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