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Long-range spin correlations in a honeycomb spin model with magnetic field
Strongly Correlated Electrons · Submitted 16 Oct 2016
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Such a perturbation treated in the second order over $h$ leads to the power-law decay of irreducible spin correlation function $S(\mathbf{r},t)=\left\langle \left\langle s^{z}_r(t)s^{z}_0(0)\right\rangle \right\rangle \propto h_{z}^{2}f(t,\mathbf{r})$, where $f(t,\mathbf{r})\propto \lbrack \max (t,Jr)]^{-4}$ is an oscillating function of $\mathbf{r}$, with a wavelength equal to 3 lattice constants.
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We consider spin-$\frac{1}{2}$ model on the honeycomb lattice in the presence of weak magnetic field $h\ll J$. Such a perturbation treated in the second order over $h$ leads to the power-law decay of irreducible spin correlation function $S(\mathbf{r},t)=\left\langle \left\langle s^{z}_r(t)s^{z}_0(0)\right\rangle \right\rangle \propto h_{z}^{2}f(t,\mathbf{r})$, where $f(t,\mathbf{r})\propto \lbrack \max (t,Jr)]^{-4}$ is an oscillating function of $\mathbf{r}$, with a wavelength equal to 3 lattice constants. In the present Letter we sum main terms in all orders of the perturbation theory for the correlation function $S(\mathbf{r},t)$ in the limit of large $r,t$. Our results can be understood in terms of the effective low-energy Hamiltonian written in terms of Majorana fermions, which in the presence of magnetic field acquire vector potential $A_x \propto h_z^2$. Correspondingly, the wave vector of the oscillations in $S(\mathbf{r},t)$ changes according to $\delta k \propto h_z^2$. We also compute the dynamic structure factor $S(\mathbf{p},\omega)$; in the vicinity of $\mathbf{p}_K$ corresponding to the inter-conical points excitations it reads as $S(\mathbf{p},\omega)-S(\mathbf{p}_K,\omega)\propto\sqrt{\omega^2-3J^2(\mathbf{p}-\mathbf{p}_K)^2}$.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We consider spin-$\frac{1}{2}$ model on the honeycomb lattice in the presence of weak magnetic field $h\ll J$. | background 0.75 | 0.54 | 0.02 | asserted 0.81 |
| s1 | Such a perturbation treated in the second order over $h$ leads to the power-law decay of irreducible spin correlation function $S(\mathbf{r},t)=\left\langle \left\langle s^{z}_r(t)s^{z}_0(0)\right\rangle \right\rangle \propto h_{z}^{2}f(t,\mathbf{r})$, where $f(t,\mathbf{r})\propto \lbrack \max (t,Jr)]^{-4}$ is an oscillating function of $\mathbf{r}$, with a wavelength equal to 3 lattice constants. | result 0.81 | 0.66 | 0.23 | asserted 1.00 |
| s2 | In the present Letter we sum main terms in all orders of the perturbation theory for the correlation function $S(\mathbf{r},t)$ in the limit of large $r,t$. | contribution 0.89 | 0.93 | 0.08 | asserted 0.94 |
| s3 | Our results can be understood in terms of the effective low-energy Hamiltonian written in terms of Majorana fermions, which in the presence of magnetic field acquire vector potential $A_x \propto h_z^2$. | interpretation 0.97 | 0.74 | 0.13 | asserted 0.73 |
| s4 | Correspondingly, the wave vector of the oscillations in $S(\mathbf{r},t)$ changes according to $\delta k \propto h_z^2$. | result 0.52 | 0.84 | 0.15 | asserted 1.00 |
| s5 | We also compute the dynamic structure factor $S(\mathbf{p},\omega)$; in the vicinity of $\mathbf{p}_K$ corresponding to the inter-conical points excitations it reads as $S(\mathbf{p},\omega)-S(\mathbf{p}_K,\omega)\propto\sqrt{\omega^2-3J^2(\mathbf{p}-\mathbf{p}_K)^2}$. | result 0.97 | 0.94 | 0.11 | asserted 1.00 |
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Original abstract
We consider spin-$\frac{1}{2}$ model on the honeycomb lattice in the presence of weak magnetic field $h\ll J$. Such a perturbation treated in the second order over $h$ leads to the power-law decay of irreducible spin correlation function $S(\mathbf{r},t)=\left\langle \left\langle s^{z}_r(t)s^{z}_0(0)\right\rangle \right\rangle \propto h_{z}^{2}f(t,\mathbf{r})$, where $f(t,\mathbf{r})\propto \lbrack \max (t,Jr)]^{-4}$ is an oscillating function of $\mathbf{r}$, with a wavelength equal to 3 lattice constants. In the present Letter we sum main terms in all orders of the perturbation theory for the correlation function $S(\mathbf{r},t)$ in the limit of large $r,t$. Our results can be understood in terms of the effective low-energy Hamiltonian written in terms of Majorana fermions, which in the presence of magnetic field acquire vector potential $A_x \propto h_z^2$. Correspondingly, the wave vector of the oscillations in $S(\mathbf{r},t)$ changes according to $\delta k \propto h_z^2$. We also compute the dynamic structure factor $S(\mathbf{p},\omega)$; in the vicinity of $\mathbf{p}_K$ corresponding to the inter-conical points excitations it reads as $S(\mathbf{p},\omega)-S(\mathbf{p}_K,\omega)\propto\sqrt{\omega^2-3J^2(\mathbf{p}-\mathbf{p}_K)^2}$.
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In our case, the structure factor is proportional $ω$ when $𝐩→0,𝐩_K$ unlike $ω^3$ obtained in Ref. [ref] .
Low-energy Spin Dynamics of the Honeycomb Spin Liquid Beyond the Kitaev Limit · Introduction · 0.95
Cites as background 2 papers
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One exactly solvable case of the critical QSL is presented by the celebrated Kitaev honeycomb spin model [ref] , for a more recent review see Ref. [ref] .
Compass and Kitaev models -- Theory and Physical Motivations · Introduction · 0.95
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Quantum spin liquids, QSL's (see e.g. Refs. [ref] ) present examples of strongly correlated quantum phases which do not develop any kind of local order, while their specific entropy vanishes at zero temperature.
Quantum spin liquids · Introduction · 1.00
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