Short-time-evolved wave functions for solving quantum many-body problems
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The exact ground state of a strongly interacting quantum many-body system can be obtained by evolving a trial state with finite overlap with the ground state to infinite imaginary time. In many cases, since the convergence is exponential, the system converges essentially to the exact ground state in a relatively short time. Thus a short-time evolved wave function can be an excellent approximation to the exact ground state. Such a short-time-evolved wave function can be obtained by factorizing, or splitting, the evolution operator to high order. However, for the imaginary time Schrodinger equation, which contains an irreversible diffusion kernel, all coefficients, or time steps, must be positive. (Negative time steps would require evolving the diffusion process backward in time, which is impossible.) Heretofore, only second-order factorization schemes can have all positive coefficients, but without further iterations, these cannot be used to evolve the system long enough to be close to the exact ground state. In this work, we use a newly discovered fourth-order positive factorization scheme which requires knowing both the potential and its gradient. We show that the resulting fourth-order wave function alone, without further iterations, gives an excellent description of strongly interacting quantum systems such as liquid He-4, comparable to the best variational results in the literature. This suggests that such a fourth-order wave function can be used to study the ground state of diverse quantum many-body systems, including Bose-Einstein condensates and Fermi systems.
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