Focusing on two paradigmatic models -- interacting spinless fermions and the Hubbard model -- we confirm the universal operator growth hypothesis in the fermionic case, compute infinite-temperature current-current autocorrelation functions, and determine the charge diffusion constant and the high-temperature conductivity. The diffusion constant is obtained in both the perturbative and the nonperturbative regime of the interaction strength, and we locate the boundary between them. We compare our approach with the Majorana propagation method, which converges up to intermediate times and agrees with ours where converged. Our results highlight a symbolic computational paradigm in which the most expensive step is performed once, producing reusable symbolic output that yields physical observables for arbitrary model parameters.

cond-mat.str-el↗
arXiv2026

Anomalous Diffusion and Superdiffusion in Integrable Spin Chains via a Soliton Gas Mapping

We introduce a multi-species soliton gas in which each species has a distinct effective scattering length, and the repulsive scattering shift is set by the smaller of the two colliding particles. We argue that this model shares key quasiparticle and scattering features with the XXZ spin chain. We show that fixing only the functional decay of bare velocities with particle size is sufficient to reproduce the XXZ spin-transport phase diagram: diffusion (with anomalous fluctuations) in the anisotropic regime and superdiffusion at the isotropic point. We then demonstrate that the statistics of charge transfer differs qualitatively from that of \textit{particle trajectories}. For large particles, trajectories are Gaussian in the diffusive regime and appear to exhibit KPZ statistics at the isotropic point, providing a direct microscopic signature of KPZ physics in integrable quasiparticle motion. In contrast, charge-transfer fluctuations are anomalous in the anisotropic regime, while they cross over to Gaussian statistics at late times at the isotropic point, reconciling non-Gaussian trajectory fluctuations with Gaussian charge-transfer statistics. Our results establish this soliton gas as a minimal framework for anomalous spin and charge transport in integrable systems, and offer new insight into the origin of KPZ fluctuations in isotropic integrable models.

cond-mat.str-el↗