Finite-temperature real-time properties of magnetic polarons in two-dimensional quantum antiferromagnets

Due to significant progress in quantum gas microscopy in recent years, there is a rapidly growing interest in real-space properties of single mobile dopands created in correlated antiferromagnetic (AFM) Mott insulators. However, a detailed numerical description remains challenging, even for simple toy models. As a consequence, previous numerical simulations for large systems were largely limited to <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>T</a:mi> <a:mo>=</a:mo> <a:mn>0</a:mn> </a:mrow> </a:math> . To provide guidance for cold-atom experiments, numerical calculations at finite temperature are required. Here, we numerically study the real-time properties of a single mobile hole in the 2D <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mi>t</b:mi> <b:mtext>−</b:mtext> <b:mi>J</b:mi> </b:mrow> </b:math> model at finite temperature and draw a comparison to features observed at <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mi>T</c:mi> <c:mo>=</c:mo> <c:mn>0</c:mn> </c:mrow> </c:math> . We find that a three-stage process of hole motion, which was reported at <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mi>T</d:mi> <d:mo>=</d:mo> <d:mn>0</d:mn> </d:mrow> </d:math> , is valid even at finite temperature. However, already at low temperatures, the average hole velocity at long times is not simply proportional to the spin coupling, contrary to the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:mi>T</e:mi> <e:mo>=</e:mo> <e:mn>0</e:mn> </e:mrow> </e:math> behavior. Comparing our finite-temperature numerical results with the experimental data from quantum gas microscopy we find a qualitative disagreement: in experiment, hole spreading speeds up with increasing <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mrow> <f:mi>J</f:mi> <f:mo>/</f:mo> <f:mi>t</f:mi> </f:mrow> </f:math> , while in our numerics it slows down. The latter is consistent with the numerical findings previously reported at <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:mi>T</g:mi> <g:mo>=</g:mo> <g:mn>0</g:mn> </g:mrow> </g:math> .