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

Singh, Sukhwinder; Vidal, Guifré

doi:10.1103/physrevb.83.115125

Cited by 228 publications

(250 citation statements)

References 74 publications

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“…In general, global symmetries impose strong constraints on the PEPS [12][13][14][15][16][17][18][19] . To serve our purpose, we choose the 'entangled pairs' to be multiplets of SO(3) symmetric spins and, thus, will refer to them as the 'slave-spin' PEPS.…”

Section: 5mentioning

confidence: 99%

Existence of featureless paramagnets on the square and the honeycomb lattices in 2+1 dimensions

Jian

Zaletel

2016

Phys. Rev. B

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The peculiar features of quantum magnetism sometimes forbid the existence of gapped 'featureless' paramagnets which are fully symmetric and unfractionalized. The Lieb-Schultz-Mattis theorem is an example of such a constraint, but it is not known what the most general restriction might be. We focus on the existence of featureless paramagnets on the spin-1 square lattice and the spin-1 and spin-1/2 honeycomb lattice with spin rotation and space group symmetries in 2+1D. Although featureless paramagnet phases are not ruled out by any existing theorem, field theoretic arguments disfavor their existence. Nevertheless, by generalizing the construction of Affleck, Kennedy, Lieb and Tasaki to a class we call 'slave-spin' states, we propose featureless wave functions for these models. The featureless-ness of the spin-1 slave-spin states on the square and honeycomb lattice are verified both analytically and numerically, but the status of the spin-1/2 honeycomb state remains unclear.

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Section: 5mentioning

confidence: 99%

Existence of featureless paramagnets on the square and the honeycomb lattices in 2+1 dimensions

Jian

Zaletel

2016

Phys. Rev. B

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confidence: 99%

“…The contraction of the infinite tensor network is done with the corner-transfer matrix method [37,40,41]. For the plateau phases we used tensors with U(1) symmetry to increase the efficiency [42,43].Ground state in the 1/8 plateau -We first focus on the 1/8 plateau in the physically relevant regime for SrCu 2 (BO 3 ) 2 , J /J = 0.63, as a first example to show that crystals made of bound states have a lower variational energy than crystals made of triplets. Two triplet crystals have been proposed: the diamond pattern shown in Fig.…”

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confidence: 99%

Crystals of Bound States in the Magnetization Plateaus of the Shastry-Sutherland Model

2014

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Using infinite projected entangled-pair states (iPEPS), we show that the Shastry-Sutherland model in an external magnetic field has low-magnetization plateaus which, in contrast to previous predictions, correspond to crystals of bound states of triplets, and not to crystals of triplets. The first sizable plateaus appear at magnetization 1/8, 2/15 and 1/6, in agreement with experiments on the orthogonal-dimer antiferromagnet SrCu2(BO3)2, and they can be naturally understood as regular patterns of bound states, including the intriguing 2/15 one. We also show that, even in a confined geometry, two triplets bind into a localized bound state with Sz = 2. Finally, we discuss the role of competing domain-wall and supersolid phases as well as that of additional anisotropic interactions. PACS numbers: 75.10.Jm, 75.40.Mg, 75.10.Kt, Predicting the phases of frustrated spin systems is one of the major challenges in theoretical condensed matter physics [1]. A famous example is the Shastry-Sutherland model (SSM) [2], which is believed to accurately capture the physics of the orthogonal-dimer antiferromagnet SrCu 2 (BO 3 ) 2 . A big effort has been invested in understanding the appearance of various magnetization plateaus observed in experiments [3][4][5][6][7][8][9][10][11][12][13]. Early on it was found that the SSM has almost localized triplet excitations [5,14] which suggests that each plateau corresponds to a particular crystal of localized triplets. This viewpoint has been supported by many analytical and (approximate) numerical studies over the last 15 years [14][15][16][17][18][19][20][21][22][23][24][25].The SSM is given by the Hamiltonianwhere the i, j bonds with coupling strength J build an array of orthogonal dimers while the bonds with coupling J denote inter-dimer couplings, and h the strength of the external magnetic field. The main result of this Letter is that -in contrast to the standard belief -the plateaus are not crystals of S z = 1 triplets (see Fig. 1(a)), but of S z = 2 bound states of triplets, which form a pinwheel pattern as shown in Fig. 1(b), and which are shown to be stable even if they are localized. Bound states have previously been predicted to be relevant in the dilute limit of excitations [16,[26][27][28][29], but not for the formation of crystals. The only hint so far that bound states can form crystals was found in a one-dimensional analog -a SSM spin tube [30]. It is also shown that the crystals formed by the bound states naturally explain the sequence of magnetization plateaus observed in SrCu 2 (BO 3 ) 2 . In particular, the 2/15 plateau is made of a simple and regular pattern of bound states, in contrast to the more complicated patterns of triplets which were previously suggested [12,21,24].Method -Our results have been obtained with infinite projected entangled-pair states (iPEPS) -a variational tensornetwork ansatz to represent a two-dimensional wave function in the thermodynamic limit [31][32][33]. It consists of a cell of tensors which is periodically repeated on the lattice, where ...

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“…While symmetric tensor networks and the use of conserved quantities in tensor network algorithms have been addressed in numerous previous works [7,[14][15][16][17][18], we reiterate here in detail their consistent use in the context of MPS in the thermodynamic limit.…”

Section: Symmetric Uniform Mpsmentioning

confidence: 99%

Topological nature of spinons and holons: Elementary excitations from matrix product states with conserved symmetries

et al. 2018

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We develop variational matrix product state (MPS) methods with symmetries to determine dispersion relations of one-dimensional quantum lattices as a function of momentum and preset quantum number. We test our methods on the XXZ spin chain, the Hubbard model, and a nonintegrable extended Hubbard model and determine the excitation spectra with a precision similar to the one of the ground state. The formulation in terms of quantum numbers makes the topological nature of spinons and holons very explicit. In addition, the method also enables an easy and efficient direct calculation of the necessary magnetic field or chemical potential required for a certain ground state magnetization or particle density.

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

Cited by 228 publications

References 74 publications

Existence of featureless paramagnets on the square and the honeycomb lattices in 2+1 dimensions

Existence of featureless paramagnets on the square and the honeycomb lattices in 2+1 dimensions

Crystals of Bound States in the Magnetization Plateaus of the Shastry-Sutherland Model

Topological nature of spinons and holons: Elementary excitations from matrix product states with conserved symmetries

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