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Chinese Physics B
Vol. 29, Issue 9, (2020)

Some experimental schemes to identify quantum spin liquids

Yonghao Gao¹ and Gang Chen^1,2,†

Author Affiliations

¹State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China

²Department of Physics and HKU-UCAS Joint Institute for Theoretical and Computational Physics at Hong Kong, The University of Hong Kong, Hong Kong, China

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DOI: 10.1088/1674-1056/ab9df0 Cite this Article

Yonghao Gao, Gang Chen. Some experimental schemes to identify quantum spin liquids[J]. Chinese Physics B, 2020, 29(9): Copy Citation Text

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Abstract

Despite the apparent ubiquity and variety of quantum spin liquids in theory, experimental confirmation of spin liquids remains to be a huge challenge. Motivated by the recent surge of evidences for spin liquids in a series of candidate materials, we highlight the experimental schemes, involving the thermal Hall transport and spectrum measurements, that can result in smoking-gun signatures of spin liquids beyond the usual ones. For clarity, we investigate the square lattice spin liquids and theoretically predict the possible phenomena that may emerge in the corresponding spin liquids candidates. The mechanisms for these signatures can be traced back to either the intrinsic characters of spin liquids or the external field-driven behaviors. Our conclusion does not depend on the geometry of lattices and can broadly apply to other relevant spin liquids.

Keywords

fractionalization neutron scattering quantum spin liquids thermal Hall effect

\begin{array}{r} H = J_{1} \sum_{⟨ i j ⟩} {\boldsymbol S}_{i} \cdot {\boldsymbol S}_{j} + J_{2} \sum_{⟨ ⟨ i j ⟩ ⟩} {\boldsymbol S}_{i} \cdot {\boldsymbol S}_{j}, \end{array}

(1)

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\begin{array}{r} {\boldsymbol S}_{i}^{} = \frac{1}{2} \sum_{α, β} f_{i α}^{†} {\boldsymbol σ}_{α β} f_{i β}, \end{array}

(2)

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\begin{array}{r} \begin{array}{ll} H_{M F} = & - \sum_{i j, α} (t_{1, i j} f_{i, α}^{†} f_{j, α} + t_{2, i j} f_{i, α}^{†} f_{j, α} + h . c .) \\ - μ \sum_{i, α} f_{i, α}^{†} f_{i, α}, \end{array} \end{array}

(3)

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\begin{array}{r} G_{T_{1}} (i) = 1, G_{T_{2}} (i) = η_{x y}^{i_{x} + i_{y}}, \end{array}

(4)

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\begin{array}{r} \begin{array}{ll} S (\boldsymbol q, ω) & = \frac{1}{N} \sum_{i, j} e^{i \boldsymbol q \cdot ({\boldsymbol r}_{i} - {\boldsymbol r}_{j})} \int d t e^{- i ω t} ⟨ {\boldsymbol S}_{i}^{-} (t) \cdot {\boldsymbol S}_{j}^{+} (0) ⟩ \\ = \sum_{n} δ [ω - ξ_{n} (\boldsymbol q)] | ⟨ n | {\boldsymbol S}_{q}^{+} | G ⟩ |^{2}, \end{array} \end{array}

(5)

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\begin{array}{r} \begin{array}{lll} \boldsymbol q & = & {\boldsymbol k}_{1} - {\boldsymbol k}_{2}, \end{array} \end{array}

(6)

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\begin{array}{r} \begin{array}{lll} ξ (\boldsymbol q) & = & ω_{1} ({\boldsymbol k}_{1}) - ω_{2} ({\boldsymbol k}_{2}), \end{array} \end{array}

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\begin{array}{r} {\tilde{T}}_{1} {\tilde{T}}_{2} {\tilde{T}}_{1}^{- 1} {\tilde{T}}_{2}^{- 1} = η_{x y}, \end{array}

(8)

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\begin{array}{r} e d g e (\boldsymbol q) = max_{k} [ω_{1} (\boldsymbol k + \boldsymbol q) - ω_{2} (\boldsymbol k)] \end{array}

(9)

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\begin{array}{r} H_{B} = - \frac{B_{z}}{2} \sum_{i, α β} f_{i, α}^{†} σ_{α β}^{z} f_{i, β}, \end{array}

(10)

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\begin{array}{r} H_{χ} = J_{χ} \sum_{i, j, k \in △} \sin Φ {\boldsymbol S}_{i} \cdot {\boldsymbol S}_{j} \times {\boldsymbol S}_{k}, \end{array}

(11)

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\begin{array}{r} \begin{array}{ll} t_{2} + t_{2}^{^{'}} e^{i θ_{i j}} & = (t_{2} + t_{2^{^{'}}} \cos θ_{i j}) + i t_{2}^{^{'}} \sin θ_{i j} \\ = \sqrt{t_{2}^{2} + t_{2}^{' 2} + 2 t_{2} {t^{^{'}}}_{2} \cos (θ_{i j})} e^{ϕ_{i j}} \\ = t_{2}^{*} e^{ϕ_{i j}}, \end{array} \end{array}

(12)

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\begin{array}{r} κ_{x y} = - \frac{k_{B}^{2}}{T} \int d ε {(ε - μ)}^{2} \frac{\partial f (ε, μ, T)}{\partial ε} σ_{x y} (ε), \end{array}

(13)

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\begin{array}{r} σ_{x y} (ε) = - \frac{1}{ℏ} \sum_{\boldsymbol k, ξ_{n, \boldsymbol k} < ε} Ω_{n, \boldsymbol k} \end{array}

(14)

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\begin{array}{r} \frac{κ_{x y}}{T} = - \frac{π k_{B}^{2}}{6 ℏ} \sum_{n = 1, 2} C_{n}, \end{array}

(15)

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Yonghao Gao, Gang Chen. Some experimental schemes to identify quantum spin liquids[J]. Chinese Physics B, 2020, 29(9):

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