# Variational optimization algorithms for uniform matrix product states

## TL;DR

This paper introduces VUMPS, a variational algorithm combining DMRG and tangent space concepts, which improves convergence and precision for ground state calculations of 1D quantum systems, including long-range and 2D models.

## Contribution

The paper presents VUMPS, a novel variational uniform MPS algorithm that outperforms existing methods like IDMRG and ITEBD in speed and accuracy for various quantum lattice models.

## Key findings

- VUMPS converges faster than IDMRG and ITEBD.
- VUMPS achieves higher precision in ground state energies.
- VUMPS efficiently handles long-range interactions and 2D models.

## Abstract

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.