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# Projector Monte Carlo / FCIQMC | ||
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The purpose of Projector Monte Carlo is to stochastically sample the ground state, i.e. the | ||
eigenvector corresponding to the lowest eigenvalue of a quantum Hamiltonian, or more generally, | ||
a very large matrix. Rimu implements a flavor of Projector Monte Carlo called | ||
Full Configuration Interaction Quantum Monte Carlo (FCIQMC). | ||
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## `ProjectorMonteCarloProblem` | ||
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To run a projector Monte Carlo simulation you set up a problem with `ProjectorMonteCarloProblem` | ||
and solve it with `solve`. Alternatively you can initialize a `PMCSimulation` struct, `step!` | ||
through time steps, and `solve!` it to completion. | ||
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```@docs; canonical=false | ||
ProjectorMonteCarloProblem | ||
init | ||
solve | ||
solve! | ||
step! | ||
``` | ||
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After `solve` or `solve!` have been called the returned `PMCSimulation` contains the results of | ||
the projector Monte Carlo calculation. | ||
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### `PMCSimulation` and report as a `DataFrame` | ||
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```@docs; canonical=false | ||
Rimu.PMCSimulation | ||
``` | ||
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The `DataFrame` returned from `DataFrame(::PMCSimulation)` contains the time series data from | ||
the projector Monte Carlo simulation that is of primary interest for analysis. Depending on the | ||
`reporting_strategy` and other options passed as keyword arguments to | ||
`ProjectorMonteCarloProblem` it can have different numbers of rows and columns. The rows | ||
correspond to the reported time steps (Monte Carlo steps). There is at least one column with the name `:step`. Further columns are usually present with additional data reported from the simulation. | ||
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For the default option `algorithm = FCIQMC(; shift_strategy, time_step_strategy)` with a single | ||
replica (`n_replicas = 1`) and single spectral state, the fields `:shift`, `:norm`, `:len` will | ||
be present as well as others depending on the `style` argument and the `post_step_strategy`. | ||
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If multiple replicas or spectral states are requested, then the relevant field names in the | ||
`DataFrame` will have a suffix identifying the respective replica simulation, e.g. the `shift`s will be reported as `shift_1`, `shift_2`, ... | ||
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Many tools for analysing the time series data obtained from a | ||
[`ProjectorMonteCarloProblem`](@ref) are contained in the [Module `StatsTools`](@ref). |
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