We study the phase diagram and critical properties of quantum Ising chains with long-range ferromagnetic interactions decaying in a power-law fashion with exponent $\alpha$, in regimes of direct interest for current trapped ion experiments. Using large-scale path integral Monte Carlo simulations, we investigate both the ground-state and the nonzero-temperature regimes. We identify the phase boundary of the ferromagnetic phase and obtain accurate estimates for the ferromagnetic-paramagnetic transition temperatures. We further determine the critical exponents of the respective transitions. Our results are in agreement with existing predictions for interaction exponents $\alpha > 1$ up to small deviations in some critical exponents. We also address the elusive regime $\alpha < 1$, where we find that the universality class of both the ground-state and nonzero-temperature transition is consistent with the mean-field limit at $\alpha = 0$. Our work not only contributes to the understanding of the equilibrium properties of long-range interacting quantum Ising models, but can also be important for addressing fundamental dynamical aspects, such as issues concerning the open question of thermalization in such models.
Authors / Affiliations: mappings to Contributors and OrganizationsSee all Organizations.
- 1 Centro Internazionale di Fisica Teorica Abdus Salam / Abdus Salam International Centre for Theoretical Physics [ICTP]
- 2 Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies [SISSA]
- 3 Max-Planck-Institut für Physik komplexer Systeme / Max Planck Institute for the Physics of Complex Systems
- 4 Laboratoire de Physique Théorique de la Matière Condensée, Université Pierre et Marie Curie [LPTMC]
- Deutsche Forschungsgemeinschaft / German Research FoundationDeutsche Forschungsgemeinschaft [DFG]
- European Research Council [ERC]
- Horizon 2020 (through Organization: European Commission [EC])