Interaction-enhanced nesting in spin-fermion and Fermi-Hubbard models

The spin-fermion (SF) model postulates that the dominant coupling between low-energy fermions in near critical metals is mediated by collective spin fluctuations (paramagnons) peaked at the Néel wave vector, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi mathvariant="bold">Q</a:mi><a:mi>N</a:mi></a:msub></a:math>, connecting hot spots on opposite sides of the Fermi surface. It has been argued that strong correlations at hot spots lead to a Fermi surface deformation (FSD) featuring flat regions and increased nesting. This conjecture was confirmed in the perturbative self-consistent calculations when the paramagnon propagator dependence on momentum deviation from <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:msub><c:mi mathvariant="bold">Q</c:mi><c:mi>N</c:mi></c:msub></c:math> is given by <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:msup><e:mi>χ</e:mi><e:mrow><e:mo>−</e:mo><e:mn>1</e:mn></e:mrow></e:msup><e:mo>∝</e:mo><e:mrow><e:mo>|</e:mo><e:mi mathvariant="normal">Δ</e:mi><e:mi>q</e:mi><e:mo>|</e:mo></e:mrow></e:mrow></e:math>. Using diagrammatic Monte Carlo (diagMC) technique we show that such a dependence holds only at temperatures orders of magnitude smaller than any other energy scale in the problem, indicating that a different mechanism may be at play. Instead, we find that a <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:msup><g:mi>χ</g:mi><g:mrow><g:mo>−</g:mo><g:mn>1</g:mn></g:mrow></g:msup><g:mo>∝</g:mo><g:msup><g:mrow><g:mo>|</g:mo><g:mi mathvariant="normal">Δ</g:mi><g:mi>q</g:mi><g:mo>|</g:mo></g:mrow><g:mn>2</g:mn></g:msup></g:mrow></g:math> dependence yields a robust finite-<i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mi>T</i:mi></i:math> scenario for achieving FSD. To link phenomenological and microscopic descriptions, we applied the connected determinant diagMC method to the <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:mrow><j:mo>(</j:mo><j:mi>t</j:mi><j:mo>−</j:mo><j:msup><j:mi>t</j:mi><j:mo>′</j:mo></j:msup><j:mo>)</j:mo></j:mrow></j:math> Hubbard model and found that at large <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:mrow><k:mi>U</k:mi><k:mo>/</k:mo><k:mi>t</k:mi><k:mo>&gt;</k:mo><k:mn>5.5</k:mn></k:mrow></k:math> before the formation of electron and hole pockets (i) the FSD defined as a maximum of the spectral function is not very pronounced; instead, it is the lines of zeros of the renormalized dispersion relation that deforms toward nesting, and (ii) the static spin susceptibility is well described by <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"><l:mrow><l:msup><l:mi>χ</l:mi><l:mrow><l:mo>−</l:mo><l:mn>1</l:mn></l:mrow></l:msup><l:mo>∝</l:mo><l:msup><l:mrow><l:mo>|</l:mo><l:mi mathvariant="normal">Δ</l:mi><l:mi>q</l:mi><l:mo>|</l:mo></l:mrow><l:mn>2</l:mn></l:msup></l:mrow></l:math>. Flat FS regions yield a nontrivial scenario for realizing a non-Fermi liquid state. Published by the American Physical Society 2024