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Finite-temperature critical behavior of long-range quantum Ising models
by E. Gonzalez-Lazo, M. Heyl, M. Dalmonte, A. Angelone
Submission summary
| Authors (as registered SciPost users): | Marcello Dalmonte · Eduardo Gonzalez Lazo |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2104.15070v2 (pdf) |
| Date accepted: | Sept. 29, 2021 |
| Date submitted: | Aug. 11, 2021, 2:22 p.m. |
| Submitted by: | Eduardo Gonzalez Lazo |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Computational |
Abstract
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.
List of changes
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Acronyms for paramagnetic (PM) and ferromagnetic (FM) were introduced.
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A citation to J. Phys. A: Math. Theor. 53 013001 have been added at line 55.
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The paragraph
"Similarly, $p$-wave superconductors with long-range pairing[] have been shown to display exotic critical behavior, even if, due to the presence of Jordan-Wigner strings, those models do in general differ from Ising chains with similarly decaying interactions" have been added at line 63.
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We have changed
"While this picture has been essentially confirmed for the case \yellow{$\alpha = 3$}" to "While this picture has been essentially confirmed for the case \yellow{$\alpha = 2$}" at line 72.
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We have changed
" be of the mean-field type" to "belong to the Gaussian UC" at line 135.
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References to the exponent $\sigma$ were changed to the corresponding $\alpha$ depending value in lines 205 and 265.
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We have changed
"errorbar(s) " to "error bar(s)" .
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We have changed
"while the susceptibility one displays deviations at most up to the order" to "while the susceptibility exponent displays deviations at most up to the order" at line 368.
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The paragraph
"For future works, it would be interesting to verify if some of these findings also apply to long-range $p$-wave superconductors [], that, while described by free theories, could still display some of the phenomenology we discuss." have been added at line 371.
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The style of Figure 1 has been changed.
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A citation to Phys. Rev. B 96, 104436 have been added at line 379.
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A citation to Phys. Rev. B 95, 024302 have been added at line 381.
Published as SciPost Phys. 11, 076 (2021)
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The following article is already piblished:
J. A. Koziol, A. Langheld, S. C. Kapfer, K. P. Schmidt
Quantum-critical properties of the long-range transverse-field Ising model from quantum Monte Carlo simulations
Physical Review B 103, 245135 (2021)