Superfluid transition of bond bipolarons with long-range Coulomb repulsion in two dimensions

Abstract

Using numerically exact diagrammatic Monte Carlo simulations in the two-electron (single-bipolaron) sector, we explore the impact of long-range Coulomb repulsion on the dilute-limit Berezinskii--Kosterlitz--Thouless (BKT) transition temperature $T_c$ of bipolarons on a two-dimensional square lattice. We study the bond Su--Schrieffer--Heeger model, in which bond phonons modulate the electron hopping. In the absence of long-range repulsion, this model was shown to support small, light bipolarons with a comparatively high transition temperature \cite{PhysRevX.13.011010}. Here we find that long-range Coulomb repulsion suppresses the optimal $T_c$ but leaves it appreciable over a broad parameter window, including the adiabatic regime $ω/t=0.5$ at a representative Coulomb strength $V=U/10$ (with $U$ the on-site repulsion). Our results provide controlled single-bipolaron inputs for dilute-limit $T_c$ estimates in the presence of long-range repulsion.

Figures (5)

• Figure 1: Dilute-limit BKT estimates of $T_c/\omega$ for bond (SSH) bipolarons as a function of the dimensionless coupling $\lambda$ [defined in Eq. \ref{['lambda']}], for Coulomb strengths $V=0$ (black dots), $V=U/20$ (red squares), and $V=U/10$ (blue triangles), at fixed $\omega/t=1.0$ and $U/t=8.0$. The estimates are obtained from Eq. \ref{['Eq2']} using diagrammatic Monte Carlo results for the single-bipolaron effective mass $m^{*}_{\mathrm{BP}}$ and mean-square radius $R^2_{\mathrm{BP}}$ in the two-electron sector. Error bars denote one standard deviation (statistical).
• Figure 2: Single-bipolaron properties computed from diagrammatic Monte Carlo simulations of Eq. \ref{['Eq1']} at $\omega/t=1.0$ as a function of the dimensionless coupling $\lambda$, for $U/t=8.0$ and Coulomb strengths $V=0$ (black dots), $V=U/20$ (red squares), and $V=U/10$ (blue triangles). (a) Binding energy $\Delta_{\mathrm{BP}}$ in units of $t$. (b) Effective mass $m^{*}_{\mathrm{BP}}/m_0$. (c) Mean-square radius $R_{\mathrm{BP}}^2$. Error bars denote one standard deviation (statistical).
• Figure 3: Dilute-limit BKT estimates of $T_c/\omega$ for bond (SSH) bipolarons as a function of the dimensionless coupling $\lambda$, for Coulomb strengths $V=0$ (black dots), $V=U/20$ (red squares), $V=U/10$ (blue triangles), and $V=U/4$ (purple diamonds), at fixed $\omega/t=0.5$ and $U/t=8.0$. The estimates are obtained from Eq. \ref{['Eq2']} using diagrammatic Monte Carlo results for the single-bipolaron effective mass $m^{*}_{\mathrm{BP}}$ and mean-square radius $R^2_{\mathrm{BP}}$ in the two-electron sector. Error bars denote one standard deviation (statistical).
• Figure 4: Single-bipolaron properties from diagrammatic Monte Carlo simulations of Eq. \ref{['Eq1']} at $\omega/t=0.5$ as a function of the dimensionless coupling $\lambda$, for $U/t=8.0$ and Coulomb strengths $V=0$ (black dots), $V=U/20$ (red squares), $V=U/10$ (blue triangles), and $V=U/4$ (purple diamonds). (a) Binding energy $\Delta_{\mathrm{BP}}$ in units of $t$. (b) Effective mass $m^{*}_{\mathrm{BP}}/m_0$. (c) Mean-square radius $R^2_{\mathrm{BP}}$. Error bars denote one standard deviation (statistical).
• Figure 5: Optimized dilute-limit BKT estimates of $T_c/\omega$ as a function of the dimensionless coupling $\lambda$ for fixed $V=U/10$ and $\omega/t=0.5$, shown for $U/t=4$ (red squares), $6$ (blue down-triangles), and $8$ (green up-triangles). Error bars denote one standard deviation (statistical).