Balents, L. Spin liquids in frustrated magnets. Nature 464, 199 (2010).

Article 
CAS 
PubMed 
ADS 

Google Scholar
 

Kohno, M., Starykh, O. A. & Balents, L. Spinons and triplons in spatially anisotropic frustrated antiferromagnets. Nat. Phys. 3, 790 (2007).

Article 
CAS 

Google Scholar
 

Norman, M. R. Colloquium: herbertsmithite and the search for the quantum spin liquid. Rev. Mod. Phys. 88, 041002 (2016).

Article 
MathSciNet 
ADS 

Google Scholar
 

Ma, J. et al. Static and dynamical properties of the spin-1/2 equilateral triangular-lattice antiferromagnet Ba3CoSb2O9. Phys. Rev. Lett. 116, 087201 (2016).

Article 
CAS 
PubMed 
ADS 

Google Scholar
 

Dai, P.-L. et al. Spinon Fermi surface spin liquid in a triangular lattice antiferromagnet NaYbSe2. Phys. Rev. X 11, 021044 (2021).

CAS 

Google Scholar
 

Ortiz, B. R. et al. Quantum disordered ground state in the triangular-lattice magnet NaRuO2. Nat. Phys. 19, 943 (2023).

Article 
CAS 

Google Scholar
 

Weihong, Z., McKenzie, R. H. & Singh, R. R. P. Phase diagram for a class of spin-\(\frac{1}{2}\) Heisenberg models interpolating between the square-lattice, the triangular-lattice, and the linear-chain limits. Phys. Rev. B 59, 14367 (1999).

Article 
ADS 

Google Scholar
 

Chung, C.-H., Voelker, K. & Kim, Y. B. Statistics of spinons in the spin-liquid phase of Cs2CuCl4. Phys. Rev. B 68, 094412 (2003).

Article 
ADS 

Google Scholar
 

Yunoki, S. & Sorella, S. Resonating valence bond wave function for the two-dimensional fractional spin liquid. Phys. Rev. Lett. 92, 157003 (2004).

Article 
CAS 
PubMed 
ADS 

Google Scholar
 

Zheng, W., Singh, R. R. P., McKenzie, R. H. & Coldea, R. Temperature dependence of the magnetic susceptibility for triangular-lattice antiferromagnets with spatially anisotropic exchange constants. Phys. Rev. B 71, 134422 (2005).

Article 
ADS 

Google Scholar
 

Zheng, W., Fjærestad, J. O., Singh, R. R. P., McKenzie, R. H. & Coldea, R. Anomalous excitation spectra of frustrated quantum antiferromagnets. Phys. Rev. Lett. 96, 057201 (2006).

Article 
PubMed 
ADS 

Google Scholar
 

Yunoki, S. & Sorella, S. Two spin liquid phases in the spatially anisotropic triangular Heisenberg model. Phys. Rev. B 74, 014408 (2006).

Article 
ADS 

Google Scholar
 

Weng, M. Q., Sheng, D. N., Weng, Z. Y. & Bursill, R. J. Spin-liquid phase in an anisotropic triangular-lattice Heisenberg model: exact diagonalization and density-matrix renormalization group calculations. Phys. Rev. B 74, 012407 (2006).

Article 
ADS 

Google Scholar
 

Starykh, O. A. & Balents, L. Ordering in spatially anisotropic triangular antiferromagnets. Phys. Rev. Lett. 98, 077205 (2007).

Article 
PubMed 
ADS 

Google Scholar
 

Hayashi, Y. & Ogata, M. Possibility of gapless spin liquid state by one-dimensionalization. J. Phys. Soc. Jpn. 76, 053705 (2007).

Article 
ADS 

Google Scholar
 

Heidarian, D., Sorella, S. & Becca, F. Spin-\(\frac{1}{2}\) Heisenberg model on the anisotropic triangular lattice: from magnetism to a one-dimensional spin liquid. Phys. Rev. B 80, 012404 (2009).

Article 
ADS 

Google Scholar
 

Starykh, O. A., Katsura, H. & Balents, L. Extreme sensitivity of a frustrated quantum magnet: Cs2CuCl4. Phys. Rev. B 82, 014421 (2010).

Article 
ADS 

Google Scholar
 

Reuther, J. & Thomale, R. Functional renormalization group for the anisotropic triangular antiferromagnet. Phys. Rev. B 83, 024402 (2011).

Article 
ADS 

Google Scholar
 

Harada, K. Numerical study of incommensurability of the spiral state on spin-\(\frac{1}{2}\) spatially anisotropic triangular antiferromagnets using entanglement renormalization. Phys. Rev. B 86, 184421 (2012).

Article 
ADS 

Google Scholar
 

Starykh, O. A., Jin, W. & Chubukov, A. V. Phases of a triangular-lattice antiferromagnet near saturation. Phys. Rev. Lett. 113, 087204 (2014).

Article 
CAS 
PubMed 
ADS 

Google Scholar
 

Ghorbani, E., Tocchio, L. F. & Becca, F. Variational wave functions for the \(S=\frac{1}{2}\) Heisenberg model on the anisotropic triangular lattice: spin liquids and spiral orders. Phys. Rev. B 93, 085111 (2016).

Article 
ADS 

Google Scholar
 

Morita, K. Isothermal and adiabatic magnetization processes of the spin-\(\frac{1}{2}\) Heisenberg model on an anisotropic triangular lattice. Phys. Rev. B 105, 064428 (2022).

Article 
CAS 
ADS 

Google Scholar
 

Yu, Y., Li, S., Isk, S. & Gul, E. Magnetic phases of the anisotropic triangular lattice Hubbard model. Phys. Rev. B 107, 075106 (2023).

Article 
CAS 
ADS 

Google Scholar
 

Bernu, B., Lecheminant, P., Lhuillier, C. & Pierre, L. Exact spectra, spin susceptibilities, and order parameter of the quantum Heisenberg antiferromagnet on the triangular lattice. Phys. Rev. B 50, 10048 (1994).

Article 
CAS 
ADS 

Google Scholar
 

White, S. R. & Chernyshev, A. L. Neél order in square and triangular lattice Heisenberg models. Phys. Rev. Lett. 99, 127004 (2007).

Article 
PubMed 
ADS 

Google Scholar
 

Endoh, Y., Shirane, G., Birgeneau, R. J., Richards, P. M. & Holt, S. L. Dynamics of an \(S=\frac{1}{2}\), one-dimensional Heisenberg antiferromagnet. Phys. Rev. Lett. 32, 170 (1974).

Article 
CAS 
ADS 

Google Scholar
 

Tennant, D. A., Perring, T. G., Cowley, R. A. & Nagler, S. E. Unbound spinons in the S = 1/2 antiferromagnetic chain KCuF3. Phys. Rev. Lett. 70, 4003 (1993).

Article 
CAS 
PubMed 
ADS 

Google Scholar
 

Coldea, R. et al. Neutron scattering study of the magnetic structure of Cs2CuCl4. J. Phys. Condens. Matter 8, 7473 (1996).

Article 
CAS 
ADS 

Google Scholar
 

Coldea, R., Tennant, D. A., Tsvelik, A. M. & Tylczynski, Z. Experimental realization of a 2D fractional quantum spin liquid. Phys. Rev. Lett. 86, 1335 (2001).

Article 
CAS 
PubMed 
ADS 

Google Scholar
 

Coldea, R. et al. Direct measurement of the spin hamiltonian and observation of condensation of magnons in the 2D frustrated quantum magnet Cs2CuCl4. Phys. Rev. Lett. 88, 137203 (2002).

Article 
CAS 
PubMed 
ADS 

Google Scholar
 

Coldea, R., Tennant, D. A. & Tylczynski, Z. Extended scattering continua characteristic of spin fractionalization in the two-dimensional frustrated quantum magnet Cs2CuCl4 observed by neutron scattering. Phys. Rev. B 68, 134424 (2003).

Article 
ADS 

Google Scholar
 

Radu, T. et al. Bose-Einstein condensation of magnons in Cs2CuCl4. Phys. Rev. Lett. 95, 127202 (2005).

Article 
CAS 
PubMed 
ADS 

Google Scholar
 

Tokiwa, Y. et al. Magnetic phase transitions in the two-dimensional frustrated quantum antiferromagnet Cs2CuCl4. Phys. Rev. B 73, 134414 (2006).

Article 
ADS 

Google Scholar
 

Povarov, K. Y., Smirnov, A. I., Starykh, O. A., Petrov, S. V. & Shapiro, A. Y. Modes of magnetic resonance in the spin-liquid phase of Cs2CuCl4. Phys. Rev. Lett. 107, 037204 (2011).

Article 
PubMed 
ADS 

Google Scholar
 

Smirnov, A. I., Povarov, K. Y., Petrov, S. V. & Shapiro, A. Y. Magnetic resonance in the ordered phases of the two-dimensional frustrated quantum magnet Cs2CuCl4. Phys. Rev. B 85, 184423 (2012).

Article 
ADS 

Google Scholar
 

Zvyagin, S. A. et al. Direct determination of exchange parameters in Cs2CuBr4 and Cs2CuCl4: high-field electron-spin-resonance studies. Phys. Rev. Lett. 112, 077206 (2014).

Article 
CAS 
PubMed 
ADS 

Google Scholar
 

Zvyagin, S. A. et al. Pressure-tuning the quantum spin Hamiltonian of the triangular lattice antiferromagnet Cs2CuCl4. Nat. Commun. 10, 1064 (2019).

Article 
CAS 
PubMed 
PubMed Central 
ADS 

Google Scholar
 

Schulze, E. et al. Evidence of one-dimensional magnetic heat transport in the triangular-lattice antiferromagnet Cs2CuCl4. Phys. Rev. Res. 1, 032022(R) (2019).

Article 

Google Scholar
 

Ono, T. et al. Magnetization plateau in the frustrated quantum spin system Cs2CuBr4. Phys. Rev. B 67, 104431 (2003).

Article 
ADS 

Google Scholar
 

Ono, T. et al. Magnetization plateaux of the S = 1/2 two-dimensional frustrated antiferromagnet Cs2CuBr4. J. Phys. Condens. Matter 16, S773 (2004).

Article 
CAS 

Google Scholar
 

Tsujii, H. et al. Thermodynamics of the up-up-down phase of the \(S=\frac{1}{2}\) triangular-lattice antiferromagnet Cs2CuBr4. Phys. Rev. B 76, 060406(R) (2007).

Article 
ADS 

Google Scholar
 

Fortune, N. A. et al. Cascade of magnetic-field-induced quantum phase transitions in a Spin-1/2 triangular-lattice antiferromagnet. Phys. Rev. Lett. 102, 257201 (2009).

Article 
CAS 
PubMed 
ADS 

Google Scholar
 

Shimizu, Y., Miyagawa, K., Kanoda, K., Maesato, M. & Saito, G. Spin liquid state in an organic Mott insulator with a triangular lattice. Phys. Rev. Lett. 91, 107001 (2003).

Article 
CAS 
PubMed 
ADS 

Google Scholar
 

Kandpal, H. C., Opahle, I., Zhang, Y.-Z., Jeschke, H. O. & Valentí, R. Revision of model parameters for κ-type charge transfer salts: an ab initio study. Phys. Rev. Lett. 103, 067004 (2009).

Article 
PubMed 
ADS 

Google Scholar
 

Koretsune, T. & Hotta, C. Evaluating model parameters of the κ- and β’-type Mott insulating organic solids. Phys. Rev. B 89, 045102 (2014).

Article 
ADS 

Google Scholar
 

Yoshida, Y. et al. Spin-disordered quantum phases in a quasi-one-dimensional triangular lattice. Nat. Phys. 11, 679 (2015).

Article 
CAS 

Google Scholar
 

Komatsu, T., Matsukawa, N., Inoue, T. & Saito, G. Realization of superconductivity at ambient pressure by band-filling control in κ-(BEDT-TTF)2Cu2(CN)3. J. Phys. Soc. Jpn. 65, 1340 (1996).

Article 
CAS 
ADS 

Google Scholar
 

Kato, R., Kashimura, Y., Aonuma, S., Hanasaki, N. & Tajima, H. A new molecular superconductor \({\beta }^{{\prime} }\)-Et2Me2P[Pd(dmit)2]2 (dmit = 2-thioxo-1,3-dithiole-4,5-dithiolate). Solid State Commun. 105, 561 (1998).

Article 
CAS 
ADS 

Google Scholar
 

Shimizu, Y. et al. Magnetic field driven transition between valence bond solid and antiferromagnetic order in a distorted triangular lattice. Phys. Rev. Res. 3, 023145 (2021).

Article 
CAS 

Google Scholar
 

Powell, B. J., Kenny, E. P. & Merino, J. Dynamical reduction of the dimensionality of exchange interactions and the “spin-liquid” phase of κ–(BEDT–TTF)2X. Phys. Rev. Lett. 119, 087204 (2017).

Article 
CAS 
PubMed 
ADS 

Google Scholar
 

Hirai, D. et al. “Visible” 5d orbital states in a pleochroic oxychloride. J. Am. Chem. Soc. 139, 10784 (2017).

Article 
CAS 
PubMed 
ADS 

Google Scholar
 

Hirai, D., Nawa, K., Kawamura, M., Misawa, T. & Hiroi, Z. One-dimensionalization by geometrical frustration in the anisotropic triangular lattice of the 5d quantum antiferromagnet Ca3ReO5Cl2. J. Phys. Soc. Jpn. 88, 044708 (2019).

Article 
ADS 

Google Scholar
 

Hirai, D., Yajima, T., Nawa, K., Kawamura, M. & Hiroi, Z. Anisotropic triangular lattice realized in rhenium oxychlorides A3ReO5Cl2 (A = Ba. Sr). Inorg. Chem. 59, 10025 (2020).

Nawa, K. et al. Bound spinon excitations in the spin-\(\frac{1}{2}\) anisotropic triangular antiferromagnet Ca3ReO5Cl2. Phys. Rev. Res. 2, 043121 (2020).

Article 
CAS 

Google Scholar
 

Zvyagin, S. A. et al. Dimensional reduction and incommensurate dynamic correlations in the \(S=\frac{1}{2}\) triangular-lattice antiferromagnet Ca3ReO5Cl2. Nat. Commun. 13, 6310 (2022).

Article 
CAS 
PubMed 
PubMed Central 
ADS 

Google Scholar
 

Choi, Y. et al. Bosonic spinons in anisotropic triangular antiferromagnets. Nat. Commun. 12, 6453 (2021).

Article 
CAS 
PubMed 
PubMed Central 
ADS 

Google Scholar
 

Bonner, J. C. & Fisher, M. E. Linear magnetic chains with anisotropic coupling. Phys. Rev. 135, A640 (1964).

Article 
ADS 

Google Scholar
 

Gen, M., Okamoto, Y., Mori, M., Takenaka, K. & Kohama, Y. Magnetization process of the breathing pyrochlore magnet CuInCr4S8 in ultrahigh magnetic fields up to 150 T. Phys. Rev. B 101, 054434 (2020).

Article 
CAS 
ADS 

Google Scholar
 

Morita, K. & Tohyama, T. Finite-temperature properties of the Kitaev-Heisenberg models on kagome and triangular lattices studied by improved finite-temperature Lanczos methods. Phys. Rev. Res. 2, 013205 (2020).

Article 
CAS 

Google Scholar
 

Jaklič, J. & Prelovšek, P. Lanczos method for the calculation of finite-temperature quantities in correlated systems. Phys. Rev. B 49, 5065(R) (1994).

Article 
ADS 

Google Scholar
 

Uemura, Y. J. et al. Spin fluctuations in frustrated Kagomé lattice system SrCr8Ga4O19 studied by muon spin relaxation. Phys. Rev. Lett. 73, 3306 (1994).

Article 
CAS 
PubMed 
ADS 

Google Scholar
 

Povarov, K. Y. et al. Electron spin resonance of the interacting spinon liquid. Phys. Rev. Lett. 128, 187202 (2022).

Article 
CAS 
PubMed 
ADS 

Google Scholar
 

Izumi, F. & Momma, K. Three-dimensional visualization in powder diffraction. Solid State Phenom. 130, 15 (2007).

Article 
CAS 

Google Scholar
 

Nakajima, K. et al. AMATERAS: a cold-neutron disk chopper spectrometer. J. Phys. Soc. Jpn. 80, SB028 (2011).

Article 

Google Scholar
 

Nakamura, M. et al. First demonstration of novel method for inelastic neutron scattering measurement utilizing multiple incident energies. J. Phys. Soc. Jpn. 78, 093002 (2009).

Article 
ADS 

Google Scholar
 

Inamura, Y., Nakatani, T., Suzuki, J. & Otomo, T. Development status of software ‘Utsusemi’ for Chopper Spectrometers at MLF. J.-PARC J. Phys. Soc. Jpn. 82, SA031 (2013).

Article 
ADS 

Google Scholar
 

Kadowaki, H. https://github.com/kadowaki-h/absorptionfactoramateras.

Bougourzi, A. H., Couture, M. & Kacir, M. Exact two-spinon dynamical correlation function of the one-dimensional Heisenberg model. Phys. Rev. B 54, R12669(R) (1996).

Article 
ADS 

Google Scholar
 

Karbach, M., Müller, G., Bougourzi, A. H., Fledderjohann, A. & Mütter, K.-H. Two-spinon dynamic structure factor of the one-dimensional \(s=\frac{1}{2}\) Heisenberg antiferromagnet. Phys. Rev. B 55, 12510 (1997).

Article 
CAS 
ADS 

Google Scholar
 

Kajimoto, R., Sato, K., Inamura, Y. & Fujita, M. in Proceedings of the Joint Conference on Quasielastic Neutron Scattering and the Workshopon Inelastic Neutron Spectrometers QENS/WINS 2016: Probing Nanoscale Dynamics in Energy Related Materials (eds, Fernandez-Alonso, F., Price, D. L., Grzimek, V., Lohstroh, W., Schneidewind, A., & Russina, M.) 050004 (AIP, New York, 2018).

Giannozzi, P. et al. Advanced capabilities for materials modelling with Quantum ESPRESSO. J. Phys. Condens. Matter 29, 465901 (2017).

Article 
CAS 
PubMed 

Google Scholar
 

Hamann, D. R. Optimized norm-conserving Vanderbilt pseudopotentials. Phys. Rev. B 88, 085117 (2013).

Article 
ADS 

Google Scholar
 

Schlipf, M. & Gygi, F. Optimization algorithm for the generation of ONCV pseudopotentials. Comp. Phys. Commun. 196, 36 (2015).

Article 
CAS 
ADS 

Google Scholar
 

Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996).

Article 
CAS 
PubMed 
ADS 

Google Scholar
 

Kawamura, M., Gohda, Y. & Tsuneyuki, S. Improved tetrahedron method for the Brillouin-zone integration applicable to response functions. Phys. Rev. B 89, 094515 (2014).

Article 
ADS 

Google Scholar
 

Marzari, N. & Vanderbilt, D. Maximally localized generalized Wannier functions for composite energy bands. Phys. Rev. B 56, 12847 (1997).

Article 
CAS 
ADS 

Google Scholar
 

Miyake, T., Aryasetiawan, F. & Imada, M. Ab initio procedure for constructing effective models of correlated materials with entangled band structure. Phys. Rev. B 80, 155134 (2009).

Article 
ADS 

Google Scholar
 

Nakamura, K. et al. RESPACK: An ab initio tool for derivation of effective low-energy model of material. Comp. Phys. Commun. 261, 107781 (2021).

Article 
MathSciNet 
CAS 

Google Scholar
 

Suzumura, T. et al. mdx: A cloud platform for supporting data science and cross-disciplinary research collaborations. In Proceedings of the IEEE International Conference on Cloud and Big Data Computing, pp. 1–7 (IEEE, 2022).

Momma, K. & Izumi, F. VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. J. Appl. Crystallogr. 44, 1272 (2011).

Article 
CAS 
ADS 

Google Scholar