With the team surrounding our previous paper on
reduced-basis methods for quantum spin systems,
Matteo Rizzi, Benjamin Stamm and Stefan Wessel and myself,
we recently worked on a follow-up, extending our approach to tensor-network methods.
Most of the work was done by Paul Brehmer,
a master student in Stefan's group, whom I had the pleasure to co-supervise.
Paul did an excellent job in cleaning up and extending the original code we had,
which we have now released in open-source form as the ReducedBasis.jl
Julia package.
The extension towards tensor-network methods and the integration
with libraries such as ITensor.jl
following the standard density-matrix renormalisation group (DMRG) approach,
finally allows us to treat larger quantum spin systems,
closer or at the level of the state of the art.
In this work we demonstrate this by a number of different one-dimensional
quantum spin-1 models, where our approach allowed us even to
identify a few new phases, which have not been studied so far.
The full abstract of our paper reads
Within the reduced basis methods approach, an effective low-dimensional
subspace of a quantum many-body Hilbert space is constructed in order to
investigate, e.g., the ground-state phase diagram. The basis of this
subspace is built from solutions of snapshots, i.e., ground states
corresponding to particular and well-chosen parameter values. Here, we show
how a greedy strategy to assemble the reduced basis and thus to select the
parameter points can be implemented based on matrix-product-states (MPS)
calculations. Once the reduced basis has been obtained, observables required
for the computation of phase diagrams can be computed with a computational
complexity independent of the underlying Hilbert space for any parameter
value. We illustrate the efficiency and accuracy of this approach for
different one-dimensional quantum spin-1 models, including anisotropic as
well as biquadratic exchange interactions, leading to rich quantum phase
diagrams.
