Spin-spin correlation functions of the <i>q</i>-valence-bond-solid state of an integer spin model

Arita, Chikashi; Motegi, Kohei

doi:10.1063/1.3598424

Cited by 9 publications

(20 citation statements)

References 32 publications

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“…On the other hand, we have already seen that the Bloch spin-coherent state enables us to relate the Laughlin-Haldane wave functions to the VBS states. In correspondence with such QHE, a variety of VBS models have been constructed with the symmetries, such as SO (5), SO(2n + 1) [107,108,109], SU (N + 1) [110,111,112,113], Sp(N ) [114,115], and q-deformed SU (2) [21,22,116,117,118] [see Fig. 2].…”

Section: Introductionmentioning

confidence: 99%

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Topological Many-Body States in Quantum Antiferromagnets via Fuzzy Supergeometry

Hasebe

Totsuka

2013

Symmetry

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Recent vigorous investigations of topological order have not only discovered new topological states of matter, but also shed new light on "already known" topological states. One established example with topological order is the valence bond solid (VBS) states in quantum antiferromagnets. The VBS states are disordered spin liquids with no spontaneous symmetry breaking, but most typically manifest a topological order known as a hidden string order on the 1D chain. Interestingly, the VBS models are based on mathematics analogous to fuzzy geometry. We review applications of the mathematics of fuzzy supergeometry in the construction of supersymmetric versions of VBS (SVBS) states and give a pedagogical introduction of SVBS models and their properties. As concrete examples, we present detailed analysis of supersymmetric versions of SU (2) and SO(5) VBS states, i.e., U OSp(N |2) and U OSp(N |4) SVBS states, whose mathematics are closely related to fuzzy two-and four-superspheres. The SVBS states are physically interpreted as hole-doped VBS states with a superconducting property that interpolates various VBS states, depending on the value of a hole-doping parameter. The parent Hamiltonians for SVBS states are explicitly constructed, and their gapped excitations are derived within the single-mode approximation on 1D SVBS chains. Prominent features of the SVBS chains are discussed in detail, such as a generalized string order parameter and entanglement spectra. It is realized that the entanglement spectra are at least doubly degenerate, regardless of the parity of bulk (super)spins. The stability of the topological phase with supersymmetry is discussed, with emphasis on its relation to particular edge (super)spin states.

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Section: Introductionmentioning

confidence: 99%

“…For(117), the order parameter ∆ k = c † k c † −k , the electron number n k = c † k c k , and its fluctuation δn k , are…”

mentioning

confidence: 99%

Topological Many-Body States in Quantum Antiferromagnets via Fuzzy Supergeometry

Hasebe

Totsuka

2013

Symmetry

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“…Recently Santos et al found surprisingly simple and useful formula for calculating the reduced density matrix for matrix product ground states [32,33]. They applied it to the AKLT model of spin-1 and general integer spin S with quantum group symmetry (q-AKLT model) [3,5,10,19,20,24,35], and another massive Klümper-Schadschneider-Zittartz model [21] to study anisotropic effect.…”

Section: Introductionmentioning

confidence: 99%

“…We obtain the expression of the geometric entanglement for → ∞ and its finite size corrections with help of numerical calculations. For the evaluation of the entanglement entropies and the geometric entanglement, the spectral structure of the transfer matrix of the q-VBS state in the matrix product representation [3,24] will be helpful. This article is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

“…This article is organized as follows. In Section 2, we briefly review the matrix product representation [3,24] of the VBS ground state of the q-AKLT model, which helps us for evaluating the entanglement entropies and the geometric entanglement. In Section 3, the finite-size correction terms of the entanglement entropies from the double scaling limit are calculated by perturbative analysis.…”

Section: Introductionmentioning

confidence: 99%

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Entanglement Properties of a Higher-Integer-Spin AKLT Model with Quantum Group Symmetry

Arita¹

2012

SIGMA

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Abstract. We study the entanglement properties of a higher-integer-spin Affleck-KennedyLieb-Tasaki model with quantum group symmetry in the periodic boundary condition. We exactly calculate the finite size correction terms of the entanglement entropies from the double scaling limit. We also evaluate the geometric entanglement, which serves as another measure for entanglement. We find the geometric entanglement reaches its maximum at the isotropic point, and decreases with the increase of the anisotropy. This behavior is similar to that of the entanglement entropies.

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Entanglement spectra ofq-deformed higher spin VBS states

Santos¹,

Paraan²,

Korepin³

et al. 2012

J. Phys. A: Math. Theor.

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We calculate the reduced density matrix of a block of integer spin-S's in a q-deformed valence-bond-solid (VBS) state. This matrix is diagonalized exactly for an infinitely long block in an infinitely long chain. We construct an effective Hamiltonian with the same spectrum as the logarithm of the density matrix. We also derive analytic expressions for the von Neumann and Rényi entanglement entropies. For blocks of finite length, we calculate the eigenvalues of the reduced density matrix by perturbation theory and numerical diagonalization. These results enable us to describe the effects of finite-size corrections on the entanglement spectrum and entropy in this generalized VBS model.

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Spin-spin correlation functions of the q-valence-bond-solid state of an integer spin model

Cited by 9 publications

References 32 publications

Topological Many-Body States in Quantum Antiferromagnets via Fuzzy Supergeometry

Topological Many-Body States in Quantum Antiferromagnets via Fuzzy Supergeometry

Entanglement Properties of a Higher-Integer-Spin AKLT Model with Quantum Group Symmetry

Entanglement spectra ofq-deformed higher spin VBS states

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