Continuous Matrix Product States for Quantum Fields: an Energy Minimization Algorithm

Abstract

The generalization of matrix product states (MPS) to continuous systems, as proposed in the breakthrough paper [F. Verstraete, J.I. Cirac, Phys. Rev. Lett. 104, 190405(2010)], provides a powerful variational ansatz for the ground state of strongly interacting quantum field theories in one spatial dimension. A continuous MPS (cMPS) approximation to the ground state can be obtained by simulating an Euclidean time evolution. In this Letter we propose a cMPS optimization algorithm based instead on energy minimization by gradient methods, and demonstrate its performance by applying it to the Lieb Liniger model (an integrable model of an interacting bosonic field) directly in the thermodynamic limit. We observe a very significant computational speed-up, of more than two orders of magnitude, with respect to simulating an Euclidean time evolution. As a result, much larger cMPS bond dimension D can be reached (e.g. D = 256 with moderate computational resources) thus helping unlock the full potential of the cMPS representation for ground state studies.

4.5 + 8 pages, additional results added in appendix; removed some typos; as accepted for publication in Phys. Rev. Lett

References in corpus (17)

• The density-matrix renormalization group in the age of matrix product states
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Real time evolution using the density matrix renormalization group
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Bosonizing one-dimensional cold atomic gases
• Scaling of entanglement support for Matrix Product States
• Continuous Matrix Product States for Quantum Fields
• Pinning quantum phase transition for a Luttinger liquid of strongly interacting bosons
• Time-step targetting methods for real-time dynamics using DMRG
• Matrix product states for critical spin chains: finite size scaling versus finite entanglement scaling
• Matrix product ansatz for Fermi fields in one dimension
• Real-Space Parallel Density Matrix Renormalization Group
• Kohn-Sham calculations with the exact functional
• Multigrid Algorithms for Tensor Network States
• Dynamics of pair correlations in the attractive Lieb-Liniger gas
• Continuous matrix product states with periodic boundary conditions and an application to atomtronics
• Ground state energy of the $\delta$-Bose and Fermi gas at weak coupling from double extrapolation

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