Rényi entropy shown to follow universal behavior across dimensions
Researchers have discovered a new framework for characterizing entanglement in higher-dimensional quantum systems. The framework applies to vacuum states of conformal field theories under an ultraviolet cutoff and allows estimation of the density of states governed by the modular Hamiltonian.
Credit: Zoltan Tasi/ Unsplash
A new study published in Physical Review Letters on August 5, 2025, reveals universal principles underlying quantum entanglement, extending across multiple dimensions of conformal field theory (CFT).
The research, led by Yuya Kusuki, Hirosi Ooguri, and Sridip Pal, introduces the thermal effective theory as a powerful tool to characterize the entanglement structure in higher-dimensional quantum systems.
The results apply to the vacuum state of conformal field theories in arbitrary dimensions under an ultraviolet cutoff.
The study shows that the theory-dependence of Rényi entropy is fully encoded in the cosmological constant within the thermal effective action. Using this result, the authors estimated the density of states associated with large eigenvalues of the modular Hamiltonian, a central operator governing entanglement in quantum systems.
In two-dimensional systems, the team employed the “hot spot” method — an effective action approach that treats the high-temperature limit with spatially varying temperature — to derive generalized formulas valid for any positive Rényi index.
The work distinguishes between two-dimensional and higher-dimensional cases, clarifies the applicability of the hot spot method, and derives an analogue of the Cardy formula for boundary operators in higher dimensions.
These findings establish a new universal principle connecting entanglement structure with conformal field theories, with potential implications for fields ranging from quantum simulations to black hole physics.
Entanglement entropy has long been a key quantity for probing the quantum structure of spacetime, but explicit calculations beyond 1+1 dimensions have remained challenging. The thermal effective theory reduces this complexity by extracting universal behavior from a limited set of physical quantities, allowing physicists to bypass intractable calculations.
The framework enables new possibilities for analyzing entanglement in systems relevant to quantum field theory, condensed matter physics, and holographic duality.
1 Kusuki, Y., Ooguri, H., & Pal, S. – Universality of Rényi Entropy in Conformal Field Theory – Physical Review Letters – https://doi.org/10.1103/fsg7-bs7q – August 5, 2025
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