dc.contributor.author
Osorio Iregui, Juan
dc.contributor.supervisor
Troyer, Matthias
dc.contributor.supervisor
Corboz, Philippe
dc.date.accessioned
2017-12-05T15:38:49Z
dc.date.available
2017-12-05T14:55:43Z
dc.date.available
2017-12-05T15:38:49Z
dc.date.issued
2017
dc.identifier.uri
http://hdl.handle.net/20.500.11850/217773
dc.identifier.doi
10.3929/ethz-b-000217773
dc.description.abstract
Tensor network algorithms (TNAs) represent one of the most recent developments in the field of numerical methods for the simulation of strongly-correlated many-body systems. Arising as a natural consequence of an improved understanding of the entanglement structures intrinsic to the ground-state manifolds of many-body Hilbert spaces, they correspond to algorithms exploiting entropic constraints expected to arise in various classes of many-body ground states. In this work we apply and develop TNAs for the simulation of various strongly-correlated lattice models. Concretely, we apply tensor network renormalization (TNR) to the study of the classical Blume-Capel model (BCM). We propose to exploit the RG features specific to TNR to obtain an indicator for the vicinity of (multi-)critical points. We show that in the case of the BCM it leads to a location of its tricritical point matching the accuracy of state-of-the-art Monte Carlo approaches. This allows us to characterize the underlying $c=7/10$ conformal field theory with an excellent accuracy. We then present a self-contained introduction to the most widely used techniques for the simulation of one- and two-dimensional quantum systems, where we cover matrix product states (MPS) and projected entangled-pair states (PEPS) in detail. We briefly discuss the multi-scale entanglement renormalization Ansatz (MERA). We apply infinite PEPS (iPEPS) to the simulation of the Kitaev-Heisenberg (KH) model, proposed as an effective low-energy theory for the so-called Iridate compounds of the form $\mathrm{A_2IrO_3}$ ($\mathrm{A=Na,Li}$). We show the ability of iPEPS to accurately encode the complex ground-state physics of Kitaev's honeycomb model. When considering the KH model we confirm the existence of all previously found phases, locate all phase transitions in the phase diagram, finding good agreement with previous studies, and provide estimates for the survival regions of the spin-liquid phases in the thermodynamic limit. We briefly discuss the nature of these transitions. We conclude this work with a study of various formulations of iPEPS on cylindrical geometries. We benchmark the proposed formulations by studying the transverse-field Ising model and find good performance for a subset of the formulations studied. We then carry out a comparison between iPEPS and iMPS methods for the Heisenberg and Hubbard models and find a range of cylinder widths over which both methods exhibit comparable performance. We find evidence for the potential of iPEPS simulations on cylinders and argue that our findings provide support for future studies employing both MPS and PEPS methods in conjunction.
en_US
dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.publisher
ETH Zurich
en_US
dc.rights.uri
http://rightsstatements.org/page/InC-NC/1.0/
dc.subject
MANY-BODY PROBLEM/QUANTUM MECHANICS
en_US
dc.subject
NUMERICAL METHODS IN PHYSICS (NUMERICAL MATHEMATICS)
en_US
dc.subject
CONDENSED MATTER PHYSICS
en_US
dc.subject
STRONGLY CORRELATED SYSTEMS (CONDENSED MATTER PHYSICS)
en_US
dc.title
Connecting the Dots: Tensor Network Algorithms for Two-Dimensional Strongly-Correlated Systems
en_US
dc.type
Doctoral Thesis
In Copyright - Non-Commercial Use Permitted
ethz.size
131 p.
en_US
ethz.code.ddc
DDC - DDC::5 - Science::530 - Physics
ethz.identifier.diss
24560
en_US
ethz.publication.place
Zurich
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02010 - Dep. Physik / Dep. of Physics::02511 - Institut für Theoretische Physik / Institute for Theoretical Physics::03622 - Troyer, Matthias (ehemalig) / Troyer, Matthias (former)
en_US
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02010 - Dep. Physik / Dep. of Physics::02511 - Institut für Theoretische Physik / Institute for Theoretical Physics::03622 - Troyer, Matthias (ehemalig) / Troyer, Matthias (former)
en_US
ethz.date.deposited
2017-12-05T14:55:44Z
ethz.source
FORM
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2017-12-05T15:39:02Z
ethz.rosetta.lastUpdated
2020-02-15T10:09:44Z
ethz.rosetta.exportRequired
true
ethz.rosetta.versionExported
true
ethz.COinS
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