Sine-square Deformation Method Advances Understanding of Quantum Phase Boundaries in One Dimension
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Understanding the behaviour of matter at its most fundamental level requires pinpointing quantum critical points, the precise locations where materials undergo dramatic changes in state. Yuki Miyazaki from RIKEN Center for Computational Science, Shiori Tanigawa and Giacomo Marmorini from Nihon University, along with Nobuo Furukawa and Daisuke Yamamoto, have developed a novel method to identify these critical points in one-dimensional systems. Their approach utilises a ‘sine-square deformation’ technique, which effectively probes the system’s properties and reveals the critical point as the location where a measurable characteristic becomes uniform throughout the material. This method, demonstrated on models of magnetic chains, allows for precise determination of critical points and potentially the extraction of other key properties, even with relatively small system sizes, offering a significant advancement in the study of quantum materials and potentially informing new experimental designs using Rydberg atom arrays. Entanglement, Criticality and Rydberg System Theory This compilation details research spanning quantum computing, many-body physics, and experimental realizations using Rydberg atom arrays. The work broadly focuses on theoretical foundations, experimental platforms, and applications in the emerging field of Noisy Intermediate-Scale Quantum (NISQ) computing. Research establishes the Density Matrix Renormalization Group (DMRG) as a powerful numerical method for studying strongly correlated systems. Investigations explore entanglement properties and edge modes in various quantum systems, revealing their behavior under different conditions.
Conformal Field Theory (CFT) receives significant attention, with research delving into its connection to sine-square deformation and its applications in understanding quantum systems. Experimental work details the creation and control of Rydberg atom arrays using optical tweezers, serving as a platform for simulating quantum systems. Advancements in controlling and connecting Rydberg atoms within arrays enable more complex simulations. Researchers demonstrate the realization of extremely anisotropic Heisenberg magnets in Rydberg atom array systems. The Rydberg atom array work directly contributes to NISQ computing, as these arrays can be programmed to simulate quantum systems that are difficult to study classically. Research focuses on the anisotropic Heisenberg model and the transverse field Ising chain, often in relation to entanglement and quantum criticality. The research highlights a strong interplay between theoretical developments and experimental efforts. The primary goal is to use Rydberg atom arrays as a platform for simulating complex quantum systems beyond the reach of classical computers. The work is highly relevant to the current era of NISQ computing, and the sine-square deformation technique serves as a recurring mathematical tool for analyzing and modifying quantum systems. Sine-Square Deformation Maps Quantum Phase Boundaries Scientists have developed a novel method to precisely determine the boundaries between different quantum phases in one-dimensional systems, utilizing sine-square deformation (SSD). This approach centers on the principle that, for gapless one-dimensional systems, the expectation value of any local observable in the ground state exhibits translational symmetry when subjected to SSD, allowing for accurate identification of critical points.
The team implemented this method using the density-matrix renormalization-group algorithm to calculate the ground state of antiferromagnetic Ising chains with both nearest-neighbor and long-range interactions, evaluating the local transverse magnetization as a key observable. For the nearest-neighbor model, the researchers demonstrated that the quantum critical point could be accurately estimated using systems containing up to 84 sites, aligning closely with previously established results from other analytical approaches. Investigations into the long-range interaction model revealed a slight shift in the phase boundary compared to the nearest-neighbor case, resulting in a reduced region exhibiting antiferromagnetic order.
The team proposes an experimental realization of these antiferromagnetic couplings with SSD using Rydberg atom arrays in optical tweezers, achieving a high degree of approximation in the system’s parameters. Specifically, they demonstrated control over the ratio J2/J1 over a wide range, effectively realizing a well-approximated SSD of the nearest-neighbor model. The study highlights that the SSD approach naturally incorporates multiple independent scaling conditions, enabling precise determination of quantum critical points even with relatively small system sizes. Furthermore, this method holds the potential to extract additional critical phenomena, such as critical exponents. Measurements confirm that the SSD technique effectively minimizes boundary effects, almost completely eliminating spatial oscillations of local observables typically observed in open chains, providing a robust framework for exploring quantum many-body physics. Sine-Square Deformation Locates Quantum Phase Boundaries This research introduces a novel method for determining the boundaries between different quantum phases in one-dimensional systems, employing sine-square deformation (SSD).
The team demonstrates that, under specific conditions, the expectation value of local properties within the system remains consistent across different locations, allowing for precise identification of the critical point defining the phase transition. This approach relies on applying SSD, a smooth modulation of the system’s energy scale, and analyzing the resulting behavior of local observables. The effectiveness of this method was confirmed through detailed calculations on two models, an antiferromagnetic Ising chain with both short-range and long-range interactions, using advanced computational techniques. Results indicate that the SSD method accurately estimates critical points, even with relatively small system sizes, and reveals subtle differences in the phase boundaries between systems with differing interaction ranges. Furthermore, the researchers propose a practical implementation of this technique using current quantum simulation technology, specifically Rydberg atom arrays, opening avenues for experimental verification and exploration of quantum phenomena. They acknowledge that the current work focuses on one-dimensional systems and that extending the method to higher dimensions presents a significant challenge. Future research will likely focus on adapting the SSD technique for use in more complex systems and exploring its potential for characterizing a wider range of quantum critical phenomena. 👉 More information 🗞 A sine-square deformation approach to quantum critical points in one-dimensional systems 🧠 ArXiv: https://arxiv.org/abs/2512.14149 Tags: