Superdiffusive Transport in Chaotic Quantum Systems with Nodal Interactions

We introduce a class of interacting fermionic quantum models in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>d</a:mi></a:math> dimensions with nodal interactions that exhibit superdiffusive transport. We establish nonperturbatively that the nodal structure of the interactions gives rise to long-lived quasiparticle excitations that result in a diverging diffusion constant, even though the system is fully chaotic. Using a Boltzmann equation approach, we find that the charge mode acquires an anomalous dispersion relation at long wavelength <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mi>ω</c:mi><c:mo stretchy="false">(</c:mo><c:mi>q</c:mi><c:mo stretchy="false">)</c:mo><c:mo>∼</c:mo><c:msup><c:mrow><c:mi>q</c:mi></c:mrow><c:mrow><c:mi>z</c:mi></c:mrow></c:msup></c:mrow></c:math> with dynamical exponent <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:mi>z</g:mi><g:mo>=</g:mo><g:mi>min</g:mi><g:mo stretchy="false">[</g:mo><g:mo stretchy="false">(</g:mo><g:mn>2</g:mn><g:mi>n</g:mi><g:mo>+</g:mo><g:mi>d</g:mi><g:mo stretchy="false">)</g:mo><g:mo>/</g:mo><g:mn>2</g:mn><g:mi>n</g:mi><g:mo>,</g:mo><g:mn>2</g:mn><g:mo stretchy="false">]</g:mo></g:mrow></g:math>, where <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>n</m:mi></m:math> is the order of the nodal point in momentum space. We verify our predictions in one-dimensional systems using tensor-network techniques.