Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2505.09910

Hidden Bose-Einstein Singularities in Correlated Electron Systems: II. Pseudogap Phase in the Weakly Attractive Hubbard Model

Takafumi Kita
View original source ↗Read source document ↗Export metadata ↓

Abstract

The hidden Bose-Einstein singularities of correlated electron systems, whose possible existence has been pointed out in a previous paper based on quantum field theory of ordered phases [T. Kita, J. Phys. Soc. Jpn. {\bf 93}, 124704 (2024)], are studied in more detail in terms of the attractive Hubbard model, for which the mean-field theory predicts that spin-singlet superconductivity is realized at low enough temperatures for any band structure and interaction strength. It is shown that incorporating correlation effects should change the mean-field superconducting solution substantially and qualitatively even in the weak coupling, implying that the system lies in the strong-coupling region perturbatively. The hidden singularity is found to be present around the mean-field superconducting temperature $T_{{\rm c}0}$, below which the standard self-consistent treatment by quantum field theory cannot be used due to divergences in the zero Matsubara frequency branch obeying Bose-Einstein statistics. Our method to recover the applicability with a Lagrange multiplier predicts that the singularity is a physical entity signaling the threshold of a pseudogap phase with a characteristic V-shape structure in the density of states near zero energy, which lies above the superconducting phase and originates from the emerging one-particle-reducible structure in the self-energy.

Explore related subjects

cond-mat.str-elcond-mat.quant-gascond-mat.stat-mechcond-mat.supr-con

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Takafumi Kita. 2025-07-08. Hidden Bose-Einstein Singularities in Correlated Electron Systems: II. Pseudogap Phase in the Weakly Attractive Hubbard Model. https://doi.org/10.7566/jpsj.94.084703

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

KEEP EXPLORING

Related papers

arXiv2026

Electronic crystals and quasicrystals in semiconductor quantum wells: an AI-powered discovery

The homogeneous electron gas is a cornerstone of quantum condensed matter physics, providing the foundation for developing density functional theory and understanding electronic phases in semiconductors. However, theoretical understanding of strongly-correlated electrons in realistic semiconductor systems remains limited. In this work, we develop a neural network based variational approach to study quantum wells in three dimensional geometry for a variety of electron densities and well thicknesses. Starting from first principles, our unbiased AI-powered method reveals metallic and crystalline phases with both monolayer and bilayer charge distributions. In the emergent bilayer, we discover a new quantum phase of matter: the electronic quasicrystal.

cond-mat.str-el↗
arXiv2026

Graph-Theoretic Formulation of Hamiltonian and Ground-State Sign Structures in Heisenberg Antiferromagnets

We study Heisenberg antiferromagnets through a graph-theoretic representation of their Hamiltonians. In the computational basis of a fixed-magnetization sector, the Heisenberg Hamiltonian equals a constant minus the weighted Laplacian of a graph whose vertices are spin configurations and whose edges connect configurations related by exchanging two antiparallel spins on a lattice bond. We call this graph the Hilbert graph (HG) which is isomorphic to the token graph of the lattice over which the Hamiltonian is defined. The exact ground-state energy is then determined by the largest eigenvalue of the HG Laplacian, which is the spectral relaxation of weighted Max-Cut on the HG. With the amplitudes fixed, the phase-dependent part of the variational energy defines an antiferromagnetic classical XY model on the HG, with couplings set by the amplitudes. Restricting the variational state to be real, i.e., restricting its phases to $\{0,π\}$, reduces the fixed-amplitude energy minimization to solving an antiferromagnetic Ising model and hence a weighted Max-Cut on the HG. When the weights are generated from non-degenerate ground-state amplitudes, the optimal phases give the ground-state sign structure which can be recovered from the weights in time polynomial in the size of the HG. On the Hamiltonian side, a diagonal sign transformation removes all positive off-diagonal matrix elements if and only if the HG is bipartite, which reproduces the Marshall sign rule on bipartite lattices through the graph two-coloring problem; otherwise, the minimal remaining positive weight equals the sum of HG edge weights left uncut by the Max-Cut. This graph formulation establishes a common framework for understanding wave function sign structure, Hamiltonian stoquasticity, non-convexity of phase optimization in variational Monte Carlo, and the average sign in quantum Monte Carlo.

cond-mat.str-el↗
arXiv2026

Compact representation of strongly correlated Green's functions: the MOR+EC way to explore phase space

Repeated evaluation of the single-particle Green's function (GF) across parameter space is a recurring bottleneck in many-body methods, limiting the resolution at which phase boundaries may be probed and the frequency resolution of computed spectra. We introduce MOR+EC, a framework that constructs reusable reduced-order models for computing single-particle Green's functions by combining eigenvector continuation (EC) for parameter space exploration and model order reduction (MOR) for extrapolation in frequency space. Contrary to conventional parameterized MOR, we construct these reduced-order models with a parameter-independent resolvent, further reducing the number of required full-space evaluations. Benchmarking against exact diagonalization as the impurity solver for our example case of DMFT calculations for single- and two-band models, MOR+EC reproduces the DMFT-converged impurity GF to an average relative error below $10^{-3}$, with a median wall-time speedup of $9.5$-$92\times$. This accuracy and efficiency together resolve a fine-grained scan of the impurity occupation as doping is tuned and produce a high-resolution phase diagram of an orbital-selective Mott transition. The reduced-order model also reproduces real- and imaginary-frequency spectra at no additional cost in full-space evaluations. This framework applies broadly to GF-based methods requiring repeated parametric evaluation and high resolution of the frequency axis.

cond-mat.str-el↗