Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.32710

Discrete WKB approach to density profiles in inhomogeneous two-band free-fermion chains

Federico Finkel·Artemio González-López·Martín Zapata
View original source ↗Read source document ↗Export metadata ↓

Abstract

We extend the discrete WKB method to one-dimensional bipartite tight-binding chains of free fermions with slowly varying hopping amplitudes and on-site potentials. We focus on the inhomogeneous Rice-Mele model, suggesting possible experimental realizations thereof in optical superlattices. We derive explicit semiclassical expressions for the single-particle wave functions and density of states, as well as the sublattice-resolved local particle densities and filling fraction at arbitrary Fermi energy. In particular, we show that the WKB density profiles agree with those obtained from the local-density approximation. We analyze the spatial dependence of the local band edges and its consequences for the global spectral structure, and clarify the role played by the phase-space topology in determining the Bohr-Sommerfeld quantization conditions. Finally, we illustrate our results with two representative examples: a homogeneous Rice-Mele chain subject to a harmonic trap and a fully inhomogeneous chain containing a domain wall.

Explore related subjects

cond-mat.str-elmath-phmath.MPquant-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Federico Finkel, Artemio González-López, Martín Zapata. 2026-10-23. Discrete WKB approach to density profiles in inhomogeneous two-band free-fermion chains. https://arxiv.org/abs/2610.32710

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

KEEP EXPLORING

Related papers

arXiv2026

Stabilizing the parquet problem

We systematically analyze the stability of the iterative solution of the parquet equations by studying the spectrum of the Jacobian associated with the commonly used damped fixed-point iteration procedure. In this context, we provide an explicit criterion that determines when the physical fixed point of the parquet iteration becomes unstable. Importantly, we demonstrate that misleading convergence issues, observed in parquet calculations at intermediate-to-high interaction values, are not restricted to parameter regions where the two-particle irreducible vertex diverges, but can also arise in absence of vertex divergences. Hence, the misleading convergence issues of parquet-based algorithms are not directly caused by the crossings of two solutions of the (multivalued) Luttinger-Ward functional, that are associated with vertex divergences. Building on these insights, we apply the controlled stabilization strategy of Phys. Rev. Lett. 137, 016502 (2026) to the challenging case of the parquet iteration. This strategy allows the convergence to the physical solution in the instability regimes. We apply this procedure to the zero-point model and the Hubbard model in the atomic limit, where we successfully stabilize the physical solution deep in the non-perturbative regime, even across multiple divergence lines. Further, we compare our stabilization strategy to alternative fixed-point solvers that can be used to solve the parquet problem.

cond-mat.str-el↗
arXiv2026

Importance of effective Coulomb interactions for $T_c$ in cuprates

Cuprate superconductors exhibit the highest observed superconducting $T_c$ at atmospheric pressure. However, the magnitude of $T_c$ varies significantly between different cuprates. At present, it is unclear what properties of the crystal structure affect $T_c$ most strongly, yet such an understanding must underpin any efforts toward high-$T_c$ materials design. To address this issue, we perform a large scale systematic study, employing a combination of data collection, state-of-the-art numerical methods, and statistical analysis. We identify about 40 different cuprate compounds, and we compile detailed data about their $T_c$'s and crystal structures from literature and the available databases. Using a fully automated procedure, for each compound we compute the DFT bandstructure and downfold it to two of the most commonly studied low-energy lattice models, namely the single-band Hubbard and the three-band Emery models. The downfolding is based on the approach of MLWFs and cRPA. Finally, we apply a thorough and unbiased statistical analysis to investigate the correlations between the experimentally measured $T_c$'s and the computed parameters of our theoretical models. Our data indicates that more sophisticated models might be needed to describe all cuprates on the same footing. Nevertheless, we find that $T_c$ scales well with simple functions of model parameters. We confirm a previously observed trend that $t'$ in the single-band model correlates with the experimental $T_c$, and we find that $T_c$ appears to vanish below a finite value of $t'$, in agreement with recent ground-state calculations for the Hubbard model. However, we find that the coupling strength also plays a role: throughout our entire dataset, $T_c$ correlates the most with the Coulomb coupling on the $p$-orbitals in the 3-band model, highlighting the importance of the oxygen sites in the copper-oxide planes.

cond-mat.str-el↗
arXiv2026

Kinetic competition controls loss-induced exceptional points of Hubbard pairs

Two-body loss can bind two fermions in a Hubbard lattice, yet the binding threshold in the infinite lattice need not be an exceptional point (EP). At fixed total momentum $\mathbf{K}$, the hops of the two particles interfere into a relative-motion hopping along each lattice direction, which sets the kinetic energy of the relative motion. On a hypercubic lattice, the threshold $g_c=1/[πρ_2(0)]$ is an EP precisely when the maximum kinetic energy along one direction exceeds the sum of the transverse maxima. This dominance keeps every transverse-momentum scattering channel propagating near the band center, making the local pair Green function purely imaginary there. Two real-energy scattering zeros associated with coherent perfect absorption then coalesce at the threshold into a second-order EP of the analytically continued pair problem, where loss restores the parity-time symmetry of the pair's scattering solutions. Without a dominant direction, binding occurs without coalescence and without breaking of that symmetry. Total momentum can therefore select EP sectors even on isotropic lattices. More broadly, the kinetic structure of the two-particle continuum determines whether loss-induced binding and exceptional degeneracy coincide.

cond-mat.str-el↗