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| Format: | Preprint |
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2026
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| Online-Zugang: | https://arxiv.org/abs/2601.18869 |
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| _version_ | 1866915757379551232 |
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| author | White, Christopher David Winer, Michael Bernstein, Noam |
| author_facet | White, Christopher David Winer, Michael Bernstein, Noam |
| contents | Random quantum states drawn from the Haar ensemble with a constraint on the energy expectation value $E_{\mathrm{av}} = \langle ψ| H | ψ\rangle$ display \textit{eigenstate condensation}: for $E_{\mathrm{av}}$ below a critical value $E_c$, they develop macroscopic overlap with the ground state. We study eigenstate condensation in systems with finite-dimensional Hilbert spaces. These systems display three phases: a ground-state phase, in which energy-constrained random states have macroscopic overlap with the ground state; a high-temperature phase, in which they have exponentially small overlap with each energy eigenstate; and an anti-ground-state phase, in which they have macroscopic overlap with the most highly excited state. In local spin systems the ground-state and anti-ground-state phases approach the middle of the spectrum as $1/[\text{system size}]$, but -- because the condensation phase transitions have exponential, rather than polynomial, finite-size scaling -- the crossover becomes exponentially sharp in system size and the high-temperature phase is best understood as an extended phase. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18869 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Eigenstate condensation in quantum systems with finite-dimensional Hilbert spaces White, Christopher David Winer, Michael Bernstein, Noam Quantum Physics Disordered Systems and Neural Networks Statistical Mechanics Strongly Correlated Electrons Random quantum states drawn from the Haar ensemble with a constraint on the energy expectation value $E_{\mathrm{av}} = \langle ψ| H | ψ\rangle$ display \textit{eigenstate condensation}: for $E_{\mathrm{av}}$ below a critical value $E_c$, they develop macroscopic overlap with the ground state. We study eigenstate condensation in systems with finite-dimensional Hilbert spaces. These systems display three phases: a ground-state phase, in which energy-constrained random states have macroscopic overlap with the ground state; a high-temperature phase, in which they have exponentially small overlap with each energy eigenstate; and an anti-ground-state phase, in which they have macroscopic overlap with the most highly excited state. In local spin systems the ground-state and anti-ground-state phases approach the middle of the spectrum as $1/[\text{system size}]$, but -- because the condensation phase transitions have exponential, rather than polynomial, finite-size scaling -- the crossover becomes exponentially sharp in system size and the high-temperature phase is best understood as an extended phase. |
| title | Eigenstate condensation in quantum systems with finite-dimensional Hilbert spaces |
| topic | Quantum Physics Disordered Systems and Neural Networks Statistical Mechanics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2601.18869 |