Generalization of the Jordan-Wigner transformation in three dimensions and its application to the Heisenberg bilayer antiferromagnet

Bock, Bounghun; Azzouz, Mohamed

doi:10.1103/physrevb.64.054410

Cited by 13 publications

(12 citation statements)

References 23 publications

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“…Notice that if θ → 0, Eqs. (14) reduce to (12) in the absence of shear force. For a nonzero small θ, we write cos θ ≈ 1 − θ 2 /2, and sin θ ≈ θ ≈ u/a.…”

Section: A Tube Without Shear Strainmentioning

confidence: 95%

Topological Monopoles in Quantum Antiferromagnets

Azzouz¹

2019

Preprint

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While the observation of magnetic monopoles has defied all experimental attempts in high-energy physics and astrophysics, sound theoretical approaches predict they should exist, and they have indeed been observed as quasiparticle excitations in certain condensed-matter systems. This indicates that, even though they are not ubiquitous contrary to electrons, it is possible to get them as excitations above a ground state. In this report, we show that phonons or lattice shear strain generate topological monopoles in some low-dimensional quantum antiferromagnets. For the Heisenberg ladder, phonons are found to generate topological monopoles with nonzero density due to quantum spin fluctuations. For the four-leg Heisenberg tube, longitudinal shear stress generates topological monopoles with density proportional to the strain deformation. The present theory is based on mapping the spin degrees of freedom onto spinless fermions using the generalized Jordan-Wigner transformation in dimensions higher than one. The effective magnetic field generated by the motion of the spinless fermions has non-zero divergence when phonons or shear stress are present. A possible system where the present kind of monopoles could be observed is BiCu$_2$PO$_6$.

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“…Notice that if θ → 0, Eqs. (14) reduce to (12) in the absence of shear force. For a nonzero small θ, we write cos θ ≈ 1 − θ 2 /2, and sin θ ≈ θ ≈ u/a.…”

Section: A Tube Without Shear Strainmentioning

confidence: 95%

Topological Monopoles in Quantum Antiferromagnets

Azzouz¹

2019

Preprint

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“…In BMFT, the interacting terms of the JW fermions are decoupled using the spin bond parameters. This approximation neglects fluctuations around the mean-field points: ͑O − ͗O͒͘ ϫ͑OЈ − ͗OЈ͒͘ Ϸ 0, where O and OЈ are any operators which are quadratic in c † and c. 22 This yields…”

Section: A Jordan-wigner Transformation and Bond-mean-field Theorymentioning

confidence: 99%

Effect of temperature on quantum criticality in the frustrated two-leg Heisenberg ladder

Ramakko

Azzouz

2007

Phys. Rev. B

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The antiferromagnetic Heisenberg model on the two-leg ladder with exchange interactions along the chains, rungs, and diagonals is studied using the Jordan-Wigner transformation and bond-mean-field theory. The inclusion of all three couplings introduces frustration to the system and depending on their relative strengths the ladder can adopt one of three possible magnetically disordered gapped states. The phase diagram found in this mean-field approach is in very good agreement with the one calculated by Weihong et al. ͓Phys. Rev. B 57, 11439 ͑1998͔͒ using the Lanczos exact diagonalization method. By analyzing the ground-state energy, we study quantum criticality when the coupling parameters are varied at zero temperature. We study the effect of temperature on the phase boundaries and find that the system shows thermally induced criticality for some values of the rung and diagonal coupling constants. All the phase transitions encountered in this system occur between disordered phases and are all caused by frustration.

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“…The Jordan-Wigner (JW) transformation establishes a connection between spin-1/2 operators and spinless fermion operators [1], and it has become a powerful tool for solving one-dimensional (1D) spin models and a few two-dimensional Ising models [2][3][4]. Besides, it is remarkable that the JW transformation has been generalized to higher dimensions in recent decades [5][6][7][8][9][10][11][12][13]. Typical examples of applications are provided in [2].…”

Section: Introductionmentioning

confidence: 99%

Exact Solutions and Degenerate Properties of Spin Chains with Reducible Hamiltonians

Fan

2018

Condensed Matter

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The Jordan-Wigner transformation plays an important role in spin models. However, the nonlocality of the transformation implies that a periodic chain of N spins is not mapped to a periodic or an anti-periodic chain of lattice fermions. Since only the N − 1 bond is different, the effect is negligible for large systems, while it is significant for small systems. In this paper, it is interesting to find that a class of periodic spin chains can be exactly mapped to a periodic chain and an antiperiodic chain of lattice fermions without redundancy when the Jordan-Wigner transformation is implemented. For these systems, possible high degeneracy is found to appear in not only the ground state, but also the excitation states. Further, we take the one-dimensional compass model and a new XY-XY model (σxσy − σxσy) as examples to demonstrate our proposition. Except for the well-known one-dimensional compass model, we will see that in the XY-XY model, the degeneracy also grows exponentially with the number of sites.

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Generalization of the Jordan-Wigner transformation in three dimensions and its application to the Heisenberg bilayer antiferromagnet

Cited by 13 publications

References 23 publications

Topological Monopoles in Quantum Antiferromagnets

Topological Monopoles in Quantum Antiferromagnets

Effect of temperature on quantum criticality in the frustrated two-leg Heisenberg ladder

Exact Solutions and Degenerate Properties of Spin Chains with Reducible Hamiltonians

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