Pair binding and Hund’s rule breaking in high-symmetry fullerenes

Highly-symmetric molecules often exhibit degenerate tight-binding states at the Fermi edge. This typically results in a magnetic ground state if small interactions are introduced in accordance with Hund’s rule. In some cases, Hund’s rule may be broken, which signals pair binding and goes hand-in-hand with an attractive pair-binding energy. We investigate pair binding and Hund’s rule breaking for the Hubbard model on high-symmetry fullerenes C _{20} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi/> <mml:mn>20</mml:mn> </mml:msub> </mml:math> , C _{20} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi/> <mml:mn>20</mml:mn> </mml:msub> </mml:math> , C _{40} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi/> <mml:mn>40</mml:mn> </mml:msub> </mml:math> , and C _{60} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi/> <mml:mn>60</mml:mn> </mml:msub> </mml:math> by using large-scale density-matrix renormalization group calculations. We exploit the SU(2) spin symmetry, the U(1) charge symmetry, and optionally the \mathbb{Z}_N <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mstyle mathvariant="double-struck"> <mml:mi>ℤ</mml:mi> </mml:mstyle> <mml:mi>N</mml:mi> </mml:msub> </mml:math> spatial rotation symmetry of the problem. For C _{20} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi/> <mml:mn>20</mml:mn> </mml:msub> </mml:math> , our results agree well with available exact-diagonalization data, but our approach is numerically much cheaper. We find a Mott transition at U_c\sim2.2t <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mi>U</mml:mi> <mml:mi>c</mml:mi> </mml:msub> <mml:mo>∼</mml:mo> <mml:mn>2.2</mml:mn> <mml:mi>t</mml:mi> </mml:mrow> </mml:math> , which is much smaller than the previously reported value of U_c\sim4.1t <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mi>U</mml:mi> <mml:mi>c</mml:mi> </mml:msub> <mml:mo>∼</mml:mo> <mml:mn>4.1</mml:mn> <mml:mi>t</mml:mi> </mml:mrow> </mml:math> that was extrapolated from a few datapoints. We compute the pair-binding energy for arbitrary values of U <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>U</mml:mi> </mml:math> and observe that it remains overall repulsive. For larger fullerenes, we are not able to evaluate the pair binding energy with sufficient precision, but we can still investigate Hund’s rule breaking. For C _{28} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi/> <mml:mn>28</mml:mn> </mml:msub> </mml:math> , we find that Hund’s rule is fulfilled with a magnetic spin-2 ground state that transitions to a spin-1 state at U_{c,1}\sim 5.4t <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mi>U</mml:mi> <mml:mrow> <mml:mi>c</mml:mi> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> <mml:mo>∼</mml:mo> <mml:mn>5.4</mml:mn> <mml:mi>t</mml:mi> </mml:mrow> </mml:math> before the eventual Mott transition to a spin singlet takes place at U_{c,2}\sim 11.6t <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mi>U</mml:mi> <mml:mrow> <mml:mi>c</mml:mi> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:mo>∼</mml:mo> <mml:mn>11.6</mml:mn> <mml:mi>t</mml:mi> </mml:mrow> </mml:math> . For C _{40} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi/> <mml:mn>40</mml:mn> </mml:msub> </mml:math> , Hund’s rule is broken in the singlet ground state at half filling, but is restored if the system is doped with one electron. Hund’s ru