Matrix product states and variational methods applied to critical quantum field theory
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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.
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A reduced version of the ansatz appeared earlier in Refs.[39,40], and it was explored in full generality in Refs.[15,41].
“In the context of MPS, a reduced version of the ansatz appeared earlier in Refs.[39,40], but it was explored in full generality in Refs.[15,41].”
From Tangent-space methods for uniform matrix product states (2019) · cites this paper as [39]
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Tangent-space methods for uniform matrix product states
Vanderstraeten, L., Haegeman, J., & Verstraete, F. (2019) · SciPost Physics Lecture Notes · doi:10.21468/scipostphyslectnotes.7 · Cited by 233 · see citing works
“In recent years, the ansatz has been succesfully applied to spin chains [13, 42, 43], spin ladders [44], spin chains with long-range interactions [45], field theories [46], and local gauge theories [29].”
BackgroundSelf-citation
- Authors
- Milsted, A., Haegeman, J., & Osborne, T. J.
- Affiliations
- Leibniz University Hannover (DE)
- University of Vienna (AT)
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2013-10-24
- Volume
- 88
- Issue
- 8
- ISSN
- 0556-2821 (ISSN-L)
- 1550-7998
- 1550-2368
- OpenAlex
- W2009298903
- Cited by
- 88
- References
- 5
- Citations by year
- 2026: 4 · 2025: 3 · 2024: 5 · 2023: 5 · 2022: 6 · 2021: 13 · 2020: 8 · 2019: 9 · 2018: 3 · 2017: 14 · 2016: 6 · 2015: 8 · 2014: 3 · 2013: 1
- FWCI
- 3.09
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- public-domain
- link.aps.org/licenses/aps-default-license (vor)
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion, public-domain)
- arXiv (Cornell University) (submittedVersion)
- Ghent University Academic Bibliography (Ghent University) (submittedVersion, public-domain)
- Institutional Repository of Leibniz Universität Hannover (Leibniz Universität Hannover) (submittedVersion, cc-by-nc-nd)
- arXiv (Cornell University)
- Leibniz Universität Hannover
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Physics of Superconductivity and Magnetism
- Keywords
- matrix product states, variational methods, quartic interaction, second-order quantum phase transition, time-dependent variational principle, imaginary time, ground state, soliton mass, power spectrum, central charge, critical exponents, transverse-field Ising model, mean-field theory, one-dimensional field theory
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