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Symmetry in mixed quantum states can manifest in two distinct forms: , where each individual pure state in the quantum ensemble is symmetric with the same charge, and , which applies only to the entire ensemble. This paper explores a novel type of spontaneous symmetry breaking (SSB) where a strong symmetry is broken to a weak one. While the SSB of a weak symmetry is measured by the long-ranged two-point correlation function, the strong-to-weak SSB (SWSSB) is measured by the . We prove that SWSSB is a universal property of mixed-state quantum phases, in the sense that the phenomenon of SWSSB is robust against symmetric low-depth local quantum channels. We also show that the symmetry breaking is “spontaneous” in the sense that the effect of a local symmetry-breaking measurement cannot be recovered locally. We argue that a thermal state at a nonzero temperature in the canonical ensemble (with fixed symmetry charge) should have spontaneously broken strong symmetry. Additionally, we study nonthermal scenarios where decoherence induces SWSSB, leading to phase transitions described by classical statistical models with bond randomness. In particular, the SWSSB transition of a decohered Ising model can be viewed as the “ungauged” version of the celebrated toric-code decodability transition. We confirm that, in the decohered Ising model, the SWSSB transition defined by the fidelity correlator is the only physical transition in terms of channel recoverability. We also comment on other (inequivalent) definitions of SWSSB, through correlation functions with higher Rényi indices. Published by the American Physical Society2025 

Abstract Motivated by recent experimental observations of opposite Chern numbers in R-type twisted MoTe₂and WSe₂homobilayers, we perform large-scale density-functional-theory calculations with machine learning force fields to investigate moiré band topology across a range of twist angles in both materials. We find that the Chern numbers of the moiré frontier bands change sign as a function of twist angle, and this change is driven by the competition between moiré ferroelectricity and piezoelectricity. Our large-scale calculations, enabled by machine learning methods, reveal crucial insights into interactions across different scales in twisted bilayer systems. The interplay between atomic-level relaxation effects and moiré-scale electrostatic potential variation opens new avenues for the design of intertwined topological and correlated states, including the possibility of mimicking higher Landau level physics in the absence of magnetic field. 

Abstract Noncollinear ferroic materials are sought after as testbeds to explore the intimate connections between topology and symmetry, which result in electronic, optical, and magnetic functionalities not observed in collinear ferroic materials. For example, ferroaxial materials have rotational structural distortions that break mirror symmetry and induce chirality. When ferroaxial order is coupled with ferroelectricity arising from a broken inversion symmetry, it offers the prospect of electric‐field‐control of the ferroaxial distortions and opens up new tunable functionalities. However, chiral multiferroics, especially ones stable at room temperature, are rare. A strain‐stabilized, room‐temperature chiral multiferroic phase in single crystals of BaTiS₃is reported here. Using first‐principles calculations, the stabilization of this multiferroic phase havingP6₃space group for biaxial tensile strains exceeding 1.5% applied on the basalab‐plane of the room temperatureP6₃cmphase of BaTiS₃is predicted. The chiral multiferroic phase is characterized by rotational distortions of TiS₆octahedra around the longc‐axis and polar displacement of Ti atoms along thec‐axis. The ferroaxial and ferroelectric distortions and their domains inP6₃‐BaTiS₃are directly resolved using atomic resolution scanning transmission electron microscopy. Landau‐based phenomenological modeling predicts a strong coupling between the ferroelectric and the ferroaxial order makingP6₃‐BaTiS₃an attractive test bed for achieving electric‐field‐control of chirality. 

Abstract Understanding the relationship between biodiversity and ecosystem stability is a central goal of ecologists. Recent studies have concluded that biodiversity increases community temporal stability by increasing the asynchrony between the dynamics of different species. Theoretically, this enhancement can occur through either increased between-species compensatory dynamics, a fundamentally biological mechanism; or through an averaging effect, primarily a statistical mechanism. Yet it remains unclear which mechanism is dominant in explaining the diversity-stability relationship. We address this issue by mathematically decomposing asynchrony into components separately quantifying the compensatory and statistical-averaging effects. We applied the new decomposition approach to plant survey and experimental data from North American grasslands. We show that statistical averaging, rather than compensatory dynamics, was the principal mediator of biodiversity effects on community stability. Our simple decomposition approach helps integrate concepts of stability, asynchrony, statistical averaging, and compensatory dynamics, and suggests that statistical averaging, rather than compensatory dynamics, is the primary means by which biodiversity confers ecological stability.