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This paper presents a rigorous numerical method for extracting spectral gaps in infinite-dimensional quantum systems by analyzing imaginary-time evolution, specifically addressing cases where excitations lie at the edge of a continuous spectrum. The authors demonstrate that gap detection depends critically on the coupling between initial states and low-energy excitations, offering a new approach to many-body physics that requires only ground-state calculations.
Beyond the Gap: What Imaginary-Time Evolution Reveals About the Edge of the Continuum
arXiv:2611.06454v1 Announce Type: new Abstract: The spectral gap, the energy separating the ground state from the first excitation, governs many quantum phenomena, yet it is far harder to compute than the ground state. We propose a mathematically rigorous method for extracting the gap from imaginary-time evolution in infinite-dimensional Hamiltonians, where the first excitation typically marks the edge of a continuous spectrum. We show that a gap is not automatically detected: detection depends on how the initial state and observable couple the ground state to excitations at the bottom of the continuum. When this coupling follows a power law, the gap is recovered together with a logarithmic correction whose coefficient yields the exponent of the spectral density near the edge of the continuum, which reflects the physics of the excitations. We confirm both predictions numerically for an exactly solvable model. Our results offer a new numerical approach to many-body quantum physics, in which both the gap and the threshold exponent are obtained merely at the cost of a ground-state calculation.
Abstract:The spectral gap, the energy separating the ground state from the first excitation, governs many quantum phenomena, yet it is far harder to compute than the ground state. We propose a mathematically rigorous method for extracting the gap from imaginary-time evolution in infinite-dimensional Hamiltonians, where the first excitation typically marks the edge of a continuous spectrum. We show that a gap is not automatically detected: detection depends on how the initial state and observable couple the ground state to excitations at the bottom of the continuum. When this coupling follows a power law, the gap is recovered together with a logarithmic correction whose coefficient yields the exponent of the spectral density near the edge of the continuum, which reflects the physics of the excitations. We confirm both predictions numerically for an exactly solvable model. Our results offer a new numerical approach to many-body quantum physics, in which both the gap and the threshold exponent are obtained merely at the cost of a ground-state calculation.
Quantum Physics (quant-ph); Spectral Theory (math.SP)
arXiv:2611.06454 [quant-ph]
(or arXiv:2611.06454v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2611.06454 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 261 words