Physical Review X最新文献

{"title":"Construction and Classification of Crystalline Topological Superconductor and Insulators in Three-Dimensional Interacting Fermion Systems","authors":"Jian-Hao Zhang, Shang-Qiang Ning, Yang Qi, Zheng-Cheng Gu","doi":"10.1103/physrevx.15.031029","DOIUrl":"https://doi.org/10.1103/physrevx.15.031029","url":null,"abstract":"The natural existence of crystalline symmetry in real materials manifests the importance of understanding crystalline symmetry-protected topological phases, especially for interacting systems. In this paper, we systematically construct and classify all the point-group crystalline topological superconductors and insulators in three-dimensional (3D) interacting fermion systems using the novel concept of a topological crystal. The corresponding higher-order topological surface theory can also be systematically studied via higher-order bulk-boundary correspondence. In particular, we discover several intrinsically interacting topological phases that cannot be realized in any free-fermion systems. Moreover, the crystalline equivalence principle for 3D interacting fermionic systems is also verified, with an additional subtle “twist” on the spin of fermions.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"1 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144715374","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Coherent Structure Interactions in Spatially Extended Systems Driven by Excited Hidden Modes","authors":"Alex Round, Te-Sheng Lin, Marc Pradas, Dmitri Tseluiko, Serafim Kalliadasis","doi":"10.1103/physrevx.15.031010","DOIUrl":"https://doi.org/10.1103/physrevx.15.031010","url":null,"abstract":"We study the emergence of strong interactions between dissipative coherent structures (pulses) in spatially extended systems. Focusing first on a prototypical model problem from fluid dynamics, that of liquid film flowing down a vertical plane, we show that under certain conditions, a two-pulse system undergoes a transition from a regime of decaying oscillatory dynamics to one with self-sustained oscillations. Intriguingly, such a transition is not governed by the standard Hopf bifurcation. Instead, a novel governing mechanism for transition to oscillatory dynamics is unraveled via a peculiar and atypical Hopf bifurcation in which a complex-conjugate resonance pair crosses the imaginary axis in the complex plane. Prior to crossing the essential spectrum (including at the bifurcation point), this resonance pair does not appear in the standard L</a:mi>C</a:mi>2</a:mn></a:msubsup></a:math>-based spectral analysis but reveals itself when appropriate weighted functional spaces are used. We show that such a resonance pair originates from the splitting of a resonance pole of the single-pulse system. While this object is not part of the classical spectrum, it plays a vital role in shaping the system’s dynamics. We further demonstrate that this resonance-pole mechanism extends to a broad range of systems. Specifically, in the generalised Kuramoto-Sivashinsky equation—a model prototype applicable across a wide range of fields from fluid dynamics to geophysics and plasma physics—we observe the same bifurcation and resulting oscillatory pulse interactions. By contrast, in the FitzHugh-Nagumo model—a central model prototype in reaction-diffusion systems—the resonance pole splits into real eigenvalues, and monotonic pulse interactions occur. In addition, we illustrate that the resonance pole may induce oscillatory interactions in three-pulse systems and eventually lead to chaotic dynamics in strongly interacting multipulse systems, which can be quantified in terms of a positive Lyapunov exponent. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"24 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144629484","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Noninvertible Peccei-Quinn Symmetry and the Massless Quark Solution to the Strong CP Problem","authors":"Clay Córdova, Sungwoo Hong, Seth Koren","doi":"10.1103/physrevx.15.031011","DOIUrl":"https://doi.org/10.1103/physrevx.15.031011","url":null,"abstract":"We consider theories of gauged quark flavor and identify noninvertible Peccei-Quinn symmetries arising from fractional instantons when the resulting gauge group has nontrivial global structure. Such symmetries exist solely because the standard model has the same number of generations as colors, N</a:mi>g</a:mi></a:msub>=</a:mo>N</a:mi>c</a:mi></a:msub></a:math>, which leads to a massless down-type quark solution to the strong <c:math xmlns:c=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><c:mi>C</c:mi><c:mi>P</c:mi></c:math> problem in an ultraviolet <e:math xmlns:e=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><e:mi>S</e:mi><e:mi>U</e:mi><e:mo stretchy=\"false\">(</e:mo><e:mn>9</e:mn><e:mo stretchy=\"false\">)</e:mo></e:math> theory of quark color-flavor unification. We show how the Cabibbo-Kobayashi-Maskawa flavor structure and weak <i:math xmlns:i=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><i:mi>C</i:mi><i:mi>P</i:mi></i:math> violation can be generated without upsetting our solution. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"51 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144629485","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multipolar Anisotropy in Anomalous Hall Effect from Spin-Group Symmetry Breaking","authors":"Zheng Liu, Mengjie Wei, Wenzhi Peng, Dazhi Hou, Yang Gao, Qian Niu","doi":"10.1103/physrevx.15.031006","DOIUrl":"https://doi.org/10.1103/physrevx.15.031006","url":null,"abstract":"The traditional view of the anomalous Hall effect (AHE) in ferromagnets is that it arises from the magnetization perpendicular to the measurement plane and that there is a linear dependence on the latter. Underlying such a view is the thinking that the AHE is a time-reversal symmetry breaking phenomenon and can therefore be treated in terms of a power series in the magnetic order. However, this view is squarely challenged by a number of recent experiments, urging for a thorough theoretical investigation on the fundamental level. We find that for strong magnets, it is more appropriate and fruitful to regard the AHE as a spin-group symmetry breaking phenomenon where the critical parameter is the spin-orbit interaction strength, which involves a much smaller energy scale. In collinear ferromagnets, the spin-orbit coupling breaks the ∞</a:mi>2</a:mn>′</a:mo></a:msup></a:math> spin rotation symmetry, and the key to characterizing such symmetry breaking is the identification of spin-orbit vectors which transform regularly under spin-group operations. Born out of our framework is a rich multipolar relationship between the anomalous Hall conductivity and the magnetization direction, with each pole being expanded progressively in powers of the spin-orbit coupling strength. For the leading order contribution, i.e., the dipole, its isotropic part corresponds to the traditional view, and its anisotropic part can lead to the in-plane AHE where the magnetization lies within the measurement plane. Beyond the dipolar structure, the octupolar structure offers the leading order source of nonlinearity and hence introduces unique anisotropy where the dipolar structure cannot. Our theory thus offers a unified explanation for the in-plane AHE recently observed in various ferromagnets, and further extends the candidate material systems. It can also be generalized to study the anomalous Hall effect in crystals with any periodic spin structure and to study the nonlinear Hall effect and the spin Hall effect. Our theory lays the ground for decoding the coupling between various transport and optical phenomena and the magnetic orders. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"9 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144577863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Flat-Band (De)localization Emulated with a Superconducting Qubit Array","authors":"Ilan T. Rosen, Sarah Muschinske, Cora N. Barrett, David A. Rower, Rabindra Das, David K. Kim, Bethany M. Niedzielski, Meghan Schuldt, Kyle Serniak, Mollie E. Schwartz, Jonilyn L. Yoder, Jeffrey A. Grover, William D. Oliver","doi":"10.1103/physrevx.15.021091","DOIUrl":"https://doi.org/10.1103/physrevx.15.021091","url":null,"abstract":"Arrays of coupled superconducting qubits are analog quantum simulators able to emulate a wide range of tight-binding models in parameter regimes that are difficult to access or adjust in natural materials. In this work, we use a superconducting qubit array to emulate a tight-binding model on the rhombic lattice, which features flat bands. Enabled by broad adjustability of the dispersion of the energy bands and of on-site disorder, we examine regimes where flat-band localization and Anderson localization compete. We observe disorder-induced localization for dispersive bands and disorder-induced delocalization for flat bands. Remarkably, we find a sudden transition between the two regimes and, in its vicinity, the semblance of quantum critical scaling. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"70 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144304494","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fault-Tolerant Logical Measurements via Homological Measurement","authors":"Benjamin Ide, Manoj G. Gowda, Priya J. Nadkarni, Guillaume Dauphinais","doi":"10.1103/physrevx.15.021088","DOIUrl":"https://doi.org/10.1103/physrevx.15.021088","url":null,"abstract":"We introduce homological measurement, a framework for measuring the logical Pauli operators encoded in Calderbank-Shor-Steane stabilizer codes. The framework is based on the algebraic description of such codes as chain complexes. Protocols such as lattice surgery and some of its recent generalizations are shown to be special cases of homological measurement. Using this framework, we develop a specific protocol called edge expanded homological measurement for fault-tolerant measurement of arbitrary logical Pauli operators of general quantum low density parity-check codes, requiring a number of ancillary qubits growing only linearly with the weight of the logical operator measured, and guarantee that the distance of the code is preserved. We further benchmark our protocol numerically in a photonic architecture based on Gottesman-Kitaev-Preskill qubits, showing that the logical error rates of various codes are on par with other methods requiring more ancilla qubits. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"40 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2025-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144260069","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Nonequilibrium Dynamics of Long-Range Interacting Fermions","authors":"T. Zwettler, G. Del Pace, F. Marijanovic, S. Chattopadhyay, T. Bühler, C.-M. Halati, L. Skolc, L. Tolle, V. Helson, G. Bolognini, A. Fabre, S. Uchino, T. Giamarchi, E. Demler, J. P. Brantut","doi":"10.1103/physrevx.15.021089","DOIUrl":"https://doi.org/10.1103/physrevx.15.021089","url":null,"abstract":"A fundamental problem of out-of-equilibrium physics is the speed at which the order parameter grows upon crossing a phase transition. Here, we investigate the ordering dynamics in a Fermi gas undergoing a density-wave phase transition induced by quenching infinite-range, cavity-mediated interactions. We observe, in real time, the exponential rise of the order parameter and track its growth over several orders of magnitude. Remarkably, the growth rate can exceed the Fermi energy by an order of magnitude, consistent with predictions from a linearized instability analysis. This case contrasts with the ordering process driven by short-range interactions. We then generalize our results to linear interaction ramps, where deviations from the adiabatic behavior are captured by a simple dynamical ansatz. Our study offers a paradigmatic example of the interplay between strong short- and long-range interactions in quantum nonequilibrium dynamics. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"88 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2025-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144260070","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Nonlocal Moments and Mott Semimetal in the Chern Bands of Twisted Bilayer Graphene","authors":"Patrick J. Ledwith, Junkai Dong, Ashvin Vishwanath, Eslam Khalaf","doi":"10.1103/physrevx.15.021087","DOIUrl":"https://doi.org/10.1103/physrevx.15.021087","url":null,"abstract":"Twisted bilayer graphene (TBG) has elements in common with two paradigmatic examples of strongly correlated physics: quantum Hall physics and Hubbard physics. On one hand, TBG hosts flat topological Landau-level-like bands which exhibit the quantum anomalous Hall effects under the right conditions. On the other hand, these bands are characterized by concentrated charge density and show signs of extensive entropy usually attributed to local moments. The combination of these features leads to a question: Can decoupled moments emerge in an isolated topological band, despite the lack of exponentially localized Wannier orbitals? In this work, we answer the question affirmatively by proposing a minimal model for the flat topological bands in TBG that combines topology and charge concentration at the AA sites, leading to analytic wave functions that closely approximate those of the Bistritzer-MacDonald model with realistic parameters. Importantly, charge concentration also leads to Berry curvature concentration at Γ&lt;/a:mi&gt;&lt;/a:math&gt;, giving rise to a small parameter &lt;d:math xmlns:d=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"&gt;&lt;d:mi&gt;s&lt;/d:mi&gt;&lt;/d:math&gt; that makes the model analytically tractable. We show that, rather surprisingly, the model hosts nearly decoupled flavor moments without invoking any extra degrees of freedom. These moments are nonlocal due to topology-enforced power-law tails, yet have parametrically small overlap. We develop a systematic diagrammatic expansion in which the self-energy can be computed exactly to leading order in &lt;f:math xmlns:f=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"&gt;&lt;f:msup&gt;&lt;f:mi&gt;s&lt;/f:mi&gt;&lt;f:mn&gt;2&lt;/f:mn&gt;&lt;/f:msup&gt;&lt;/f:math&gt; in the fluctuating moment regime and predict momentum-resolved spectral functions for future experiments to verify. Our key discovery is a charge-neutrality state we refer to as the “Mott semimetal” characterized by high flavor entropy and a Mott gap that exists throughout most of the Brillouin zone but closes at the &lt;h:math xmlns:h=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"&gt;&lt;h:mi mathvariant=\"normal\"&gt;Γ&lt;/h:mi&gt;&lt;/h:math&gt; point. At &lt;k:math xmlns:k=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"&gt;&lt;k:mi mathvariant=\"normal\"&gt;Γ&lt;/k:mi&gt;&lt;/k:math&gt;, the spectral function contains a single Dirac cone per spin per valley and responds to perturbations in an exotic manner that is distinct from any other theoretical picture of TBG. Away from neutrality, the Mott semimetal gaps out in a spectrally imbalanced manner, with one Mott band having zero quasiparticle residue at the &lt;n:math xmlns:n=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"&gt;&lt;n:mi mathvariant=\"normal\"&gt;Γ&lt;/n:mi&gt;&lt;/n:math&gt; point. The model accurately reproduces results from finite-temperature thermodynamic measurements, leads to new experimental predictions, and resolves the problem of the emergence of Hubbard physics in isolated topological bands. &lt;jats:supplementary-material&gt; &lt;jats:copyright-statement&gt;Published by the Ame","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"50 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144252030","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Emergent Dimer-Model Topological Order and Quasiparticle Excitations in Liquid Crystals: Combinatorial Vortex Lattices","authors":"Cuiling Meng, Jin-Sheng Wu, Žiga Kos, Jörn Dunkel, Cristiano Nisoli, Ivan I. Smalyukh","doi":"10.1103/physrevx.15.021084","DOIUrl":"https://doi.org/10.1103/physrevx.15.021084","url":null,"abstract":"Liquid crystals have proven to provide a versatile experimental and theoretical platform for studying topological objects such as vortices, skyrmions, and hopfions. In parallel, in hard condensed matter physics, the concept of topological phases and topological order has been introduced in the context of spin liquids to investigate emergent phenomena like quantum Hall effects and high-temperature superconductivity. Here, we bridge these two seemingly disparate perspectives on topology in physics. Combining experiments and simulations, we show how topological defects in liquid crystals can be used as versatile building blocks to create complex, highly degenerate topological phases, which we refer to as “combinatorial vortex lattices” (CVLs). CVLs exhibit extensive residual entropy and support locally stable quasiparticle excitations in the form of charge-conserving topological monopoles, which can act as mobile information carriers and be linked via Dirac strings. CVLs can be rewritten and reconfigured on demand, endowed with various symmetries, and modified through laser-induced topological surgery—an essential capability for information storage and retrieval. We demonstrate experimentally the realization, stability, and precise optical manipulation of CVLs, thus opening new avenues for understanding and technologically exploiting higher-hierarchy topology in liquid crystals and other ordered media. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"36 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144236905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Phase Diagram of Extensive-Rank Symmetric Matrix Denoising beyond Rotational Invariance","authors":"Jean Barbier, Francesco Camilli, Justin Ko, Koki Okajima","doi":"10.1103/physrevx.15.021085","DOIUrl":"https://doi.org/10.1103/physrevx.15.021085","url":null,"abstract":"Matrix denoising is central to signal processing and machine learning. Its statistical analysis when the matrix to infer has a factorized structure with a rank growing proportionally to its dimension remains a challenge, except when it is rotationally invariant. In this case, the information-theoretic limits and an efficient Bayes-optimal denoising algorithm, called the rotational invariant estimator, are known. Beyond this setting, few results can be found. The reason is that the model is not a usual spin system because of the growing rank dimension, nor a matrix model (as appearing in high-energy physics) due to the lack of rotation symmetry, but rather a hybrid between the two. In this paper, we make progress toward the understanding of Bayesian matrix denoising when the hidden signal is a factored matrix X</a:mi></a:mrow>X</a:mi></a:mrow>⊺</a:mo></a:mrow></a:msup></a:mrow></a:math> that is not rotationally invariant. Monte Carlo simulations suggest the existence of a denoising-factorization transition separating a phase where denoising using the rotational-invariant estimator remains Bayes-optimal due to universality properties of the same nature as in random matrix theory, from one where universality breaks down and better denoising is possible, though algorithmically hard. We also argue that it is only beyond the transition that factorization, i.e., estimating <e:math xmlns:e=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><e:mrow><e:mi mathvariant=\"bold\">X</e:mi></e:mrow></e:math> itself, becomes possible up to irresolvable ambiguities. On the theoretical side, we combine mean-field techniques in an interpretable multiscale fashion in order to access the minimum mean-square error and mutual information. Interestingly, our alternative method yields equations reproducible by the replica approach of Sakata and Kabashima. Using numerical insights, we delimit the portion of phase diagram where we conjecture the mean-field theory to be exact and correct it using universality when it is not. Our complete matches well the numerics in the whole phase diagram when considering finite-size effects. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"42 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144236906","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}