Details
| Original language | English |
|---|---|
| Article number | 085030 |
| Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |
| Volume | 88 |
| Issue number | 8 |
| Publication status | Published - 24 Oct 2013 |
Abstract
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.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Nuclear and High Energy Physics
- Physics and Astronomy(all)
- Physics and Astronomy (miscellaneous)
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Physical Review D - Particles, Fields, Gravitation and Cosmology, Vol. 88, No. 8, 085030, 24.10.2013.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Matrix product states and variational methods applied to critical quantum field theory
AU - Milsted, Ashley
AU - Haegeman, Jutho
AU - Osborne, Tobias J.
PY - 2013/10/24
Y1 - 2013/10/24
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84887078735&partnerID=8YFLogxK
U2 - 10.1103/PhysRevD.88.085030
DO - 10.1103/PhysRevD.88.085030
M3 - Article
AN - SCOPUS:84887078735
VL - 88
JO - Physical Review D - Particles, Fields, Gravitation and Cosmology
JF - Physical Review D - Particles, Fields, Gravitation and Cosmology
SN - 1550-7998
IS - 8
M1 - 085030
ER -