Berlin 2014 – wissenschaftliches Programm

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Q: Fachverband Quantenoptik und Photonik

Q 71: Quantum information: Concepts and methods VI

Q 71.8: Vortrag

Freitag, 21. März 2014, 18:15–18:30, Kinosaal

Matrix product states and variational methods applied to critical quantum field theory — •Ashley Milsted¹, Jutho Haegeman^2,3, and Tobias J. Osborne¹ — ¹Leibniz Universität Hannover, Institute of Theoretical Physics, Appelstrasse 2, D-30167 Hannover, Germany — ²Vienna Center for Quantum Science and Technology, Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Wien, Austria — ³Faculty of Physics and Astronomy, University of Ghent, Krijgslaan 281 S9, 9000 Gent, Belgium

The density matrix renormalization group (DMRG) has revolutionized the numerics of condensed matter systems in one dimension. Insight from quantum information explains its success in terms of the entanglement structure of low energy states, recognizing that DMRG ground states are matrix product states (MPS). We investigate whether such techniques are also advantageous when applied to a strongly coupled quantum field (φ⁴ theory), where the usual method is quantum Monte Carlo (QMC). Using MPS in the thermodynamic limit (uMPS), we apply recently developed variational techniques, including a novel conjugate gradient solver, to obtain approximate ground states and low-lying excitations from which we extrapolate the φ⁴ theory critical point in the continuum limit using only modest computational resources. Our estimate agrees well with QMC results, despite QMC being very different. We improve on a conflicting DMRG study by accounting for finite entanglement effects. The methods used are implemented as free software http://amilsted.github.io/evoMPS/.