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Matrix product states and variational methods applied to critical quantum field theory

Autor(en)
Ashley Milsted, Jutho Haegeman, Tobias J. Osborne
Abstrakt

We study the second-order quantum phase transition of massive real scalar field theory with a quartic interaction in (1+1) dimensions on an infinite spatial lattice using matrix product states. We introduce and apply a naive variational conjugate gradient method, based on the time-dependent variational principle for imaginary time, to obtain approximate ground states, using a related ansatz for excitations to calculate the particle and soliton masses and to obtain the spectral density. We also estimate the central charge using finite-entanglement scaling. Our value for the critical parameter agrees well with recent Monte Carlo results, improving on an earlier study which used the related density matrix normalization group method, verifying that these techniques are well-suited to studying critical field systems. We also obtain critical exponents that agree, as expected, with those of the transverse Ising model. Additionally, we treat the special case of uniform product states (mean field theory) separately, showing that they may be used to investigate noncritical quantum field theories under certain conditions.

Organisation(en)
Quantenoptik, Quantennanophysik und Quanteninformation
Externe Organisation(en)
Gottfried Wilhelm Leibniz Universität Hannover
Journal
Physical Review D
Band
88
Anzahl der Seiten
23
ISSN
1550-7998
DOI
https://doi.org/10.1103/PhysRevD.88.085030
Publikationsdatum
10-2013
Peer-reviewed
Ja
ÖFOS 2012
103025 Quantenmechanik
Schlagwörter
Link zum Portal
https://ucrisportal.univie.ac.at/de/publications/6f41bd1a-f2d9-42a5-a003-c36ae936e6a0