Eigenstate condensation in quantum systems with finite-dimensional Hilbert spaces

• URL: http://arxiv.org/abs/2601.18869v1
• Date: Mon, 26 Jan 2026 19:00:01 GMT
• Title: Eigenstate condensation in quantum systems with finite-dimensional Hilbert spaces
• Authors: Christopher David White, Michael Winer, Noam Bernstein,
• Abstract summary: We study eigenstate condensation in systems with finite-dimensional Hilbert spaces.<n>In local spin systems the ground-state and anti-ground-state phases approach the middle of the spectrum as $1/[textsystem size]$, but -- because the condensation phase transitions have exponential, rather than finite-size scaling -- the crossover becomes exponentially sharp in system size.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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