*Quantum many-body systems* are physical systems that consist of many components that obey the laws of [[quantum mechanics]]. One example are several interacting [[Spin|spins]] or [[Qubit|qubits]]. ![[many-body-system.excalidraw.light.svg]] To explain the difficulty in describing such a system, we can consider a simplified **system of arrows**. Each arrow can have two positions: up and down. When we combine these arrows, we can count the total number of possible combinations of configurations. ![[spin_system.excalidraw.light.svg]] For a single arrow, there are only two options: up or down. When we add a second arrow, the number of options rises to four, it doubles. Upon adding a third arrow, the number of configurations doubles again to eight. This is an **exponential growth**. The system is completely classical. We can describe each configuration by just giving the sequence of arrows like, up-down-up-up. In [[Quantum Mechanics|quantum mechanics]], the different configurations, also called [[Quantum State|quantum states]] may be in a [[Superposition|superposition]]. In the worst case, we have to give an amplitude for each possible configuration. Even if we used every atom in the visible universe to store a piece of information, there would not be enough atoms to store the classical representation of a quantum mechanical system of 300 arrows! Thus, physicists have to come up with clever approximations and methods to simulate quantum many-body physics. >[!read]- Further Reading >- [[Condensed Matter Physics]] >- [[Hamiltonian Operator]] >- [[Quantum Mechanics]] >- [[Emergence]] >[!ref]- References