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Classical simulations typically rely on Monte Carlo methods which may suffer from severe sign problems, which imply that real-time dynamics and certain exotic phases are so far out of reach.
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The sign problem does not appear in the regime of small screening length.
The constrained path approximation is used to control the sign problem.
Quantum Monte Carlo struggles, for example, with Fermionic statistics or frustrated models, due to the sign problem [114, 115].
The use of numerical methods such as quantum Monte Carlo is not always possible due to the so-called sign problem.
Indeed, neither fermionic models in more than one dimension nor systems with the well-known sign problem [5] can be efficiently simulated employing a classical computer.
For instance, exact diagonalization faces exponential scaling with the system size, while quantum Monte Carlo methods [11, 12] are often crippled by the infamous fermionic sign problem [13].
Since the approach suffers from a sign problem, a judicious choice of the sampling algorithm, allowing a fast statistical convergence and an efficient generation of field configurations, is of fundamental importance for a successful simulation.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com