arXiv:cond-mat/9807179 · Physical Review Letters

Thermodynamics of the One-Dimensional SU(4) Symmetric Spin-Orbital Model

Beat Frischmuth, Frédéric Mila, Matthias Troyer

Published Jan 25, 1999• 111 citations

Abstract

The ground-state properties and thermodynamics of the one-dimensional SU(4) symmetric spin system with orbital degeneracy are investigated using the quantum Monte Carlo loop algorithm. The spin-spin correlation functions exhibit a 4-site periodicity, and their low-temperature behavior is controlled by two correlation lengths that diverge like the inverse temperature, while the entropy is linear in temperature and its slope is consistent with three gapless modes of velocity $\ensuremath{\pi}/2$. The physical implications of these results are discussed.

DOI: 10.1103/physrevlett.82.835

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arXiv:cond-mat/9807179 · Physical Review Letters

Thermodynamics of the One-Dimensional SU(4) Symmetric Spin-Orbital Model

Beat Frischmuth, Frédéric Mila, Matthias Troyer

Published Jan 25, 1999• 111 citations

arXiv HTML PDF

Abstract

\ensuremath{\pi}/2

. The physical implications of these results are discussed.

DOI: 10.1103/physrevlett.82.835

Related papers

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The thermodynamic properties of a one-dimensional model describing spin dynamics in the presence of a twofold orbital degeneracy are studied numerically using the transfer-matrix renormalization group. The model contains an integrable SU(4)-symmetric point and a gapless phase which is SU(4) invariant up to a rescaling of the velocities for spin and orbital degrees of freedom which allows detailed comparison of the numerical results with conformal field theory. We pay special attention to the correlation lengths which show an intriguing evolution with temperature. We find that the model shows an intrinsic tendency towards dimerization at finite temperature even if the ground state is not dimerized.The thermodynamic properties of a one-dimensional model describing spin dynamics in the presence of a twofold orbital degeneracy are studied numerically using the transfer-matrix renormalization group. The model contains an integrable SU(4)-symmetric point and a gapless phase which is SU(4) invariant up to a rescaling of the velocities for spin and orbital degrees of freedom which allows detailed comparison of the numerical results with conformal field theory. We pay special attention to the correlation lengths which show an intriguing evolution with temperature. We find that the model shows an intrinsic tendency towards dimerization at finite temperature even if the ground state is not dimerized.

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The $\mathrm{SU}(4)$ Heisenberg model on the honeycomb lattice is expected to host a quantum spin-orbital liquid at low temperature with an astonishing candidate material, $α$ -ZrCl $_3$ . We employed the canonical thermal pure quantum state method to investigate the finite-temperature phase of this model. Exploiting the full symmetry of $\mathrm{SU}(4)$ , the calculation up to a 24-site cluster, which is equivalent to 48 sites in the spin-1/2 language, is possible. This state-of-the-art computation with large-scale parallelization enables us to capture the thermodynamic properties of the $\mathrm{SU}(4)$ Heisenberg model on the honeycomb lattice. In particular, the specific heat shows a characteristic peak-and-shoulder structure, which should be related to the nature of the low-temperature quantum spin-orbital liquid phase. We also discuss what can be concluded from the assumption that the ground state is gapped and symmetric in view of the generalized Lieb-Schultz-Mattis theorem.The $\mathrm{SU}(4)$ Heisenberg model on the honeycomb lattice is expected to host a quantum spin-orbital liquid at low temperature with an astonishing candidate material, $α$-ZrCl$_3$. We employed the canonical thermal pure quantum state method to investigate the finite-temperature phase of this model. Exploiting the full symmetry of $\mathrm{SU}(4)$, the calculation up to a 24-site cluster, which is equivalent to 48 sites in the spin-1/2 language, is possible. This state-of-the-art computation with large-scale parallelization enables us to capture the thermodynamic properties of the $\mathrm{SU}(4)$ Heisenberg model on the honeycomb lattice. In particular, the specific heat shows a characteristic peak-and-shoulder structure, which should be related to the nature of the low-temperature quantum spin-orbital liquid phase. We also discuss what can be concluded from the assumption that the ground state is gapped and symmetric in view of the generalized Lieb-Schultz-Mattis theorem.

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\ensuremath{\pi}/2

. The physical implications of these results are discussed.

{\mathit{k}}_{\mathit{F}}

spin susceptibility, our results are consistent with the form \ensuremath{\chi}(2

{\mathit{k}}_{\mathit{F}}

)\ensuremath{\sim}\ensuremath{\Vert}ln(T)${\mathrm{\ensuremath{\Vert}}}^{\mathrm{\ensuremath{\sigma}}}$${\mathit{T}}_{\mathrm{\ensuremath{\rho}}}^{\mathit{K}}$-1, with \ensuremath{\sigma}=1/2.

The one-dimensional Heisenberg model in the presence of orbital degeneracy is studied at the

\mathrm{SU}(4)

symmetric point by means of Bethe ansatz. Following Sutherland's previous work on an equivalent model, we discuss the ground state and the low-lying excitations more extensively in connection to the spin systems with orbital degeneracy. We show explicitly that the ground state is a

\mathrm{SU}(4)

singlet. We study the degeneracies of the elementary excitations and the spectra of the generalized magnons consisting of these excitations. We also discuss the complex 2-strings in the context of the Bethe ansatz solutions.

Thermodynamic signature of the

\mathrm{SU}(4)

spin-orbital liquid and symmetry fractionalization from the Lieb-Schultz-Mattis theorem

The

\mathrm{SU}(4)

Heisenberg model on the honeycomb lattice is expected to host a quantum spin-orbital liquid at low temperature with an astonishing candidate material,

α

-ZrCl

_3

. We employed the canonical thermal pure quantum state method to investigate the finite-temperature phase of this model. Exploiting the full symmetry of

\mathrm{SU}(4)

, the calculation up to a 24-site cluster, which is equivalent to 48 sites in the spin-1/2 language, is possible. This state-of-the-art computation with large-scale parallelization enables us to capture the thermodynamic properties of the

\mathrm{SU}(4)

Heisenberg model on the honeycomb lattice. In particular, the specific heat shows a characteristic peak-and-shoulder structure, which should be related to the nature of the low-temperature quantum spin-orbital liquid phase. We also discuss what can be concluded from the assumption that the ground state is gapped and symmetric in view of the generalized Lieb-Schultz-Mattis theorem.

{\mathrm{LiNiO}}_{2}

. In the SU(4) N\'eel-ordered state, spin-spin correlations can be antiferromagnetic between two neighboring sites with parallel magnetic moments.