⚛️ quantum physics

Exploring Quantum Phase Transitions Beyond Landau Theory on a Quantum Processor

Using superconducting quantum processors, this study investigates a Landau-forbidden ferromagnetic-to-valence-bond-solid transition in a frustrated spin chain, successfully resolving critical correlations and nonequilibrium dynamics that challenge the conventional Landau-Ginzburg-Wilson paradigm.

Original authors: Ruizhe Shen, Yin Zhong, Ching Hua Lee

Published 2026-10-19

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CC0 1.0

Original authors: Ruizhe Shen, Yin Zhong, Ching Hua Lee

Original paper dedicated to the public domain under CC0 1.0 (http://creativecommons.org/publicdomain/zero/1.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the world of matter, scientists have long relied on a set of rules to understand how materials change their nature. Imagine a crowd of people suddenly deciding to all face the same direction; this shift from disorder to order is called a phase transition. For decades, the standard way to explain these shifts, known as the Landau theory, suggested that when a material changes, it does so by gradually losing one specific type of order while gaining another. If two types of order were completely unrelated—like a crowd deciding to face north versus a crowd deciding to form pairs—this theory predicted they could not switch directly into one another. Instead, the change would be messy, abrupt, or require a messy middle step where both behaviors coexist. However, a newer, more exotic idea called deconfined quantum criticality suggests that nature might be more flexible. It proposes that under the right conditions, two unrelated orders can vanish and appear at the exact same moment, passing through a strange, fluid state where the rules of the old theory no longer apply. This concept has been a subject of intense debate, mostly studied in complex computer simulations, but proving it in the real world has remained a significant challenge.

A team of researchers has now taken a major step toward settling this question by using a quantum computer to watch this forbidden transition happen in real time. They focused on a specific, one-dimensional chain of magnetic particles, or spins, which can be thought of as tiny magnets that can point up or down. In their setup, they created a tug-of-war between two competing forces. One force wanted all the spins to line up in the same direction, creating a uniform magnetic state. The other force wanted the spins to pair up with their neighbors in alternating strong and weak bonds, a state known as a valence-bond solid. According to the old rules, these two states should not be able to switch directly into one another without a chaotic interruption. Yet, by carefully adjusting the strength of the competing forces, the researchers observed the system moving smoothly from the uniform state to the paired state.

To make this happen on a quantum processor, the team faced a difficult hurdle: creating the complex, entangled state of the magnetic chain requires a level of precision that current machines struggle to maintain. They solved this by using a clever trick that combined the power of a supercomputer with the quantum hardware. First, they used a powerful classical computer to calculate the exact shape of the magnetic chain's state. Then, they translated this complex mathematical description into a simplified set of instructions that the quantum processor could follow. This allowed them to prepare the system in the correct state without needing an impossibly long and error-prone sequence of operations. Once the state was ready, they measured how the spins behaved as they increased the frustration in the system.

The results were clear and matched the predictions of the exotic theory. As they turned up the competing force, the long-range alignment of the spins, which characterized the uniform state, disappeared rapidly. At the same time, the alternating bond pattern of the paired state emerged. Crucially, the researchers looked at the fluctuations—the tiny, random jitters of the spins—right at the moment of the switch. They found that the jitters of the two competing orders did not act independently. Instead, they seemed to blend together, behaving as if they were two sides of the same coin. This behavior is a hallmark of the deconfined criticality theory, suggesting that the system passed through a unique, critical point where the two unrelated orders were intimately linked.

The team did not stop at the static picture; they also watched how the system evolved over time. They started with the chain in a perfectly paired state and then applied a rhythmic, driving force to shake things up. As they did this, they watched the paired bonds weaken while the magnetic fluctuations grew stronger. This dynamic shift confirmed that the two orders were indeed competing and could be manipulated into one another. By testing chains of up to 96 quantum bits, they showed that these subtle signatures of exotic physics are accessible even on today's noisy machines, provided the right preparation methods are used.

This work does not claim to have solved every mystery surrounding these transitions, nor does it prove that the theory is perfect in all cases. The measurements were taken on finite-sized chains, and the quantum computers used were still subject to noise and limitations. However, the study successfully demonstrated that a direct, continuous transition between two unrelated magnetic orders is possible and observable. It provided a versatile new framework for probing these phenomena, showing that quantum processors can now act as powerful microscopes for studying the most complex and counterintuitive behaviors of matter. The findings suggest that the old rules of phase transitions are not the whole story, and that nature allows for a more fluid, interconnected way of changing states than previously thought.

Technical Summary: Exploring Quantum Phase Transitions Beyond Landau Theory on a Quantum Processor

Problem Statement
The conventional Landau–Ginzburg–Wilson paradigm classifies quantum phases via local order parameters and associated symmetry-breaking patterns, predicting that continuous transitions between phases breaking unrelated symmetries are generally forbidden without fine-tuning. Instead, such transitions are expected to be first-order or separated by intermediate phases. Deconfined quantum criticality (DQC) challenges this view, proposing that direct continuous transitions can occur between phases with distinct broken symmetries, mediated by fractionalized degrees of freedom and emergent symmetries. While extensively studied in two-dimensional systems (e.g., Néel-to-Valence-Bond-Solid transitions), one-dimensional analogues offer a complementary setting for studying Landau-forbidden criticality with greater numerical control. Specifically, the transition between a ferromagnetic (FM) phase (breaking Ising spin-flip symmetry) and a valence-bond-solid (VBS) phase (breaking lattice translation symmetry) in frustrated spin chains serves as a 1D realization of deconfined criticality. However, experimentally probing these competing orders and their critical dynamics on quantum hardware remains a significant challenge due to the difficulty of preparing complex many-body states with sufficient circuit depth.

Methodology
The authors investigate a frustrated one-dimensional spin-1/2 $XZ$ chain defined by the Hamiltonian:
$H = \sum_j \left[ -J_x \sigma^x_j \sigma^x_{j+1} - J_z \sigma^z_j \sigma^z_{j+1} + \frac{K}{2} (\sigma^x_j \sigma^x_{j+2} + \sigma^z_j \sigma^z_{j+2}) \right]$
where nearest-neighbor couplings ( $J_x, J_z$ ) favor FM order and next-nearest-neighbor couplings ( $K$ ) introduce frustration favoring a dimerized VBS phase.

The study employs a hybrid classical-quantum workflow:

Classical Preparation (DMRG & MPS): The ground states are first computed using Density Matrix Renormalization Group (DMRG) with a bond dimension $\chi=128$ . These states are represented as Matrix Product States (MPS).
Circuit Compilation: To map the MPS to a quantum circuit compatible with hardware connectivity, the authors utilize a tensor-network-assisted strategy.
- Site Permutation: A correlation-guided permutation $\pi$ is applied to the physical sites to bring strongly correlated sites closer in the circuit ordering, reducing the required circuit depth.
- Local Disentangling: A parameterized circuit $U^\dagger$ is optimized to approximately map the reordered MPS to a product state $|0\rangle^{\otimes L}$ . This is achieved by locally minimizing the second Rényi entanglement entropy across specific bonds using alternating layers of non-overlapping two-qubit gates.
- State Preparation: The inverse circuit $U$ is executed on quantum hardware to prepare the target state.
Quantum Hardware Execution: The compiled circuits are implemented on IBM quantum processors. Measurements are performed in the $Z$ -basis, with post-selection applied to the $G_z = +1$ symmetry sector.
Dynamics Simulation: To study non-equilibrium dynamics, the authors implement a Floquet-type drive on chains up to 96 qubits. Starting from a dimerized Bell-pair state, they apply layer-dependent unitary interactions to track the evolution of competing FM and VBS orders.

Key Results

Suppression of FM Order: Measurements of the long-distance ferromagnetic correlator $|C^{zz}_{\text{long}}|$ across the frustration parameter $K$ show a rapid suppression near the critical region ( $K_c \approx 0.4$ ), consistent with DMRG predictions. This signals the destruction of long-range ferromagnetic order.
Emergence of VBS Order: Concurrently, the VBS order parameter $O_{\text{VBS}}$ grows in the same critical region, indicating the onset of bond dimerization.
Competing Order Fluctuations: Joint probability distributions of the FM and VBS estimators, derived from $Z$ -basis snapshots, reveal a redistribution of weight. In the FM regime, weight concentrates along the FM axis; near the critical point, the distribution develops an arc-like profile extending toward the VBS direction, qualitatively consistent with the intertwining of fluctuations expected in deconfined criticality.
Finite-Size Scaling: Distance-resolved correlations and a second-moment correlation length estimator ( $\xi_{2\text{nd}}$ ) were analyzed. At $K=0.35$ , $\xi_{2\text{nd}}$ exhibits an approximately linear growth with system size ( $L$ ), a signature consistent with critical behavior near a continuous transition.
Non-Equilibrium Dynamics: In the Floquet-driven experiments, the initial bond dimerization (VBS order) is suppressed while FM fluctuations are enhanced. This demonstrates the ability to track the dynamical competition between competing orders on hardware.

Significance and Claims
The paper establishes a versatile quantum-hardware framework for probing competing orders, critical correlations, and many-body dynamics that lie beyond the conventional Landau paradigm. The authors claim that their results demonstrate that present-day quantum processors, when guided by accurate many-body target states via tensor-network-assisted circuit preparation, can access meaningful signatures of unconventional quantum phase transitions.

Specifically, the work:

Provides an experimental realization of a Landau-forbidden FM–VBS transition in a 1D spin chain.
Resolves the suppression of long-range correlations and the redistribution of competing-order fluctuations across the transition.
Validates that finite-size and finite-depth probes on current hardware can capture signatures consistent with critical behavior predicted by DMRG.
Offers a practical route for combining classical tensor-network methods with quantum-hardware measurements to study phenomena such as deconfined quantum criticality.

The authors maintain a modest stance, acknowledging that the observed signatures are finite-size and finite-depth probes affected by system size, bond dimension, circuit depth, sampling fluctuations, and hardware noise. They note that while the joint distributions are qualitatively consistent with deconfined criticality, the data alone does not definitively establish emergent $O(2)$ symmetry or criticality without further scaling analysis. Future improvements in circuit depth, error mitigation, and connectivity are identified as necessary for sharper scaling analyses and more sensitive diagnostics.

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