2024/11/29 by Gerard Pascual, Pascual, Gerard, J. Boronat +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #Nonlinear Waves and Solitons #Quantum Gases (cond-mat.quant-gas) #Strongly Correlated Electrons (cond-mat.str-el)
paper · pdf · doi:10.48550/arxiv.2411.19725
openalex publication_date 2024/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A two-dimensional spin-up ideal Fermi gas interacting attractively with a spin-down impurity in the continuum undergoes, at zero temperature, a first-order phase transition from a polaron to a dimeron state. Here we study a similar system on a square lattice, by considering the attractive 2D Fermi-Hubbard model with a single spin-down and a finite filling fraction of spin-up fermions. We study polaron and dimeron quasi-particle properties via variational Ansatz up to one particle-hole excitation. Moreover, we develop a determinant diagrammatic Monte Carlo algorithm for this problem based on expansion in bare on-site coupling U. This algorithm turns out to be sign-problem free at any filling of spin-up fermions, allowing one to sample very high diagram order (larger than 200 in our study) and to do simulations for large U/t (we go up to U/t=-20 with t the hopping strength). Both methods give qualitatively consistent results. With variational Ansatz we go to even larger on-site attraction. In contrast with the continuum case, we do not observe any polaron-to-dimeron transition for a range of spin-up filling fractions ρ\uparrow between 0.1 and 0.4. % (away from the low-filling limit). The polaron state always gives a lower energy and has a finite quasi-particle residue.