Gapped and gapless phases in quasi-one-dimensional antiferromagnetic systems

Motivated by the quasi-one-dimensional antiferromagnet CaV ${}_{2}$ O ${}_{4}$ , we explore spin-orbital systems in which the spin modes are gapped but orbitals are near a macroscopically degenerate classical transition. Within a simplified model we show that gapless orbital liquid phases possessing power-law correlations may occur without the strict condition of a continuous orbital symmetry. For the model proposed for CaV ${}_{2}$ O ${}_{4}$ , we find that an orbital phase with coexisting order parameters emerges from a multicritical point. The effective orbital model consists of zigzag-coupled transverse field Ising chains. The corresponding global phase diagram is constructed using field theory methods and analyzed near the multicritical point with the aid of an exact solution of a zigzag $\mathit{XXZ}$ model.Motivated by the quasi-one-dimensional antiferromagnet CaV${}_{2}$O${}_{4}$, we explore spin-orbital systems in which the spin modes are gapped but orbitals are near a macroscopically degenerate classical transition. Within a simplified model we show that gapless orbital liquid phases possessing power-law correlations may occur without the strict condition of a continuous orbital symmetry. For the model proposed for CaV${}_{2}$O${}_{4}$, we find that an orbital phase with coexisting order parameters emerges from a multicritical point. The effective orbital model consists of zigzag-coupled transverse field Ising chains. The corresponding global phase diagram is constructed using field theory methods and analyzed near the multicritical point with the aid of an exact solution of a zigzag $\mathit{XXZ}$ model.

arXiv:1103.2473Physical Review BJul 20, 201120 citations

One dimensional antiferromagnetic spin systems

Ping Sun

Jan 1, 20010 citations

Quantum-Critical Spin Dynamics in Quasi-One-Dimensional Antiferromagnets

S. Mukhopadhyay, M. Klanjšek, Mihael S. Grbić +8 more

By means of nuclear spin-lattice relaxation rate ${T}_{1}^{\ensuremath{-}1}$, we follow the spin dynamics as a function of the applied magnetic field in two gapped quasi-one-dimensional quantum antiferromagnets: the anisotropic spin-chain system ${\mathrm{NiCl}}_{2}\mathrm{\text{\ensuremath{-}}}4\mathrm{SC}({\mathrm{NH}}_{2}{)}_{2}$ and the spin-ladder system $({\mathrm{C}}_{5}{\mathrm{H}}_{12}\mathrm{N}{)}_{2}\mathrm{Cu}{\mathrm{Br}}_{4}$ . In both systems, spin excitations are confirmed to evolve from magnons in the gapped state to spinons in the gapless Tomonaga-Luttinger-liquid state. In between, ${T}_{1}^{\ensuremath{-}1}$ exhibits a pronounced, continuous variation, which is shown to scale in accordance with quantum criticality. We extract the critical exponent for ${T}_{1}^{\ensuremath{-}1}$, compare it to the theory, and show that this behavior is identical in both studied systems, thus demonstrating the universality of quantum-critical behavior.By means of nuclear spin-lattice relaxation rate ${T}_{1}^{\ensuremath{-}1}$, we follow the spin dynamics as a function of the applied magnetic field in two gapped quasi-one-dimensional quantum antiferromagnets: the anisotropic spin-chain system ${\mathrm{NiCl}}_{2}\mathrm{\text{\ensuremath{-}}}4\mathrm{SC}({\mathrm{NH}}_{2}{)}_{2}$ and the spin-ladder system $({\mathrm{C}}_{5}{\mathrm{H}}_{12}\mathrm{N}{)}_{2}\mathrm{Cu}{\mathrm{Br}}_{4}$. In both systems, spin excitations are confirmed to evolve from magnons in the gapped state to spinons in the gapless Tomonaga-Luttinger-liquid state. In between, ${T}_{1}^{\ensuremath{-}1}$ exhibits a pronounced, continuous variation, which is shown to scale in accordance with quantum criticality. We extract the critical exponent for ${T}_{1}^{\ensuremath{-}1}$, compare it to the theory, and show that this behavior is identical in both studied systems, thus demonstrating the universality of quantum-critical behavior.

arXiv:1208.6117Physical Review LettersOct 26, 201254 citations

Intrinsically gapless topological phases

Ryan Thorngren, Ashvin Vishwanath, Ruben Verresen

Most topological properties of quantum systems, such as the braiding of anyons or protected edge modes, are easiest to define in systems with an energy gap. While some topological phenomena persist in the presence of gapless modes, this paper explores such properties that are only possible without a gap. These systems are here dubbed intrinsically gapless topological phases. The authors study a simple model -- a hole-doped one-dimensional antiferromagnet -- and describe a mechanism based on anomalies that applies in all dimensions.Most topological properties of quantum systems, such as the braiding of anyons or protected edge modes, are easiest to define in systems with an energy gap. While some topological phenomena persist in the presence of gapless modes, this paper explores such properties that are only possible without a gap. These systems are here dubbed intrinsically gapless topological phases. The authors study a simple model -- a hole-doped one-dimensional antiferromagnet -- and describe a mechanism based on anomalies that applies in all dimensions.

arXiv:2008.06638Physical review. B./Physical review. BAug 18, 2021138 citations

Motivated by the quasi-one-dimensional antiferromagnet CaV

{}_{2}

{}_{4}

, we explore spin-orbital systems in which the spin modes are gapped but orbitals are near a macroscopically degenerate classical transition. Within a simplified model we show that gapless orbital liquid phases possessing power-law correlations may occur without the strict condition of a continuous orbital symmetry. For the model proposed for CaV

{}_{2}

{}_{4}

, we find that an orbital phase with coexisting order parameters emerges from a multicritical point. The effective orbital model consists of zigzag-coupled transverse field Ising chains. The corresponding global phase diagram is constructed using field theory methods and analyzed near the multicritical point with the aid of an exact solution of a zigzag

\mathit{XXZ}

model.

({\mathrm{C}}_{5}{\mathrm{H}}_{12}\mathrm{N}{)}_{2}\mathrm{Cu}{\mathrm{Br}}_{4}

. In both systems, spin excitations are confirmed to evolve from magnons in the gapped state to spinons in the gapless Tomonaga-Luttinger-liquid state. In between, ${T}_{1}^{\ensuremath{-}1}$ exhibits a pronounced, continuous variation, which is shown to scale in accordance with quantum criticality. We extract the critical exponent for ${T}_{1}^{\ensuremath{-}1}$, compare it to the theory, and show that this behavior is identical in both studied systems, thus demonstrating the universality of quantum-critical behavior.