Experimental observation of conformal field theory spectra

arXiv:2601.16275 · quant-ph, cond-mat.quant-gas, physics.atom-ph · Submitted 2026-01-22 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: I'm Kai, and with me are Mira and Lev, guest researcher.

Mira: Today's paper: "Experimental observation of conformal field theory spectra".

Kai: The gist The authors directly observe the energy excitation spectra of emergent conformal field theories at quantum phase transitions in a quantum simulator,

Mira: First, who's behind it and why it matters.

Title and authors: Kai: We started by looking at the title and the authors, which is "Experimental observation of conformal field theory spectra". It sounds very direct about what they are trying to achieve.

Mira: The title itself sets a high bar because it claims direct observation of CFT spectra, which usually means we're dealing with some incredibly complex physics that's hard to pin down.

Kai: They are working on this using their quantum simulator, and the authors listed include Sun, Le, Naus, Tsai, Picard, Murciano, Knap, Alicea and Endres. It’s a large group tackling this problem.

Lev: From my side as someone focused on error correction protocols for real hardware—I look at the team size because that implies a lot of different experimental setups are being tested simultaneously to confirm the universality.

Kai: Yeah, they're trying to be comprehensive in their testing across different system sizes and boundary conditions, which is what allows them to claim these universal results.

Mira: The authors are clearly drawing on established theory here because they are using Ising and tricritical Ising CFTs as the benchmarks against which they compare their experimental data.

Lev: It’s interesting how much theoretical scaffolding you need to build before you can even begin to measure these things experimentally, especially when dealing with emergent phenomena.

Kai: They’re trying to bridge that gap between the abstract predictions of CFT and what we can actually build and measure in a lab setting.

The paper's summary: Mira: So, summarizing the core of "Experimental observation of conformal field theory spectra," they are developing a modulation spectroscopy technique to directly observe the energy excitation spectra at quantum phase transitions.

Kai: They are using their Rydberg chain simulator, which is a neutral atom setup, and they tune it to be near Ising or tricritical Ising CFTs. The goal is to recover universal energy ratios characteristic of those field theories.

Lev: So, the naive question here would be how you can even access the excitation spectrum in a many-body system like this without destroying the critical state you're trying to study.

Mira: They solve that by using a modulation ramp and probe sequence to couple to excited states, and they perform a readout of changes in the number of atoms in the zero state during this process <ref:2601.16275#pg2,the number of atoms in>.

Kai: And they show that when you look at the scaling with system size, those ratios match what theory predicts for open chains, which is a very strong piece of evidence for them.

Lev: That matching is crucial because it tells us the physics being observed isn't just a random artifact of the measurement setup; it’s actually following a known theoretical curve.

Mira: They also explore boundary conditions by applying local detunings at the chain edges, which lets them see signatures consistent with tricritical Ising CFT subject to three different fixed-point boundary conditions.

Kai: And they specifically look at tuning between Ising and TCI CFT using attractive next-nearest-neighbor interactions to reach points described by V2/Omega = -zero point five one and-one point six three.

The paper's improvements: Lev: Now we get into the suggested improvements, which are really about making the experiment more powerful, moving beyond just getting a basic measurement to actually diagnosing what’s happening in the system.

Mira: One big improvement they point out is using AI to diagnose unknown universality classes by looking at the finite-size many-body excitation spectrum. This means we can use AI to figure out which field theory we are dealing with without knowing beforehand.

Kai: That’s powerful because it allows AI systems to diagnose things a priori, instead of just testing pre-programmed theories against the data. It lets them find new universality classes on the fly.

Lev: That moves it from being a verification tool for known physics to being an exploratory tool for discovering new physics, which is where real scientific exploration happens.

Mira: Another improvement involves using AI to spectroscopically distinguish between stable fixed and free boundary conditions by analyzing those universal energy ratios like E2/E1 = four/three ten/three and two <ref:2601.16275#pg1>.

Kai: That’s a direct application for AI in pattern recognition—feeding it the ratios and having it classify the boundary condition based on which known CFT signature they match.

Lev: If AI can reliably do that classification, it means we might be able to use these quantum simulators to probe more complex phase diagrams than we could manually map out.

Mira: They also suggest using the modulation-probe sequence to measure the dynamical structure factor of the underlying field correlation, which is related to an Ising conformal field.

Kai: This allows AI systems to extract universal scaling functions by measuring the system’s response right at the critical point and relating that via a specific equation to that structure factor in a continuum limit.

Conclusion: Kai: So, wrapping up this work on "Experimental observation of conformal field theory spectra," it establishes modulation spectroscopy as a powerful tool for studying general quantum phase transitions.

Mira: The main implication is that we can use these techniques to probe regimes where classical simulations are too hard, especially in the complex areas where CFTs are relevant.

Lev: For running this on real hardware, the paper suggests that resolving individual excitation energies becomes impractical for very large systems, so focusing on measuring the physically relevant dynamical structure factor might be a better path forward.

Kai: They confirm that critical spectra for system sizes L nineteen are consistent with the Ising CFT spectrum, which is a solid confirmation of their methodology <ref:2601.16275#pg2>.

Mira: Overall, this work shows that we can gain direct experimental access to the energy levels of emergent CFTs, providing concrete data on universal ratios that theory predicts.

Lev: I just want to add that for real error correction applications, the next step needs to be measuring one- and two-point correlators at these fixed points compared against universal CFT predictions.

Kai: Exactly. The technique itself is promising for larger systems, pointing toward future applications like measuring the universal sigma field correlation.

Lev: That sounds like a very ambitious goal for future work because it requires even finer control over the system to get those precise correlators right.

California Institute of Technology · Universit´e Paris-Saclay · Technical University of Munich · Munich Center for Quantum Science and Technology

quant-ph, cond-mat.quant-gas, physics.atom-ph

Submitted: 2026-01-22

Updated: 2026-01-22

Comments: 10+19 pages, 6+6 figures, 2 tables

Journal ref: Nature 657, 98-106 (2026)

DOI: 10.1038/s41586-026-10904-x

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 80/100

The gist: The gist The authors directly observe the energy excitation spectra of emergent conformal field theories at quantum phase transitions in a quantum simulator, recovering universal energy ratios

Key concepts

Conformal Field Theory (CFT)
A mathematical framework describing critical phenomena, which are physical states at a quantum phase transition. CFT predicts universal relationships between energy levels and system size that are independent of the specific microscopic details of the material, allowing researchers to identify the underlying physics.
Rydberg Chain Quantum Simulator
This is a programmable neutral atom setup where qubits are encoded in the ground state and a Rydberg state. These atoms interact via van der Waals potentials, creating a controllable system that mimics condensed matter systems like spin chains, allowing researchers to simulate quantum many-body physics.
Modulation Spectroscopy
A technique developed to resolve the energy levels (excitation spectra) of the quantum system. By applying specific modulation sequences and analyzing the resulting frequency response, researchers can extract information about the system's dynamical structure factor and identify universal signatures related to critical theories.

Terminology

Summary

The gist The authors directly observe the energy excitation spectra of emergent conformal field theories at quantum phase transitions in a quantum simulator, recovering universal energy ratios characteristic of underlying field theories.

How it works

The researchers developed and implemented a modulation technique to resolve the finite-size spectra of a Rydberg chain variably tuned to quantum phase transitions described by Ising or tricritical Ising CFTs They use a programmable neutral atom quantum simulator where each qubit is encoded between the ground state 0⟩ and a Rydberg state 1⟩ coupled via van der Waals potential In the Ising case, they experimentally resolve excitation energies whose ratios and scaling with system size agree well with universal predictions of the Ising CFT in open chains

Probing Universal Ratios and Boundary Conditions

The experiment probes the dependence of the spectrum on boundary conditions by applying additional local detunings at the chain’s edges, revealing signatures consistent with tricritical Ising CFT subject to three different fixed-point boundary conditions They experimentally probe the evolution from Ising to TCI CFT by measuring chains at critical detunings with attractive next-nearest-neighbor interactions V2/omega = −0.51 and −1.63 The tricritical Ising CFT admits stable fixed boundary conditions and stable ‘free’ boundary conditions

Dynamical Structure Factor Measurement

To study the dynamical structure factor of the critical system, which is closely related to the correlation of an underlying Ising conformal field, they utilize a variant of modulation spectroscopy They develop and show proof-of-principle of an alternative modulation scheme—the modulation-probe sequence—to measure the system’s frequency-dependent response immediately after modulating at the critical point, without an intervening ramp In the continuum limit, the measured linear response from the modulation-probe sequence is proportional to the dynamical structure factor The low-energy Ising and TCI excitation spectra are characterized by emergent right- and left-moving Majorana fermions The analysis of the k=0 global modulation reveals that the ground state predominantly couples to excited states with ka − kb = π/L

Conclusion and Outlook

The work establishes modulation spectroscopy in quantum simulators as a powerful tool to study general QPTs, including regimes where classical simulations are challenging Future work involves measuring one- and two-point correlators at the fixed points studied here to compare with universal CFT predictions The technique is promising for larger systems, pointing toward future applications like measuring the universal σ-field correlation The study suggests that resolving individual excitation energies becomes less practical in larger systems, making migration to measuring the physically relevant dynamical structure factor more appropriate The experimental results support the claim that critical spectra for system sizes L ≥ 19 are consistent with the Ising CFT spectrum

Improvements for AI systems

  1. Improved energy spectrum resolution for emergent CFTs: The modulation spectroscopy technique allows for directly observe[ing] the energy excitation spectra of emergent CFTs at quantum phase transitions—recovering universal energy ratios characteristic of the underlying field theories. This enables AI systems to diagnose a priori unknown universality classes by measuring the finite-size many-body excitation spectrum in quantum simulators.

  2. AI for identifying boundary conditions: The experimental protocol allows for probing "the dependence of the spectrum on boundary conditions by applying additional local detunings at the chain’s edges—revealing signatures consistent with the Tricritical Ising CFT subject to three different fixed-point boundary conditions. This capability enables AI to spectroscopically distinguish between stable fixed and free TCI boundary conditions by analyzing extracted universal energy ratios like E2/E1 = 4/3, 10/3, 2."

  3. AI for dynamical structure factor extraction: The modulation-probe sequence provides a way to measure the dynamical structure factor of the underlying field correlation, which is related to the correlation of an Ising conformal field. This allows AI systems to extract universal scaling functions by measuring the system’s response at the critical point and relating it via Eq. (21) to the dynamical structure factor, even in a continuum limit.

  4. AI for momentum-resolved spectroscopy: By modulating with a wavevector k, one can probe the linear dispersion relation via characteristic k dependence of the signal. This enables AI systems to resolve light-cone dispersion and extract non-universal light-cone velocity v = 2πdfth/dk," which is crucial for characterizing emergent fermion excitations.

  5. AI for quench dynamics analysis: The ability to prepare a non-equilibrium low-energy TCI state allows AI systems to observe damped oscillations whose fitted frequency is interpreted as the first excited state energy E1. This enables the AI to measure the excitation gap directly, complementing equilibrium measurements and verifying that oscillation frequencies are consistent with theoretical predictions.

Abstract

Conformal field theories (CFTs) feature prominently in high-energy physics, statistical mechanics, and condensed matter. For example, CFTs govern emergent universal properties of systems tuned to quantum phase transitions, including their entanglement, correlations, and low-energy excitation spectra. Much of the rich structure predicted by CFTs nevertheless remains unobserved in experiment. Here we directly observe the energy excitation spectra of emergent CFTs at quantum phase transitions -- recovering universal energy ratios characteristic of the underlying field theories. Specifically, we develop and implement a modulation technique to resolve a Rydberg chain's finite-size spectra, variably tuned to quantum phase transitions described by either Ising or tricritical Ising CFTs. We also employ local control to distinguish parities of excitations under reflection and, in the tricritical Ising chain, to induce transitions between distinct CFT spectra associated with changing boundary conditions. By utilizing a variant of the modulation technique, we furthermore study the dynamical structure factor of the critical system, which is closely related to the correlation of an underlying Ising conformal field. Our work not only probes the emergence of CFT features in a quantum simulator, but also provides a technique for diagnosing a priori unknown universality classes in future experiments.

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