Exact groundstates for antiferromagnetic spin-one chains with nearest and next-nearest neighbour interactions

Lange, C. de; Klümper, Andreas; Zittartz, J.

doi:10.1007/bf01313293

Cited by 21 publications

(13 citation statements)

References 16 publications

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“…The special point (33) in the RSPT phase with an exact MPS ground state has another remarkable feature. It possesses exact excited states [51] as does its cousin, the AKLT chain [52][53][54].…”

Section: Discussionmentioning

confidence: 99%

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“Not- A ”, representation symmetry-protected topological, and Potts phases in an S3 -invariant chain

O’Brien¹,

Vernier²,

Fendley³

2020

Phys. Rev. B

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We analyze in depth an S 3-invariant nearest-neighbor quantum chain in the region of a U (1)-invariant self-dual multicritical point. We find four distinct proximate gapped phases. One has three-state Potts order, corresponding to topological order in a parafermionic formulation. Another has "representation" symmetryprotected topological (RSPT) order, while its dual exhibits an unusual "not-A" order, where the spins prefer to align in two of the three directions. Within each of the four phases, we find a frustration-free point with exact ground state(s). The exact ground states in the not-A phase are product states, each an equal-amplitude sum over all states where one of the three spin states on each site is absent. Their dual, the RSPT ground state, is a matrix product state similar to that of Affleck-Kennedy-Lieb-Tasaki. A field-theory analysis shows that all transition lines are in the universality class of the critical three-state Potts model. They provide a lattice realization of a flow from a free-boson field theory to the Potts conformal field theory.

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Section: Discussionmentioning

confidence: 99%

“…The matrix-product ground state |ψ MPS in (34) is similar to the famous AKLT ground state of a spin-1 SO(3)-invariant chain [4,5]. Both the corresponding Hamiltonians are special cases of a more general model with exact ground states [32,33], whose Hamiltonian is…”

Section: B the Rspt Phasementioning

confidence: 98%

“Not- A ”, representation symmetry-protected topological, and Potts phases in an S3 -invariant chain

O’Brien¹,

Vernier²,

Fendley³

2020

Phys. Rev. B

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“…The Shastry-Sutherland model 1) is a member of the family of mathematical models in which not all but only some of the eigenstates are exactly obtained. [2][3][4][5][6][7][8][9][10][11] Among such systems, the Shastry-Sutherland model became important after a good candidate material, SrCu 2 (BO 3 ) 2 , was discovered. 12,13) The discovery was followed by extensive theoretical and experimental studies.…”

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confidence: 99%

Third Boundary of the Shastry–Sutherland Model by Numerical Diagonalization

Nakano

Sakai

2018

J. Phys. Soc. Jpn.

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The Shastry-Sutherland model -the S = 1/2 Heisenberg antiferromagnet on the square lattice accompanied by orthogonal dimerized interactions -is studied by the numerical-diagonalization method. Large-scale calculations provide results for larger clusters that have not been reported yet. The present study successfully captures the phase boundary between the dimer and plaquette-singlet phases and clarifies that the spin gap increases once when the interaction forming the square lattice is increased from the boundary. Our calculations strongly suggest that in addition to the edge of the dimer phase given by J 2 /J 1 ∼ 0.675 and the edge of the Néel-ordered phase given by J 2 /J 1 ∼ 0.76, there exists a third boundary ratio J 2 /J 1 ∼ 0.70 that divides the intermediate region into two parts, where J 1 and J 2 denote dimer and square-lattice interactions, respectively.

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“…The ground-state energy e 0 = C 1 + αC 2 is given in the last row. n D n versus distance n and algebraic lines c/n b from fits to the data for n in the range [10,25].…”

Section: Resultsmentioning

confidence: 99%

Diagrammatics forSU(2) invariant matrix product states

Fledderjohann¹,

Klümper²,

Mütter³

2011

J. Phys. A: Math. Theor.

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Abstract. We report on a systematic implementation of su(2) invariance for matrix product states (MPS) with concrete computations cast in a diagrammatic language. As an application we present a variational MPS study of a spin-1/2 quantum chain. For efficient computations we make systematic use of the su(2) symmetry at all steps of the calculations: (i) the matrix space is set up as a direct sum of irreducible representations, (ii) the local matrices with state-valued entries are set up as superposition of su(2) singlet operators, (iii) products of operators are evaluated algebraically by making use of identities for 3j and 6j symbols. The remaining numerical computations like the diagonalization of the associated transfer matrix and the minimization of the energy expectation value are done in spaces free of symmetry degeneracies. The energy expectation value is a strict upper bound of the true ground-state energy and yields definite conclusions about the accuracy of DMRG results reported in the literature. Furthermore, we present explicit results with accuracy better than 10 −4 for nearestand next-nearest neighbour spin correlators and for general dimer-dimer correlators in the thermodynamical limit of the spin-1 2 Heisenberg chain with frustration.

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Exact groundstates for antiferromagnetic spin-one chains with nearest and next-nearest neighbour interactions

Cited by 21 publications

References 16 publications

“Not- A ”, representation symmetry-protected topological, and Potts phases in an S3 -invariant chain

“Not- A ”, representation symmetry-protected topological, and Potts phases in an S3 -invariant chain

Third Boundary of the Shastry–Sutherland Model by Numerical Diagonalization

Diagrammatics forSU(2) invariant matrix product states

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