Frustrated Antiferromagnets with Entanglement Renormalization: Ground State of the Spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:math>Heisenberg Model on a Kagome Lattice

Evenbly, Glen; Vidal, Guifré

doi:10.1103/physrevlett.104.187203

Cited by 208 publications

(218 citation statements)

References 29 publications

(69 reference statements)

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“…The projected entangled-pair state (PEPS) [21][22][23][24][25][26][27][28][29][30] generalizes the MPS, whereas D > 1 versions of TTN 31,32 and MERA 33-39 also exist. Among those generalizations, PEPS and MERA stand out for offering efficient representations of many-body wave functions, thus leading to scalable simulations in D > 1 dimensions; and, importantly, for also being able to address systems that are beyond the reach of quantum Monte Carlo approaches due to the so-called sign problem, including frustrated spins 30,39 and interacting fermions [40][41][42][43][44][45][46][47][48][49][50] .…”

Section: Introductionmentioning

confidence: 99%

Tensor Network States and Geometry

2011

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Tensor network states are used to approximate ground states of local Hamiltonians on a lattice in D spatial dimensions. Different types of tensor network states can be seen to generate different geometries. Matrix product states (MPS) in D = 1 dimensions, as well as projected entangled pair states (PEPS) in D > 1 dimensions, reproduce the D-dimensional physical geometry of the lattice model; in contrast, the multi-scale entanglement renormalization ansatz (MERA) generates a (D+1)-dimensional holographic geometry. Here we focus on homogeneous tensor networks, where all the tensors in the network are copies of the same tensor, and argue that certain structural properties of the resulting many-body states are preconditioned by the geometry of the tensor network and are therefore largely independent of the choice of variational parameters. Indeed, the asymptotic decay of correlations in homogeneous MPS and MERA for D = 1 systems is seen to be determined by the structure of geodesics in the physical and holographic geometries, respectively; whereas the asymptotic scaling of entanglement entropy is seen to always obey a simple boundary lawthat is, again in the relevant geometry. This geometrical interpretation offers a simple and unifying framework to understand the structural properties of, and helps clarify the relation between, different tensor network states. In addition, it has recently motivated the branching MERA, a generalization of the MERA capable of reproducing violations of the entropic boundary law in D > 1 dimensions.

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Section: Introductionmentioning

confidence: 99%

Tensor Network States and Geometry

2011

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“…16,21 For twodimensional (2D) lattices there are generalizations of these three tensor network states, namely projected entangled pair states [22][23][24][25][26][27][28][29][30][31] (PEPS), 2D TTN, 32,33 and 2D MERA, [34][35][36][37][38][39][40] respectively. As variational Ansätze, PEPS and 2D MERA are particularly interesting since they can be used to address large two-dimensional lattices, including systems of frustrated spins 31,40 and interacting fermions, [41][42][43][44][45][46][47][48][49][50] where Monte Carlo techniques fail due to the sign problem.…”

Section: Introductionmentioning

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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“…Proposed ground states here include various types of QSL states [32][33][34] as well as valence-bond solid (VBS) states [35][36][37][38] . The literature on VBS states has a long history going back to the well known Ghosh-Majumdar model 39 .…”

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Paired electron crystal: Order from frustration in the quarter-filled band

et al. 2011

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We present a study of the effects of simultaneous charge-and spin-frustration on the twodimensional strongly correlated quarter-filled band on an anisotropic triangular lattice. Our conclusions are based on exact diagonalization studies that include electron-electron interactions as well as adiabatic electron-phonon coupling terms treated self-consistently. The broken-symmetry states that dominate in the weakly frustrated region near the rectangular lattice limit are the well known antiferromagnetic state with in-phase lattice dimerization along one direction, and the Wigner crystal state with the checkerboard charge order. For moderate to strong frustration, however, the dominant phase is a novel spin-singlet paired-electron crystal (PEC), consisting of pairs of charge-rich sites separated by pairs of charge-poor sites. The PEC, with coexisting charge-order and spin-gap in two dimension, is the quarter-filled band equivalent of the valence bond solid (VBS) that can appear in the frustrated half-filled band within antiferromagnetic spin Hamiltonians. We discuss the phase diagram as a function of on-site and intersite Coulomb interactions as well as electronphonon coupling strength. We speculate that the spin-bonded pairs of the PEC can become mobile for even stronger frustration, giving rise to a paired-electron liquid. We discuss the implications of the PEC concept for understanding several classes of quarter-filled band materials that display unconventional superconductivity, focusing in particular on organic charge transfer solids. Our work points out the need to go beyond quantum spin liquid (QSL) concepts for highly frustrated organic charge-transfer solids such as κ-(BEDT-TTF)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2, which we believe show frustration-induced charge disproportionation at low temperatures. We discuss possible application to layered cobaltates and 1 4 -filled band spinels.

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Frustrated Antiferromagnets with Entanglement Renormalization: Ground State of the Spin-12Heisenberg Model on a Kagome Lattice

Cited by 208 publications

References 29 publications

Tensor Network States and Geometry

Tensor Network States and Geometry

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

Paired electron crystal: Order from frustration in the quarter-filled band

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