Alternating cross interpolation performs elementwise operations on tensor trains in O(χ³) time with error control, improving on the standard O(χ⁴) scaling when output ranks are controlled.
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Derives an exact downfolded effective model by integrating out the rest space, states conditions for perturbative truncation, and formally recovers cRPA with corrections.
A quantics tensor train solver resolves the Gross-Pitaevskii equation across seven orders of magnitude in length scale in one dimension and on grids larger than a trillion points in two dimensions.
citing papers explorer
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Fast elementwise operations on tensor trains with alternating cross interpolation
Alternating cross interpolation performs elementwise operations on tensor trains in O(χ³) time with error control, improving on the standard O(χ⁴) scaling when output ranks are controlled.
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Exact downfolding and its perturbative approximation
Derives an exact downfolded effective model by integrating out the rest space, states conditions for perturbative truncation, and formally recovers cRPA with corrections.
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Solving the Gross-Pitaevskii equation on multiple different scales using the quantics tensor train representation
A quantics tensor train solver resolves the Gross-Pitaevskii equation across seven orders of magnitude in length scale in one dimension and on grids larger than a trillion points in two dimensions.