Fast Mixing of Weakly Interacting Fermionic Systems at Any Temperature

We study the mixing time of a recently proposed efficiently implementable Lindbladian designed to prepare the Gibbs states in the setting of weakly interacting fermionic systems. We show that at any temperature, the Lindbladian spectral gap for even parity observables is lower bounded by a constant <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi mathvariant="normal">Δ</a:mi></a:math>, when the interaction strength (e.g., the on-site interaction strength for the Fermi-Hubbard model) is below a constant threshold <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:msub><d:mi>U</d:mi><d:mi>β</d:mi></d:msub></d:math>. Both <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi mathvariant="normal">Δ</f:mi></f:math> and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>U</i:mi><i:mi>β</i:mi></i:msub></i:math> are independent of the system size. This leads to a mixing time estimate that is at most linear in the system size, thus showing that the corresponding Gibbs states can be prepared efficiently on quantum computers. Our result also implies exponential decay of correlation in these Gibbs states and efficient learnability of their properties.