Simulation of strongly correlated fermions in two spatial dimensions with fermionic projected entangled-pair states

Corboz, Philippe; Orús, Román; Bauer, Bela; Vidal, Guifré

doi:10.1103/physrevb.81.165104

Cited by 286 publications

(423 citation statements)

References 61 publications

(179 reference statements)

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“…By now, two decades after its development, MPS (or the DMRG) have become the golden standard for the simulation of 1D lattice models. Furthermore, their two-dimensional (2D) generalizations known as projected entangled-pair states (PEPS) [20,21] (and their thermodynamic limit version infinite PEPS or iPEPS) [22,23] have been successfully used to study both fermionic systems as well as frustrated magnets [24][25][26][27][28], with a notable example being the lowest variational energies for the t-J model available to date for large systems [29].…”

Section: Introductionmentioning

confidence: 99%

Probing the stability of the spin-liquid phases in the Kitaev-Heisenberg model using tensor network algorithms

2014

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Probing the stability of the spin liquid phases in the Kitaev-Heisenberg model using tensor network algorithms Iregui, J.O.; Corboz, P.R.; Troyer, M. General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. We study the extent of the spin liquid phases in the Kitaev-Heisenberg model using infinite projected entangledpair states tensor network ansatz wave functions directly in the thermodynamic limit. To assess the accuracy of the ansatz wave functions, we perform benchmarks against exact results for the Kitaev model and find very good agreement for various observables. In the case of the Kitaev-Heisenberg model, we confirm the existence of six different phases: Néel, stripy, ferromagnetic, zigzag, and two spin liquid phases. We find finite extents for both spin liquid phases and discontinuous phase transitions connecting them to symmetry-broken phases.

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Section: Introductionmentioning

confidence: 99%

Probing the stability of the spin-liquid phases in the Kitaev-Heisenberg model using tensor network algorithms

2014

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“…Similarly an index can be split into two adjacent indices by using its inverse, the sparse tensor ϒ split of Eq. (48).…”

Section: F Reshaping Of Indicesmentioning

confidence: 99%

Tensor network states and algorithms in the presence of a global U(1) symmetry

2011

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Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. In a recent paper [Phys. Rev. A 82, 050301 (2010)] we discussed how to incorporate a global internal symmetry, given by a compact, completely reducible group G, into tensor network decompositions and algorithms. Here we specialize to the case of Abelian groups and, for concreteness, to a U(1) symmetry, associated, e.g., with particle number conservation. We consider tensor networks made of tensors that are invariant (or covariant) under the symmetry, and explain how to decompose and manipulate such tensors in order to exploit their symmetry. In numerical calculations, the use of U(1)-symmetric tensors allows selection of a specific number of particles, ensures the exact preservation of particle number, and significantly reduces computational costs. We illustrate all these points in the context of the multiscale entanglement renormalization Ansatz.

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“…38 Also, recently developed tensor network state methods 39 are as of yet unable to handle critical 2D states with a singular surface (e.g., the Fermi liquid and the d-metal) due to the anomalously large amount of spatial entanglement present. 40 We thus follow the heretofore successful [22][23][24]41,42 approach of accessing such phases by studying their quasi-1D descendants on ladder geometries, relying heavily on large-scale DMRG calculations.…”

Section: Two-leg Study: Dmrg and Vmcmentioning

confidence: 99%

Non-Fermi-liquid d-wave metal phase of strongly interacting electrons

Jiang

Block

Mishmash

et al. 2012

Nature

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Developing a theoretical framework for conducting electronic fluids qualitatively distinct from those described by Landau's celebrated Fermi liquid theory is of central importance to many outstanding problems in condensed matter physics. Perhaps the most important such pursuit is a full microscopic characterization of the high-Tc cuprate superconductors, where the so-called "strange metal" behavior above Tc near optimal doping is inconsistent with being a traditional Landau Fermi liquid. Indeed, a microscopic theory of such a strange metal quantum phase could possibly shed new light on the interesting low-temperature behavior in the pseudogap regime and on the d-wave superconductor itself. Here, we present a theory for a specific example of a strange metal, which we term the "d-wave metal." Using variational wave functions, gauge theoretic arguments, and ultimately large-scale DMRG calculations, we establish compelling evidence that this remarkable quantum phase is the ground state of a reasonable microscopic Hamiltonian: the venerable t-J model supplemented with a frustrated electron ring-exchange term, which we study extensively here on the two-leg ladder. These findings constitute one of the first explicit examples of a genuine non-Fermi liquid metal existing as the ground state of a realistic model.Over the past several decades, experiments on strongly correlated materials have routinely revealed, in certain parts of the phase diagram, conducting liquids with physical properties qualitatively inconsistent with Landau's Fermi liquid theory. 1 Examples of these so-called non-Fermi liquid metals 2 include the strange metal phase of the cuprate superconductors 3,4 and heavy fermion materials near a quantum critical point. 5,6 However, such non-Fermi liquid behavior has been notoriously challenging to characterize theoretically, largely owing to the failure of a weakly interacting quasiparticle description. It is even ambiguous to define a non-Fermi liquid, although possible deviations from Fermi liquid theory include, for example, violation of Luttinger's 7 famed volume theorem, vanishing quasiparticle weight, and/or anomalous thermodynamics and transport. 5,[8][9][10][11][12] This theoretical quandary is rather unfortunate as it is likely prohibiting a full understanding of the mechanism behind high-temperature superconductivity, as well as stymying theoretically-guided searches for new exotic materials.Pioneering early theoretical work on the cuprates relied on two main premises, 3,13-17 from which we will be guided but not constrained in our pursuit and understanding of a particular non-Fermi liquid metal: (1) that the microscopics can be described by the square lattice Hubbard model with on-site Coulomb repulsion, which at strong coupling reduces in its simplest form to the t-J model; and (2) that the physics of the system can be faithfully represented by the "slave-boson" technique, wherein the physical electron operator is written as a product of a slave boson ("chargon"), which carries the electronic char...

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Simulation of strongly correlated fermions in two spatial dimensions with fermionic projected entangled-pair states

Cited by 286 publications

References 61 publications

Probing the stability of the spin-liquid phases in the Kitaev-Heisenberg model using tensor network algorithms

Probing the stability of the spin-liquid phases in the Kitaev-Heisenberg model using tensor network algorithms

Tensor network states and algorithms in the presence of a global U(1) symmetry

Non-Fermi-liquid d-wave metal phase of strongly interacting electrons

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