Seminarium Fizyki Materii Skondensowanej

Local integrals of motion (LIOMs) play a key role in understanding the stationary states of closed macroscopic systems. Generic systems have only a few conserved quantities (like Hamiltonian, particle number, magnetization) and evolve to a thermal Gibbs state. Interacting integrable systems have extensive number of LIOMs and the relevant stationary states have the form that is consistent with the generalized Gibbs ensemble. LIOMs were found for selected integrable systems via complex analytical calculations. The existence of LIOMs and their structure can also be studied via numerical methods, which, however, involve exact diagonalization of Hamiltonians, posing a bottleneck for such studies. We show that finding LIOMs in translationally invariant lattice models or unitary quantum circuits can be reduced to a problem for which one may numerically find an exact solution also in the thermodynamic limit. We develop and implement a simple algorithm and demonstrate the efficiency of this method by calculating LIOMs for infinite integrable spin chains and unitary circuits. Finally, we demonstrate that this approach correctly identifies approximate LIOMs in nearly integrable spin ladders.