Infinite size density matrix renormalization group, revisited
By Ian P. McCulloch. 2008
255 citations recorded by the source corpus.
I revisit the infinite-size variant of the Density Matrix Renormalization Group (iDMRG) algorithm for obtaining a fixed-point translationally invariant matrix product wavefunction in the context of one-dimensional quantum systems. A crucial ingredient of this algorithm is an efficient transformation for obtaining the matrix elements of the wavefunction as the lattice size is increased, and I introduce here a versatile transformation that is demonstrated to be much more effective than previous versions. The resulting algorithm has a surprisingly close relationship to Vidal's Time Evolving Block Decimation for infinite systems, but allows much faster convergence. Access to a translationally invariant matrix product state allows the calculation of correlation functions based on the transfer matrix, which directly gives the spectrum of all correlation lengths. I also show some advantages of the Matrix Product Operator (MPO) technique for constructing expectation values of higher moments, such as the exact variance $ $.
Subfields: Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/6f69892c19c1b5a38a9cbf7af6080858303818ad
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In Computational Theory and Mathematics
Citations in the corpus
- Tangent-space methods for uniform matrix product states (2018, methodology): “Traditionally, this minimization problem is not treated directly, but recourse is taken to imaginary-time evolution using the time-evolving block decimation algorithm [6, 17], or to infinite DMRG methods [18].”