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Physical Review Letters

Quantum Liquid in Antiferromagnetic Chains: A Stochastic Geometric Approach to the Haldane Gap

Hal Tasaki

Published Jul 10, 1995• 3 citations
Publisher
DOI
10.1103/physrevlett.75.354

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The S=1 quantum antiferromagnetic chain with the Hamiltonian H= ${\mathcal{J}}_{\mathit{i}}$ ${\mathrm{S}}_{\mathit{i}}^{\mathit{x}}$${\mathit{S}}_{\mathit{i}+1}^{\mathit{x}}$+${\mathit{S}}_{\mathit{i}}^{\mathit{y}}$${\mathit{S}}_{\mathit{i}+1}^{\mathit{y}}$+\ensuremath{\lambda}${\mathit{S}}_{\mathit{i}}^{\mathit{z}}$ ${\mathit{S}}_{\mathit{i}+1}^{\mathit{z}}$+D(${\mathit{S}}_{\mathit{i}}^{\mathit{z}}$${)}^{2}$ is studied. By developing a (path-integral-type) stochastic geometric representation and using the ideas of percolation, we find that the Haldane phase with a unique disordered ground state and a gap can be regarded as ``liquid''. The large-D phase and the N\'eel ordered phase are identified as ``gas'' and ``solid'', respectively. We introduce a new order parameter that distinguishes the Haldane phase from other disordered phases such as the large-D phase or the dimer phase.

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Dynamical spin excitations of the topological Haldane gapped phase in the S=1 Heisenberg antiferromagnetic chain with single-ion anisotropy

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We study the dynamical spin excitations of the one-dimensional $S=1$ Heisenberg antiferromagnetic chain with single-ion anisotropy by using quantum Monte Carlo simulations and stochastic analytic continuation of imaginary-time correlation function. Using the transverse dynamic spin structure factor, we observe the quantum phase transition with a critical point between the topological Haldane gapped phase and the trivial phase. At the quantum critical point, we find a broad continuum characterized by the Tomonaga-Luttinger liquid, and its dynamical signatures are similar to a $S=1/2$ Heisenberg antiferromagnetic chain. The broad continuum can be seen as a dynamical signature of spinons. We further identify that the elementary excitations are fractionalized spinons in the critical state.

arXiv:2003.07857•Physical review. B./Physical review. B•Jan 4, 2021•9 citations
The Haldane Gap of the S=7S=7S=7 Antiferromagnetic Chain
The S=1 quantum antiferromagnetic chain with the Hamiltonian H= Ji{\mathcal{J}}_{\mathit{i}}Ji​ Six{\mathrm{S}}_{\mathit{i}}^{\mathit{x}}Six​Si+1x{\mathit{S}}_{\mathit{i}+1}^{\mathit{x}}Si+1x​+Siy{\mathit{S}}_{\mathit{i}}^{\mathit{y}}Siy​Si+1y{\mathit{S}}_{\mathit{i}+1}^{\mathit{y}}Si+1y​+\ensuremath{\lambda}Siz{\mathit{S}}_{\mathit{i}}^{\mathit{z}}Siz​ Si+1z{\mathit{S}}_{\mathit{i}+1}^{\mathit{z}}Si+1z​+D(Siz{\mathit{S}}_{\mathit{i}}^{\mathit{z}}Siz​)2{)}^{2})2 is studied. By developing a (path-integral-type) stochastic geometric representation and using the ideas of percolation, we find that the Haldane phase with a unique disordered ground state and a gap can be regarded as ``liquid''. The large-D phase and the N\'eel ordered phase are identified as ``gas'' and ``solid'', respectively. We introduce a new order parameter that distinguishes the Haldane phase from other disordered phases such as the large-D phase or the dimer phase.
We study the dynamical spin excitations of the one-dimensional S=1S=1S=1 Heisenberg antiferromagnetic chain with single-ion anisotropy by using quantum Monte Carlo simulations and stochastic analytic continuation of imaginary-time correlation function. Using the transverse dynamic spin structure factor, we observe the quantum phase transition with a critical point between the topological Haldane gapped phase and the trivial phase. At the quantum critical point, we find a broad continuum characterized by the Tomonaga-Luttinger liquid, and its dynamical signatures are similar to a S=1/2S=1/2S=1/2 Heisenberg antiferromagnetic chain. The broad continuum can be seen as a dynamical signature of spinons. We further identify that the elementary excitations are fractionalized spinons in the critical state.