New Publication in Physical Review B.


Our publication on Variational optimization algorithms for uniform matrix product states was published in Physical Review B.

We combine the density matrix renormalization group (DMRG) with matrix product state tangent space concepts to construct a variational algorithm for finding ground states of one-dimensional quantum lattices in the thermodynamic limit. A careful comparison of this variational uniform matrix product state algorithm (VUMPS) with infinite density matrix renormalization group (IDMRG) and with infinite time evolving block decimation (ITEBD) reveals substantial gains in convergence speed and precision. We also demonstrate that VUMPS works very efficiently for Hamiltonians with long-range interactions and also for the simulation of two-dimensional models on infinite cylinders. The new algorithm can be conveniently implemented as an extension of an already existing DMRG implementation.


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Comparison of the convergence rate of the gradient norm ∥B∥ for the TFI model at h=0.55, with D=33 and 35. Convergence is roughly 4 times faster for D=33 as compared to D=35. The inset shows the Schmidt spectrum of the ground state (up to D=43). For D=35 the smallest Schmidt values form an incomplete degenerate multiplet, whereas for D=33 the multiplet is complete.