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  • Open Access

Infinite Temperature at Zero Energy

Matteo Ippoliti1,* and David M. Long2,†

  • *Contact author: ippoliti@utexas.edu
  • †Contact author: dmlong@stanford.edu
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Phys. Rev. X 16, 031030 – Published 7 August, 2026

DOI: https://doi.org/10.1103/tvny-gtzp

Abstract

We construct a family of static, geometrically local Hamiltonians that inherit eigenstate properties of periodically driven (Floquet) systems. Our construction is a variation of the Feynman-Kitaev clock—a well-known mapping between quantum circuits and local Hamiltonians—where the clock register is given periodic boundary conditions. Assuming the eigenstate thermalization hypothesis (ETH) holds for the input circuit, our construction yields Hamiltonians whose eigenstates have properties characteristic of infinite temperature, like volume-law entanglement entropy, across the whole spectrum—including the ground state. We then construct a family of exactly solvable Floquet quantum circuits whose eigenstates are shown to obey the ETH at infinite temperature. Combining the two constructions yields a new family of local Hamiltonians with provably volume-law entangled ground states, and the first such construction where the volume law holds for all contiguous subsystems.

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Popular Summary

In isolated quantum many-body systems, temperature and entanglement are closely linked: While typical high-temperature states are extensively entangled, states at low temperature tend to have short-ranged correlations and limited entanglement. This relative simplicity underpins many theoretical and computational methods in many-body physics; yet exceptions are possible. We construct static, local Hamiltonians whose ground states share some properties of periodically driven (Floquet) states, including their extensive entanglement. Since driven systems lack energy conservation and can only equilibrate to “infinite temperature,” the ground states of these new models feature an exotic coexistence of infinite-temperature and zero-energy physics, pushing the known boundaries of quantum matter at low energies. The construction is a twist on the “Feynman-Kitaev clock,” a tool from quantum complexity theory, and draws on ideas from classical pseudorandom number generation, bridging many-body physics and the theory of computation.

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Phys. Rev. X 16, 031030– Published 7 August, 2026
  • Received 30 November 2025
  • Revised 13 April 2026
  • Accepted 16 June 2026
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