Confirming established scaling relations for fluctuating quantities in complex many-body systems, a new computational technique allows researchers from Bryn Mawr College and Ursinus College to study quantum systems larger than previously possible using random sampling. The team applied this approach to Rydberg atom systems, which interact through two- and three-body forces, and confirmed that fluctuations in calculated properties decrease predictably with system size; specifically, they found these values decay as the inverse square root of the Hilbert space dimension. This method focuses on how these complex systems evolve towards thermal equilibrium by developing a novel application of random sampling allowing investigation of larger quantum systems.

Applying this approach to Rydberg atoms, which interact through multiple forces, researchers confirmed fluctuations within calculated properties diminish predictably as system size increases. Understanding this behaviour relies on concepts like the weak Eigenstate Thermalization Hypothesis (wETH); imagine shaking a snow globe, wETH describes if the resulting pattern looks random enough you couldn’t tell what it looked like before, indicating energy distributes evenly across all possibilities.

Crucially, the number of potential states in a quantum system, known as its Hilbert space dimension and akin to counting arrangements on a chessboard, dictates how quickly these fluctuations decrease with increasing complexity; is this scaling reliable for systems exhibiting unusual behaviours.

Random sampling expands access to larger Rydberg atom simulations

A new random sampling method achieved a sharp improvement in accessible system size; it now probes Rydberg atom systems up to four times larger than previously possible using exact diagonalization techniques, a traditional approach limited by computational demands. Efficiently analysing sparse Hamiltonians made this breakthrough possible, allowing statistical analysis of eigenstates without calculating every single one due to their fewer connections between quantum states compared to fully connected ones. The technique successfully probed systems containing up to 16 atoms, an increase from previous work with exact diagonalization which was limited to around eight.

The technique verified expected behaviour: fluctuations in eigenstate expectation values decreased proportionally to the inverse square root of the Hilbert space dimension (D−1/2), aligning with established weak Eigenstate Thermalization Hypothesis predictions and prior numerical findings. Both two-body and three-body dipole-dipole interactions within the Rydberg atom setup confirmed this scaling.

Benchmarking against full calculations validated its accuracy before extending it beyond those limits; however, these results do not yet demonstrate control over decoherence or other real-world effects essential for practical quantum technologies. This extended scale allows investigation of more complex atomic arrangements than previously limited by computing power.

Larger System Sizes Enable More Rigorous Thermalization Hypothesis Testing

This new sampling technique extends verification of the weak Eigenstate Thermalization Hypothesis (wETH) to larger quantum systems than ever before, a vital development because understanding thermalisation underpins progress in areas like materials science and quantum computing. A computational method employing random sampling unlocks access to otherwise inaccessible quantum systems described by ‘sparse Hamiltonians’. Sixteen atoms were successfully probed using this approach with Rydberg atoms, which interact through multiple forces, exceeding the scale achievable with traditional calculation methods. Analysis confirmed that fluctuations in calculated properties diminish predictably as system size increases, aligning with expectations from wETH; verifying theoretical predictions against increasingly realistic sizes builds confidence in models used for designing novel materials and more powerful computers.

This research developed a new random sampling technique for testing the weak Eigenstate Thermalization Hypothesis (wETH) on large quantum systems. The method enabled analysis of a Rydberg atom system containing up to sixteen atoms, significantly larger than previous studies limited to around eight, by efficiently handling ‘sparse Hamiltonians’. This expanded scale allows researchers to further validate these thermalisation principles which are important for understanding complex quantum behaviours.

👉 More information
🗞 A random sampling method to test the weak Eigenstate Thermalization Hypothesis
✍️ Nicolaus A. Chlanda, Sarah E. Spielman and Michael W. Noel (Bryn Mawr College); John Keim, Isabel Martinez-Robles and Thomas J. Carroll (Ursinus College)
🧠 ArXiv: https://arxiv.org/abs/2610.30070

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