BCS-BEC crossover in trapped one-dimensional Fermi-Hubbard chains: entanglement and correlation signatures from DMRG and effective-pairing theory

TL;DR

This paper investigates the BCS-BEC crossover in trapped one-dimensional Fermi-Hubbard chains using DMRG simulations and effective models, revealing how confinement influences pairing and superfluid correlations.

Contribution

It combines DMRG and entanglement diagnostics with effective theories to characterize the BCS-BEC crossover in confined geometries, highlighting the emergence of unconventional phases.

Findings

Confinement reshapes correlation patterns and leads to coexisting insulating and superfluid regions.

Conditioned correlation functions with power-law decay distinguish BCS-like and BEC-like regimes.

Effective models agree with DMRG results, providing a unified understanding of the crossover.

Abstract

Confined ultracold atoms in optical lattices provide a versatile platform for simulating lattice models of strongly correlated quantum systems, where pairing phenomena and superfluid phases can be explored under controlled conditions. While the crossover between the Bardeen-Cooper-Schrieffer (BCS) phase and the Bose-Einstein condensation (BEC) is well understood in homogeneous systems, spatial confinement breaks translational symmetry and reshapes correlation patterns, making the BCS-BEC identification in trapped geometries challenging and allowing unconventional phases to emerge with no direct analog in homogeneous systems. Here we present a characterization of the BCS-BEC crossover in harmonically confined one-dimensional Fermi-Hubbard chains. Our analysis combines Density Matrix Renormalization Group (DMRG) simulations and entanglement-based diagnostics with effective models describing the formation of tightly bound fermion pairs. This combined approach enables a detailed understanding of how the interplay between interactions and confinement reshapes the crossover, leading to insulating regions coexisting with persistent superfluid correlations. Within this framework, we further introduce conditioned correlation functions whose power-law decay allows a clear distinction between BCS-like and BEC-like regimes. The consistency between the effective descriptions and the numerical DMRG results yields a unified picture of the crossover in harmonically confined geometries.