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| Format: | Preprint |
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2025
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| Accès en ligne: | https://arxiv.org/abs/2512.20707 |
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| _version_ | 1866908730735460352 |
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| author | Liu, Yang-Ren Huang, Biao |
| author_facet | Liu, Yang-Ren Huang, Biao |
| contents | We introduce an analytical framework to calculate the values of key observables in a strongly disordered discrete time crystal (DTC) without fitting parameter. The perturbatively obtained closed-form formulae show quantitative agreement with numerical simulations of inverse participation ratios for eigenstate localization in Fock space, Edwards-Anderson parameters for spin-glass orders, mutual information for long-range entanglement, and the steady-state amplitudes of autocorrelators for period-doubled oscillations. Meanwhile, we demonstrate that eigenstate resonances render the scaling for the deviation of physical observables from their unperturbed values as $O(λ)$, in contrast to non-resonant situations with suppressed deviation $O(λ^2)$. Our scheme is based on the resolvent perturbation method that can directly prescribe arbitrarily higher-order corrections without iterations. With such advantages, we analytically prove that quasienergy corrections for pairwise cat eigenstates are identical up to order $O(λ^{(L/n_{\text{op}})-1})$, where perturbations of strength $λ$ involve at most $n_{\text{op}}$-spin terms. Such spectral pairing deviations quantify the DTC lifetime as $τ_* \sim (1/λ)^{L/n_{\text{op}}}$. Our analytical scheme applies to generic DTC models with dominant Ising interaction and a given number of qubits, which allows for independent quantification of physical observables beyond the system size accessible to numerical simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20707 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analytical quantification of strongly disordered discrete time crystals Liu, Yang-Ren Huang, Biao Disordered Systems and Neural Networks Strongly Correlated Electrons We introduce an analytical framework to calculate the values of key observables in a strongly disordered discrete time crystal (DTC) without fitting parameter. The perturbatively obtained closed-form formulae show quantitative agreement with numerical simulations of inverse participation ratios for eigenstate localization in Fock space, Edwards-Anderson parameters for spin-glass orders, mutual information for long-range entanglement, and the steady-state amplitudes of autocorrelators for period-doubled oscillations. Meanwhile, we demonstrate that eigenstate resonances render the scaling for the deviation of physical observables from their unperturbed values as $O(λ)$, in contrast to non-resonant situations with suppressed deviation $O(λ^2)$. Our scheme is based on the resolvent perturbation method that can directly prescribe arbitrarily higher-order corrections without iterations. With such advantages, we analytically prove that quasienergy corrections for pairwise cat eigenstates are identical up to order $O(λ^{(L/n_{\text{op}})-1})$, where perturbations of strength $λ$ involve at most $n_{\text{op}}$-spin terms. Such spectral pairing deviations quantify the DTC lifetime as $τ_* \sim (1/λ)^{L/n_{\text{op}}}$. Our analytical scheme applies to generic DTC models with dominant Ising interaction and a given number of qubits, which allows for independent quantification of physical observables beyond the system size accessible to numerical simulations. |
| title | Analytical quantification of strongly disordered discrete time crystals |
| topic | Disordered Systems and Neural Networks Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2512.20707 |