Exotic criticality in the dimerized spin-1 $XXZ$ chain with single-ion anisotropyExotic criticality in the dimerized spin-1 $XXZ$ chain with single-ion anisotropy

Satoshi Ejima, Tomoki Yamaguchi, Fabian H. L. Eßler +3 more

We consider the dimerized spin-1 XXZ chain with single-ion anisotropy D. In absence of an explicit dimerization there are three phases: a large- $D$ , an antiferromagnetically ordered and a Haldane phase. This phase structure persists up to a critical dimerization, above which the Haldane phase disappears. We show that for weak dimerization the phases are separated by Gaussian and Ising quantum phase transitions. One of the Ising transitions terminates in a critical point in the universality class of the dilute Ising model. We comment on the relevance of our results to experiments on quasi-one-dimensional anisotropic spin-1 quantum magnets.We consider the dimerized spin-1 XXZ chain with single-ion anisotropy D. In absence of an explicit dimerization there are three phases: a large-$D$, an antiferromagnetically ordered and a Haldane phase. This phase structure persists up to a critical dimerization, above which the Haldane phase disappears. We show that for weak dimerization the phases are separated by Gaussian and Ising quantum phase transitions. One of the Ising transitions terminates in a critical point in the universality class of the dilute Ising model. We comment on the relevance of our results to experiments on quasi-one-dimensional anisotropic spin-1 quantum magnets.

arXiv:1810.02195SciPost PhysicsDec 7, 201821 citations

Critical Properties of Spin Chains

Satoshi Takada

Springer series in solid-state sciencesJan 1, 19873 citations

On $\mathsf{c = 1}$ critical phases in anisotropic spin-1 chainsOn $\mathsf{c = 1}$ critical phases in anisotropic spin-1 chains

C. Degli Esposti Boschi, Elisa Ercolessi, F. Ortolani +1 more

arXiv:cond-mat/0307396The European Physical Journal BOct 1, 200362 citations

Non-Abelian bosonization of the frustrated antiferromagnetic spin-1/2 chain

Dave Allen, David Sénéchal

We study the spin-1/2 chain with nearest-neighbor (${\mathrm{\ensuremath{\kappa}}}_{1}$) and next-nearest-neighbor (${\mathrm{\ensuremath{\kappa}}}_{2}$) interactions in the regime ${\mathrm{\ensuremath{\kappa}}}_{2}$\ensuremath{\gg}:${\mathrm{\ensuremath{\kappa}}}_{1}$, which is equivalent to two chains with a ``zigzag'' interaction. In the continuum limit, this system is described in terms of two coupled level-1 Wess-Zumino-Witten field theories. We illustrate its equivalence with four off-critical Ising models (Majorana fermions). This description is used to investigate the opening of a gap as a function of ${\mathrm{\ensuremath{\kappa}}}_{1}$ and the associated spontaneous breakdown of parity. We calculate the dynamic spin structure factor near the wave vectors accessible to the continuum limit. We comment on the nonzero string order parameter and show the presence of a hidden ${\mathrm{Z}}_{2}$ \ifmmode\times\else\texttimes\fi{} ${\mathrm{Z}}_{2}$ symmetry via a nonlocal transformation on the microscopic Hamiltonian. For a ferromagnetic interchain coupling, the model is conjectured to be critical, with different velocities for the spin-singlet and spin-triplet excitations.We study the spin-1/2 chain with nearest-neighbor (${\mathrm{\ensuremath{\kappa}}}_{1}$) and next-nearest-neighbor (${\mathrm{\ensuremath{\kappa}}}_{2}$) interactions in the regime ${\mathrm{\ensuremath{\kappa}}}_{2}$\ensuremath{\gg}:${\mathrm{\ensuremath{\kappa}}}_{1}$, which is equivalent to two chains with a ``zigzag'' interaction. In the continuum limit, this system is described in terms of two coupled level-1 Wess-Zumino-Witten field theories. We illustrate its equivalence with four off-critical Ising models (Majorana fermions). This description is used to investigate the opening of a gap as a function of ${\mathrm{\ensuremath{\kappa}}}_{1}$ and the associated spontaneous breakdown of parity. We calculate the dynamic spin structure factor near the wave vectors accessible to the continuum limit. We comment on the nonzero string order parameter and show the presence of a hidden ${\mathrm{Z}}_{2}$\ifmmode\times\else\texttimes\fi{}${\mathrm{Z}}_{2}$ symmetry via a nonlocal transformation on the microscopic Hamiltonian. For a ferromagnetic interchain coupling, the model is conjectured to be critical, with different velocities for the spin-singlet and spin-triplet excitations.

arXiv:cond-mat/9606007Physical review. B, Condensed matterJan 1, 199790 citations

Exotic criticality in the dimerized spin-1

XXZ

chain with single-ion anisotropy

We consider the dimerized spin-1 XXZ chain with single-ion anisotropy D. In absence of an explicit dimerization there are three phases: a large-

D

, an antiferromagnetically ordered and a Haldane phase. This phase structure persists up to a critical dimerization, above which the Haldane phase disappears. We show that for weak dimerization the phases are separated by Gaussian and Ising quantum phase transitions. One of the Ising transitions terminates in a critical point in the universality class of the dilute Ising model. We comment on the relevance of our results to experiments on quasi-one-dimensional anisotropic spin-1 quantum magnets.

\mathsf{c = 1}

critical phases in anisotropic spin-1 chains

{\mathrm{Z}}_{2}

\ifmmode\times\else\texttimes\fi{}

{\mathrm{Z}}_{2}

symmetry via a nonlocal transformation on the microscopic Hamiltonian. For a ferromagnetic interchain coupling, the model is conjectured to be critical, with different velocities for the spin-singlet and spin-triplet excitations.