Getting Around the Sign Problem to Solve an Open Quantum System
© The Physical Society of Japan
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Lattice Lindblad simulation
(PTEP Editors' Choice)
Prog. Theor. Exp. Phys. 2022, 053B03 (2022).
Researchers from Japan have found a novel nonequilibrium quantum system that doesn’t have the sign problem. The transport properties of the system are simulated with a Monte Carlo approach.
Quantum computing and superconductivity are prospective disruptive technological advancements capable of deeply impacting our society. Our understanding of these properties depends on our understanding of complex quantum matter systems, a first step towards which involves understanding the exotic topological properties directly intertwined with the lattice of solid quantum systems through simulation.
The sign problem is one of the major unsolved problems in the physics of manyparticle systems and is present when calculating the properties of a quantum mechanical system described by many strongly interacting fermions or in field theories of a nonzero strongly interacting fermion density. As the fermionic particles are strongly interacting, analytical methods are not applicable, and neither is perturbation theory, a popular mathematical tool. The only option is to use bruteforce numerical methods, such as Monte Carlo sampling.
Because the particles are fermions, the interchange of any two particles leads to a change of sign in the wavefunction. The net quantummechanical sum over all multiparticle states is then achieved by an integral over a function that is highly oscillatory. Such an integral is hard to evaluate numerically and can be a source of significant error. The error in evaluating the system grows with the number of particles, so, the sign problem is extreme within the thermodynamic limit, unless there are cancellations arising from some symmetry of the system.
In a new study, researchers have examined a novel exceptional case of open quantum systems—a nonrelativistic spinless fermion with dissipative dynamics. The lattice formulation of the system is based on the famous SchwingerKeldysh path integral representation. Through the theoretical framework of the path integral representation of the Lindblad equation, the particularity of the dissipative term leads to an exact quenching of the fermion determinant. The researchers obtained a fermion determinant that is positive definite, meaning that the sign problem is not present in the Monte Carlo simulation.
Although an electric current operator was used in this case, the researchers suggest quenching can be achieved for any bilinear Hermitian jump operator. This work allows the use of realtime lattice simulation to investigate charge transport in a nonequilibrium freefermion theory governed systems, providing a new handy tool to the quantum mechanics’ toolbox.
Bilinear and Hermitian jump operators can only exactly describe trivial steady states, however. For the study of the formation of other nonequilibrium steady states, different example models without the sign problem need to be uncovered. This work plots a course for future discoveries, wherein circumventing the sign problem could help guide our understanding of quantum matter and its properties.
Lattice Lindblad simulation
(PTEP Editors' Choice)
Prog. Theor. Exp. Phys. 2022, 053B03 (2022).
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