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In the DQMC method, the inverse temperature is discretized to L pieces to isolate the interaction term using the Trotter approximation. The trace of the partition function is translated into a determinant of a real matrix, which contains a product of L matrixes. Since L is large at low temperatures, there is a bigger chance that the determinant becomes negative. Moreover strong interactions make the values of the elements in the matrix large, which further increases the probability of a negative determinant. Of course, the sign problem is very complex, and we only provide a qualitative expanation why it becomes severe upon lowering the temperature and increasing the interaction strength.
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