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Mermin, N. D. & Wagner, H. Absence of ferromagnetism or antiferromagnetism in one-or two-dimensional isotropic Heisenberg models. Phys. Rev, Lett. 17, 1133 (1966).
Gong, Z.-X. et al. Kaleidoscope of quantum phases in a long-range interacting spin-1 chain. Phys. Rev. B 93, 205115 (2016).
Maghrebi, M. F., Gong, Z.-X. & Gorshkov, A. V. Continuous symmetry breaking in 1d long-range interacting quantum systems. Phys. Rev. Lett. 119, 023001 (2017).
Sachdev, S. Quantum phase transitions. Phys. World 12, 33 (1999).
Giamarchi, T. Quantum Physics in One Dimension, Vol. 121 (Clarendon Press, 2003).
Cazalilla, M., Citro, R., Giamarchi, T., Orignac, E. & Rigol, M. One dimensional bosons: from condensed matter systems to ultracold gases. Rev. of Mod. Phys. 83, 1405 (2011).
Chen, X., Gu, Z.-C. & Wen, X.-G. Classification of gapped symmetric phases in one-dimensional spin systems. Phys. Rev. B 83, 035107 (2011).
Haldane, F. D. M. Nonlinear field theory of large-spin heisenberg antiferromagnets: semiclassically quantized solitons of the one-dimensional easy-axis Néel state. Phys. Rev. Lett. 50, 1153 (1983).
Dalla Torre, E. G., Berg, E. & Altman, E. Hidden order in 1d bose insulators. Phys. Rev. Lett. 97, 260401 (2006).
Gong, Z.-X. et al. Topological phases with long-range interactions. Phys. Rev. B 93, 041102 (2016).
Ren, J., Wang, Z., Chen, W. & You, W.-L. Long-range order and quantum criticality in antiferromagnetic chains with long-range staggered interactions. Phys. Rev. E 105, 034128 (2022).
Li, Z., Choudhury, S. & Liu, W. V. Long-range-ordered phase in a quantum heisenberg chain with interactions beyond nearest neighbors. Phys. Rev. A 104, 013303 (2021).
Herbrych, J. et al. Block–spiral magnetism: An exotic type of frustrated order. Proc. Natl Acad. Sci. USA 117, 16226 (2020).
Giachetti, G., Trombettoni, A., Ruffo, S. & Defenu, N. Berezinskii-Kosterlitz-Thouless transitions in classical and quantum long-range systems. Phys. Rev. B 106, 014106 (2022).
Potirniche, I.-D., Potter, A. C., Schleier-Smith, M., Vishwanath, A. & Yao, N. Y. Floquet symmetry-protected topological phases in cold-atom systems. Phys. Rev. Lett. 119, 123601 (2017).
Patrick, K., Neupert, T. & Pachos, J. K. Topological quantum liquids with long-range couplings. Phys. Rev. Lett. 118, 267002 (2017).
Bermúdez, A., Tagliacozzo, L., Sierra, G. & Richerme, P. Long-range Heisenberg models in quasiperiodically driven crystals of trapped ions. Phys. Rev. B 95, 024431 (2017).
Monroe, C. et al. Programmable quantum simulations of spin systems with trapped ions. Rev. Mod. Phys. 93, 025001 (2021).
Blatt, R. & Roos, C. F. Quantum simulations with trapped ions. Nat. Phys. 8, 277 (2012).
Joshi, M. K. et al. Observing emergent hydrodynamics in a long-range quantum magnet. Science 376, 720 (2022).
Zhang, J. et al. Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator. Nature 551, 601 (2017).
Morong, W. et al. Observation of stark many-body localization without disorder. Nature 599, 393 (2021).
Dumitrescu, P. T. et al. Dynamical topological phase realized in a trapped-ion quantum simulator. Nature 607, 463 (2022).
Maunz, P. L. W. High Optical Access Trap 2.0. Technical Report (Sandia National Lab., 2016).
Egan, L. et al. Fault-tolerant control of an error-corrected qubit. Nature 598, 281–286 (2021).
Katz, O., Feng, L., Risinger, A., Monroe, C. & Cetina, M. Demonstration of three- and four-body interactions between trapped-ion spins, Nat. Phys. https://doi.org/10.1038/s41567-023-02102-7 (2023).
Olmschenk, S. et al. Manipulation and detection of a trapped yb+ hyperfine qubit. Phys. Rev. A 76, 052314 (2007).
Egan, L. N. Scaling Quantum Computers with Long Chains of Trapped Ions. Ph.D. thesis, Univ. of Maryland (2021).
Ciavarella, A. N., Caspar, S., Illa, M. & Savage, M. J. State preparation in the Heisenberg model through adiabatic spiraling. Quantum 7, 970 (2023).
Chen, C. et al. Continuous symmetry breaking in a two-dimensional Rydberg array. Nature 616, 691 (2023).
Kim, K. et al. Entanglement and tunable spin-spin couplings between trapped ions using multiple transverse modes. Phys. Rev. Lett. 103, 120502 (2009).
Katz, O. & Monroe, C. Programmable quantum simulations of bosonic systems with trapped ions. Phys. Rev. Lett. 131, 033604 (2023).
Pagano, G. et al. Quantum approximate optimization of the long-range ising model with a trapped-ion quantum simulator. Proc. Natl Acad. Sci. USA 117, 25396 (2020).
Jaschke, D., Wall, M. L. & Carr, L. D. Open source matrix product states: opening ways to simulate entangled many-body quantum systems in one dimension. Comput. Phys. Commun. 225, 59 (2018).
Kac, M., Uhlenbeck, G. & Hemmer, P. On the Van der Waals theory of the vapor-liquid equilibrium. I. Discussion of a one-dimensional model. J. Math. Phys. 4, 216 (1963).
Defenu, N. Metastability and discrete spectrum of long-range systems. Proc. Natl Acad. Sci. USA 118, e2101785118 (2021).
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