Tsui, D. C., Stormer, H. L. & Gossard, A. C. Two-dimensional magnetotransport in the extreme quantum limit. Phys. Rev. Lett. 48, 1559–1562 (1982).
Laughlin, R. B. Anomalous quantum Hall effect: an incompressible quantum fluid with fractionally charged excitations. Phys. Rev. Lett. 50, 1395–1398 (1983).
Anderson, P. W. ‘Luttinger-liquid’ behavior of the normal metallic state of the 2D Hubbard model. Phys. Rev. Lett. 64, 1839–1841 (1990).
Castelnovo, C., Moessner, R. & Sondhi, S. L. Magnetic monopoles in spin ice. Nature 451, 42–45 (2008).
Faddeev, L. & Takhtajan, L. What is the spin of a spin wave? Phys. Lett. A 85, 375–377 (1981).
Kitaev, A. Y. Unpaired Majorana fermions in quantum wires. Phys.-Uspekhi 44, 131 (2001).
Balents, L. Spin liquids in frustrated magnets. Nature 464, 199–208 (2010).
Bethe, H. Zur Theorie der Metalle: I. Eigenwerte und Eigenfunktionen der linearen Atomkette. Z. Phys. 71, 205–226 (1931).
Haldane, F. Spontaneous dimerization in the S = 1/2 Heisenberg antiferromagnetic chain with competing interactions. Phys. Rev. B 25, 4925(R)–4928(R) (1982).
Okamoto, K. & Nomura, K. Fluid-dimer critical point in S = 1/2 antiferromagnetic Heisenberg chain with next nearest neighbor interactions. Phys. Lett. A 169, 433–437 (1992).
Bera, A. et al. Spinon confinement in a quasi-one-dimensional anisotropic Heisenberg magnet. Phys. Rev. B 96, 054423 (2017).
Ghioldi, E. A. et al. Dynamical structure factor of the triangular antiferromagnet: Schwinger boson theory beyond mean field. Phys. Rev. B 98, 184403 (2018).
Majumdar, C. K. & Ghosh, D. K. On next-nearest-neighbor interaction in linear chain. I. J. Math. Phys. 10, 1388–1398 (1969).
Majumdar, C. K. & Ghosh, D. K. On next-nearest-neighbor interaction in linear chain. II. J. Math. Phys. 10, 1399–1402 (1969).
Shastry, B. S. & Sutherland, B. Excitation spectrum of a dimerized next-neighbor antiferromagnetic chain. Phys. Rev. Lett. 47, 964–967 (1981).
Dobry, A. & Ibaceta, D. From spinons to magnons in explicit and spontaneously dimerized antiferromagnetic chains. Phys. Rev. B 59, 8660–8663 (1999).
Caspers, W., Emmett, K. & Magnus, W. The Majumdar–Ghosh chain. Twofold ground state and elementary excitations. J. Phys. A 17, 2687–2696 (1984).
Brehmer, S., Kolezhuk, A., Mikeska, H. & Neugebauer, U. Elementary excitations in the gapped phase of a frustrated S = 1/2 spin ladder: from spinons to the Haldane triplet. J. Phys. Condens. Matter 10, 1103 (1998).
Bouzerar, G., Kampf, A. P. & Japaridze, G. I. Elementary excitations in dimerized and frustrated Heisenberg chains. Phys. Rev. B 58, 3117–3123 (1998).
Uhrig, G. S. & Schulz, H. Magnetic excitation spectrum of dimerized antiferromagnetic chains. Phys. Rev. B 54, R9624(R)–R9627(R) (1996).
Uhrig, G. S., Schönfeld, F., Laukamp, M. & Dagotto, E. Unified quantum mechanical picture for confined spinons in dimerized and frustrated spin chains. Eur. Phys. J. B 7, 67–77 (1999).
Singh, R. R. & Weihong, Z. Dynamical transition from triplets to spinon excitations: a series expansion study of the J1 − J2 − δ spin-1/2 chain. Phys. Rev. B 59, 9911–9915 (1999).
Byrnes, T., Murphy, M. & Sushkov, O. One-and two-dimensional spin systems in the regime close to deconfinement of spinons. Phys. Rev. B 60, 4057–4064 (1999).
Hase, M., Terasaki, I. & Uchinokura, K. Observation of the spin-Peierls transition in linear Cu2+ (spin-1/2) chains in an inorganic compound CuGeO3. Phys. Rev. Lett. 70, 3651–3654 (1993).
Nishi, M., Fujita, O. & Akimitsu, J. Neutron-scattering study on the spin-Peierls transition in a quasi-one-dimensional magnet CuGeO3. Phys. Rev. B 50, 6508(R)–6510(R) (1994).
Pouget, J. P. et al. Structural evidence for a spin Peierls ground state in the quasi-one-dimensional compound CuGeO3. Phys. Rev. Lett. 72, 4037–4040 (1994).
Hirota, K. et al. Dimerization of CuGeO3 in the spin-Peierls state. Phys. Rev. Lett. 73, 736–739 (1994).
Kuroe, H. et al. Raman-scattering study of CuGeO3 in the spin-Peierls phase. Phys. Rev. B 50, 16468–16474 (1994).
Castilla, G., Chakravarty, S. & Emery, V. Quantum magnetism of CuGeO3. Phys. Rev. Lett. 75, 1823–1826 (1995).
Riera, J. & Dobry, A. Magnetic susceptibility in the spin-Peierls system CuGeO3. Phys. Rev. B 51, 16098–16102 (1995).
Arai, M., Fujita, M., Motokawa, M., Akimitsu, J. & Bennington, S. Quantum spin excitations in the spin-Peierls system CuGeO3. Phys. Rev. Lett. 77, 3649–3652 (1996).
Regnault, L., Ain, M., Hennion, B., Dhalenne, G. & Revcolevschi, A. Inelastic-neutron-scattering investigation of the spin-Peierls system CuGeO3. Phys. Rev. B 53, 5579–5597 (1996).
Khomskii, D., Geertsma, W. & Mostovoy, M. Elementary excitations, exchange interaction and spin-Peierls transition in CuGeO3. Czechoslov. J. Phys. 46, 3239–3246 (1996).
Ain, M. et al. Double gap and solitonic excitations in the spin-Peierls chain CuGeO3. Phys. Rev. Lett. 78, 1560–1563 (1997).
Fabricius, K. et al. Reexamination of the microscopic couplings of the quasi-one-dimensional antiferromagnet CuGeO3. Phys. Rev. B 57, 1102–1107 (1998).
Bouzerar, G., Legeza, Ö. & Ziman, T. Minimal model to describe the magnetism of CuGeO3. Phys. Rev. B 60, 15278–15284 (1999).
Fujita, M. et al. Temperature dependence of spin excitations in the frustrated spin chain system CuGeO3. J. Phys. Soc. Jpn 82, 084708 (2013).
Büchner, B. et al. Magnetic frustration induced formation of the spin-Peierls phase in CuGeO3: experimental evidence. Phys. Rev. Lett. 77, 1624–1627 (1996).
Ikeuchi, K. et al. Anisotropic spin excitations in spin-Peierls CuGeO3. J. Korean Phys. Soc. 63, 333–336 (2013).
Cowley, R., Lake, B. & Tennant, D. Models of excitations in CuGeO3. J. Phys. Condens. Matter 8, L179 (1996).
White, S. R. Density matrix formulation for quantum renormalization groups. Phys. Rev. Lett. 69, 2863–2866 (1992).
White, S. R. Density-matrix algorithms for quantum renormalization groups. Phys. Rev. B 48, 10345–10356 (1993).
Vidal, G. Efficient simulation of one-dimensional quantum many-body systems. Phys. Rev. Lett. 93, 040502 (2004).
White, S. R. & Feiguin, A. E. Real-time evolution using the density matrix renormalization group. Phys. Rev. Lett. 93, 076401 (2004).
Daley, A. J., Kollath, C., Schollwöck, U. & Vidal, G. Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces. J. Stat. Mech. Theory Exp. 2004, P04005 (2004).
Muthukumar, V. et al. J1-J2 model revisited: phenomenology of CuGeO3. Phys. Rev. B 55, 5944–5952 (1997).
Uhrig, G. S. Symmetry and dimension of the magnon dispersion of inorganic spin-Peierls systems. Phys. Rev. Lett. 79, 163–166 (1997).
Braden, M. et al. Structural analysis of CuGeO3: relation between nuclear structure and magnetic interaction. Phys. Rev. B 54, 1105–1116 (1996).
Caux, J.-S., Konno, H., Sorrell, M. & Weston, R. Tracking the effects of interactions on spinons in gapless Heisenberg chains. Phys. Rev. Lett. 106, 217203 (2011).
Sala, G. et al. Van Hove singularity in the magnon spectrum of the antiferromagnetic quantum honeycomb lattice. Nat. Commun. 12, 171 (2021).
Woodland, L. et al. Tuning the confinement potential between spinons in the Ising chain compound CoNb2O6 using longitudinal fields and quantitative determination of the microscopic Hamiltonian. Phys. Rev. B 108, 184416 (2023).
Bray, J. et al. Observation of a spin-Peierls transition in a Heisenberg antiferromagnetic linear-chain system. Phys. Rev. Lett. 35, 744–747 (1975).
Cross, M. & Fisher, D. S. A new theory of the spin-Peierls transition with special relevance to the experiments on TTFCuBDT. Phys. Rev. B 19, 402–419 (1979).
Chitra, R., Pati, S., Krishnamurthy, H., Sen, D. & Ramasesha, S. Density-matrix renormalization-group studies of the spin-1/2 Heisenberg system with dimerization and frustration. Phys. Rev. B 52, 6581–6587 (1995).
Haldane, F. D. M. ‘Luttinger liquid theory’ of one-dimensional quantum fluids. I. Properties of the Luttinger model and their extension to the general 1D interacting spinless Fermi gas. J. Phys. C 14, 2585–2609 (1981).
Revcolevschi, A., Ammerahl, U. & Dhalenne, G. Crystal growth of pure and substituted low-dimensionality cuprates CuGeO3, La2CuO4, SrCuO2, Sr2CuO3 and Sr14Cu24O41 by the floating zone and travelling solvent zone methods. J. Cryst. Growth 198–199, 593–599 (1999).
Tanaka, I., Shibuya, Y. & Kojima, H. Crystal growth of pure and Zn-doped CuGeO3 by the floating zone (fz) method. J. Cryst. Growth 169, 469–473 (1996).
Dhalenne, G., Revcolevschi, A., Rouchaud, J. & Federoff, M. Floating zone crystal growth of pure and Si- or Zn-substituted copper germanate CuGeO3. Mater. Res. Bull. 32, 939–945 (1997).
Watauchi, S., Wakihara, M. & Tanaka, I. Control of the anisotropic growth rates of oxide single crystals in floating zone growth. J. Cryst. Growth 229, 423–427 (2001).
Kajimoto, R. et al. The Fermi chopper spectrometer 4SEASONS at J-PARC. J. Phys. Soc. Jpn 80, SB025 (2011).
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).
Ewings, R. A. et al. Horace: software for the analysis of data from single crystal spectroscopy experiments at time-of-flight neutron instruments. Nucl. Instrum. Methods A 834, 132–142 (2016).
Arnold, O. et al. Mantid—data analysis and visualization package for neutron scattering and μSR experiments. Nuclear Instrum. Methods Phys. Res. A 764, 156–166 (2014).
Suzuki, M. Generalized Trotter’s formula and systematic approximants of exponential operators and inner derivations with applications to many-body problems. Commun. Math. Phys. 51, 183–190 (1976).
Verstraete, F., García-Ripoll, J. J. & Cirac, J. I. Matrix product density operators: simulation of finite-temperature and dissipative systems. Phys. Rev. Lett. 93, 207204 (2004).
Muniz, R. A., Kato, Y. & Batista, C. D. Generalized spin-wave theory: application to the bilinear-biquadratic model. Prog. Theor. Exp. Phys. 2014, 083I01 (2014).
Mourigal, M., Fuhrman, W. T., Chernyshev, A. L. & Zhitomirsky, M. E. Dynamical structure factor of the triangular-lattice antiferromagnet. Phys. Rev. B 88, 094407 (2013).
Park, P., Stone, M. B. & Christianson, A. D. Time-of-flight inelastic neutron scattering data of the quantum spin-Peierls chain CuGeO3. ONCat https://doi.org/10.14461/oncat.data/3375584 (2026).