Variational treatment of the Shastry-Sutherland antiferromagnet using projected entangled pair states

Isacsson, Andreas; Syljuåsen, Olav F.

doi:10.1103/physreve.74.026701

Cited by 39 publications

(42 citation statements)

References 38 publications

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“…In light of the fact that even critical two-dimensional systems can satisfy an area law, this would mean that they can be well described by PEPS or MERA with relatively few parameters. Numerical work in case of PEPS indicates that this is indeed the case ͑Verstraete and Cirac, 2004; Isacsson and Syljuasen, 2006;Murg et al, 2007;Verstraete et al, 2008͒. A rigorous result similar to Theorem 18, yet, is still lacking for PEPS or MERA. The intuition developed so far, however, is in one way or the other quite certainly right: Whenever an area law is satisfied, PEPS with small bond dimension should give rise to a reasonably good approximation.…”

Section: Implications On Higher-dimensional Simulationsmentioning

confidence: 95%

Colloquium: Area laws for the entanglement entropy

2010

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Physical interactions in quantum many-body systems are typically local: Individual constituents interact mainly with their few nearest neighbors. This locality of interactions is inherited by a decay of correlation functions, but also reflected by scaling laws of a quite profound quantity: the entanglement entropy of ground states. This entropy of the reduced state of a subregion often merely grows like the boundary area of the subregion, and not like its volume, in sharp contrast with an expected extensive behavior. Such "area laws" for the entanglement entropy and related quantities have received considerable attention in recent years. They emerge in several seemingly unrelated fields, in the context of black hole physics, quantum information science, and quantum many-body physics where they have important implications on the numerical simulation of lattice models. In this Colloquium the current status of area laws in these fields is reviewed. Center stage is taken by rigorous results on lattice models in one and higher spatial dimensions. The differences and similarities between bosonic and fermionic models are stressed, area laws are related to the velocity of information propagation in quantum lattice models, and disordered systems, nonequilibrium situations, and topological entanglement entropies are discussed. These questions are considered in classical and quantum systems, in their ground and thermal states, for a variety of correlation measures. A significant proportion is devoted to the clear and quantitative connection between the entanglement content of states and the possibility of their efficient numerical simulation. Matrix-product states, higher-dimensional analogs, and variational sets from entanglement renormalization are also discussed and the paper is concluded by highlighting the implications of area laws on quantifying the effective degrees of freedom that need to be considered in simulations of quantum states.

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Section: Implications On Higher-dimensional Simulationsmentioning

confidence: 95%

Colloquium: Area laws for the entanglement entropy

2010

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“…[16][17][18][19][20][21][22]. We note that a finite PEPS has been used in a previous study of the SSM, 23 however, only with a small bond dimension D = 2, and no intermediate phase has been found.…”

Section: Introductionmentioning

confidence: 99%

Tensor network study of the Shastry-Sutherland model in zero magnetic field

2013

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We simulate the Shastry-Sutherland model in two dimensions by means of infinite projected entangled-pair states (iPEPS) -a variational tensor network method where the accuracy can be systematically controlled by the so-called bond dimension. Besides the well established dimer and Néel phase iPEPS confirms the presence of an intermediate phase with plaquette long-range order, and we determine its phase boundaries with high accuracy. The first order phase transition for J = 0.675(2) between dimer and plaquette phase is compatible with previous series expansion results. iPEPS predicts a weak first-order phase transition between plaquette and Néel phase occurring for J = 0.765(15). We do not find a stable intermediate columnar-dimer phase, even when we bias the state towards this order.

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“…Conversely, AF order with gapless magnetic excitations is favored for large J ′ /J, and the RB 4 (R= Gd,Tb,Dy,Ho,Er) compounds may represent this limit [5][6][7][8]. A T=0 transition between the SL and AF phases has been predicted for J ′ /J ≃0.6 -0.7 [3,[9][10][11], although symmetry-based arguments [12] suggest that an intermediate state is required, such as a helical magnet [13], a weak SDW [12], or a plaquet ordered solid [14]. The known SSL systems have so far not provided experimental access to this transitional regime.…”

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confidence: 99%

Spin Liquids and Antiferromagnetic Order in the Shastry-Sutherland-Lattice CompoundYb2Pt2Pb

Kim

Aronson

2013

Phys. Rev. Lett.

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We present measurements of the magnetic susceptibility χ and the magnetization M of single crystals of metallic Yb2Pt2Pb, where localized Yb moments lie on the geometrically frustrated Shastry-Sutherland Lattice (SSL). Strong magnetic frustration is found in this quasi-two dimensional system, which orders antiferromagnetically (AF) at TN =2.02 K from a paramagnetic liquid of Ybdimers, having a gap ∆=4.6 K between the singlet ground state and the triplet excited states. Magnetic fields suppress the AF order, which vanishes at a 1.25 T quantum critical point. The spin gap ∆ persists to 1.5 T, indicating that the AF degenerates into a liquid of dimer triplets at T=0. Quantized steps are observed in M(B) within the AF state, a signature of SSL systems. Our results show that Yb2Pt2Pb is unique, both as a metallic SSL system that is close to an AF quantum critical point, and as a heavy fermion compound where geometrical frustration plays a decisive role.PACS numbers: 75.10. Kt,75.20.Hr,75.30.Kz Much interest has focused on systems with geometrical frustration, where conventional antiferromagnetic (AF) order is suppressed in favor of more exotic ground states. The Shastry Sutherland Lattice (SSL) is one of the simplest frustrated systems [1], consisting of planes of orthogonal dimers of moments with interdimer coupling J ′ and the intradimer coupling J. The T=0 phase diagram has two limiting behaviors, depending on J ′ /J. Nonordering dimers are found for small J ′ /J, distinguished by an energy gap ∆ between the singlet and triplet states of the dimer. Insulating SrCu 2 (BO 3 ) 2 exemplifies this disordered 'spin liquid'(SL) regime [2][3][4]. Conversely, AF order with gapless magnetic excitations is favored for large J ′ /J, and the RB 4 (R= Gd,Tb,Dy,Ho,Er) compounds may represent this limit [5][6][7][8]. A T=0 transition between the SL and AF phases has been predicted for J ′ /J ≃0.6 -0.7 [3, 9-11], although symmetry-based arguments [12]

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Variational treatment of the Shastry-Sutherland antiferromagnet using projected entangled pair states

Cited by 39 publications

References 38 publications

Colloquium: Area laws for the entanglement entropy

Colloquium: Area laws for the entanglement entropy

Tensor network study of the Shastry-Sutherland model in zero magnetic field

Spin Liquids and Antiferromagnetic Order in the Shastry-Sutherland-Lattice CompoundYb2Pt2Pb

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