Abstract The essential difficulty of a large portion of the strongly interacting systems can be traced down to the “noncanonicality” of the underlying operators which are used to formulate the theory, like t-J model, Hubbard-type models in the large-U limit, quantum spin, etc. We proposed a new Schwinger-Dyson equations-of-motion method to compute the dynamical correlation functions of quantum spins at zero temperature. This method can also compute all the static observables from the dynamical correlation functions. We propose that this method can formulate dynamical perturbation calculations for quantum spin-1/2 models.
In this article, the method of computing Greens functions recursively for interacting particles has been extended to square lattices and binary trees. The method allows for performing calculations for large lattices. Approximations, which make the method more efficient while maintaining accuracy are described for computations of dynamics and correlations of interacting particles in disordered systems. Direct informations related to spectral weights for different initial preparations of interacting particles in real space can be obtained using this method for larger system sizes with less finite size effects.
A majority of measurable dynamic quantities of a physical system is described as an equilibrium correlation function of the form
GAB(t−t′)=⟨A(t)B(t′)⟩, where
t′ represents the impact time and
t represents the response time. Conventional quantum algorithms to compute such quantities via Hamiltonian simulation such as the Hadamard test, variational methods, or linear-response-based algorithms share one feature in common: each time point
t−t′ is calculated by a different quantum circuit, leading to at least
O(Nt) total shots, and at least
O(Nt2) total quantum gates. Here, we provide a different approach: utilizing
O(logNt) ancilla qubits to store time as a quantum variable, and effectively parallelize the computation of an equilibrium correlation function by requiring only a single quantum circuit for all time points. We show that this circuit needs to be run only
O(logNt) times, which in total requires
O(NtlogNt) quantum resources in the large system size limits. We prove that this scaling is optimal, and demonstrate our algorithm calculating the Green's function of a one-dimensional spinless Hubbard model.
We propose an efficient method to numerically simulate the superradiant emission dynamics of large numbers of quantum emitters in ordered arrays in the presence of long-range dipole-dipole interactions mediated by the vacuum electromagnetic field. Using the spatial symmetries of the system, we rewrite the equations of motion in a collective spin basis and subsequently apply a higher-order cumulant expansion for the collective operators. By truncating the subradiant collective modes with a heavily suppressed decay rate and keeping only the effect from the radiating collective modes, we reduce the numerical complexity significantly. This allows to efficiently compute the dissipative dynamics of the observables of interest for linear and ring-shaped arrays of quantum emitters. In particular, we characterize the second-order intensity correlation function g ( 2 ) ( τ = 0 ) , which is challenging to compute for extended systems with traditional cumulant expansion methods.