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arXiv:2506.07788 · Physical review. B./Physical review. B

Uniform electron gas in the presence of space-time periodic potentials: Floquet-Bloch and linear-response theory

Ayan Pal, Erik G. C. P. van Loon, F. Aryasetiawan

Published Aug 31, 2026• 0 citations
arXivHTMLPDF

Abstract

Nonequilibrium quantum physics greatly simplifies in the case of time-periodic Hamiltonians, since Floquet theory provides an analog to Bloch's theorem in the time domain. Still, the formal properties of Floquet many-body theory remain underexplored. Here, we study what happens to the uniform electron gas when a space-time periodic potential of arbitrary strength is applied, which leads to band splitting. The case of a potential traveling at constant speed is special, since the problem can be made time independent by transforming to a comoving frame. We perform linear-response theory, in the sense that we apply an additional perturbatively small but nonperiodic probing field, for which we illustrate the analogy of Fermi's golden rule and the photoemission spectrum of a many-electron system. As in the equilibrium case, the latter is related to the spectral function which is positive definite. We also analyze the parameter dependence of the controllable photoemission spectra by virtue of Floquet-Bloch engineering.

DOI
10.1103/q754-jzkj

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Nonequilibrium quantum physics greatly simplifies in the case of time-periodic Hamiltonians, since Floquet theory provides an analog to Bloch's theorem in the time domain. Still, the formal properties of Floquet many-body theory remain underexplored. Here, we study what happens to the uniform electron gas when a space-time periodic potential of arbitrary strength is applied, which leads to band splitting. The case of a potential traveling at constant speed is special, since the problem can be made time independent by transforming to a comoving frame. We perform linear-response theory, in the sense that we apply an additional perturbatively small but nonperiodic probing field, for which we illustrate the analogy of Fermi's golden rule and the photoemission spectrum of a many-electron system. As in the equilibrium case, the latter is related to the spectral function which is positive definite. We also analyze the parameter dependence of the controllable photoemission spectra by virtue of Floquet-Bloch engineering.
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We propose a method to study the time evolution of correlated electrons driven by a harmonic perturbation. Combining Floquet formalism to include the time-dependent field and cluster perturbation theory to solve the many-body problem in the presence of short-range correlations, we treat the electron double dressing, by photons and by $e\text{\ensuremath{-}}e$ interactions, on the same footing. We apply the method to an extended Hubbard chain at half occupation, and we show that in the regime of small field frequency and for given values of field strength, the zero-mode Floquet band is no longer gapped and the system recovers a metallic state. Our results are indicative of an omnipresent mechanism for insulator-to-metal transitions in one-dimensional systems.
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Rabi oscillations and Floquet states are likely the most familiar concepts associated with a periodically time-varying Hamiltonian. Here, we present an exactly solvable model of a two-level system coupled to both a continuum and a classical field that varies sinusoidally with time, which sheds light on the relationship between the two problems. For a field of the rotating-wave-approximation form, results show that the dynamics of the two-level system can be mapped exactly onto that for a static field, if one shifts the energy separation between the two levels by an amount equal to ℏω, where ω is the frequency of the field and ℏ is Planck's constant. This correspondence allows one to view Rabi oscillations and Floquet states from the simpler perspective of their time-independent-problem equivalents. The comparison between the rigorous results and those from perturbation theory helps clarify some of the difficulties underlying textbook proofs of Fermi's golden rule, and the discussions on quantum decay and linear response theory.