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Twisted bilayers of two-dimensional materials have emerged as a highly tunable platform for studying broken symmetry phases. While most interest has been focused on emergent states in systems whose constituent monolayers do not feature…

We report on a study of a bilayer two-dimensional electron gas at Landau level filling factor $\nu=2$. The system exhibits both magnetic and spontaneous interlayer phase coherence broken symmetries. We propose a 3-parameter Slater…

Mesoscale and Nanoscale Physics · Physics 2009-10-31 A. H. MacDonald , R. Rajaraman , T. Jungwirth

Mixed states can exhibit two distinct kinds of symmetries, either on the level of the individual states (strong symmetry), or only on the level of the ensemble (weak symmetry). Strong symmetries can be spontaneously broken down to weak…

Statistical Mechanics · Physics 2025-09-12 Niklas Ziereis , Sanjay Moudgalya , Michael Knap

Spontaneous symmetry breaking (SSB) is the cornerstone of our understanding of quantum phases of matter. Recent works have generalized this concept to the domain of mixed states in open quantum systems, where symmetries can be realized in…

Quantum Physics · Physics 2025-12-30 Xiaozhou Feng , Zihan Cheng , Matteo Ippoliti

Symmetry in mixed quantum states can manifest in two distinct forms: strong symmetry, where each individual pure state in the quantum ensemble is symmetric with the same charge, and weak symmetry, which applies only to the entire ensemble.…

Quantum Physics · Physics 2025-03-11 Leonardo A. Lessa , Ruochen Ma , Jian-Hao Zhang , Zhen Bi , Meng Cheng , Chong Wang

In mixed quantum states, the notion of symmetry is divided into two types: strong and weak symmetry. While spontaneous symmetry breaking (SSB) for a weak symmetry is detected by two-point correlation functions, SSB for a strong symmetry is…

Strongly Correlated Electrons · Physics 2026-03-06 Takamasa Ando , Shinsei Ryu , Masataka Watanabe

Strong-to-weak spontaneous symmetry breaking (SWSSB) has recently emerged as a universal feature of quantum mixed-state phases of matter. While various information-theoretic diagnostics have been proposed to define and characterize SWSSB…

Quantum Physics · Physics 2025-05-15 Zack Weinstein

We simulate a phase-separating a bilayer in which the leaflets experience a direct coupling favouring local compositional symmetry ("registered" bilayer phases), and an indirect coupling due to hydrophobic mismatch that favours strong local…

Soft Condensed Matter · Physics 2016-04-12 John J. Williamson , Peter D. Olmsted

The combination of linear and nonlinear potentials, both shaped as a single well, enables competition between the confinement and expulsion induced by the former and latter potentials, respectively. We demonstrate that this setting leads to…

Pattern Formation and Solitons · Physics 2018-10-18 Dmitry A. Zezyulin , Mikhail E. Lebedev , Georgy L. Alfimov , Boris A. Malomed

We computer model a free-standing vitreous silica bilayer which has recently been synthesized and characterized experimentally in landmark work. Here we model the bilayer using a computer assembly procedure that starts from a single layer…

Disordered Systems and Neural Networks · Physics 2013-11-01 Mark Wilson , Avishek Kumar , David Sherrington , M. F. Thorpe

The large lattice constant of Moire superlattice formed in twisted bilayer graphene for small twist enables observing the Landau levels splitting into Hofstadter butterflies in energy spectra for moderate magnetic field. This is expected…

Mesoscale and Nanoscale Physics · Physics 2021-04-22 Tomasz Chwiej

We explore the landscape of the decoherence effect in mixed-state ensembles from a purification perspective. We analyze the spontaneous strong-to-weak symmetry breaking (SSSB) in mixed states triggered by local quantum channels by mapping…

Quantum Physics · Physics 2024-05-07 Pablo Sala , Sarang Gopalakrishnan , Masaki Oshikawa , Yizhi You

Two-dimensional multi-layer materials with an induced moir\'e pattern, either due to strain or relative twist between layers, provide a versatile platform for exploring strongly correlated and topological electronic phenomena. While these…

Strongly Correlated Electrons · Physics 2025-05-27 Mohammed M. Al Ezzi , Albert Zhu , Daniel Bennett , Daniel T. Larson , Efthimios Kaxiras

The recent realization of twisted, two-dimensional, bilayers exhibiting strongly correlated states has created a platform in which the relation between the properties of the electronic bands and the nature of the correlated states can be…

Superconductivity · Physics 2022-10-12 Enrico Rossi

We develop a general framework for studying phases of mixed states with strong and weak symmetries, including non-invertible or categorical symmetries. The central idea is to consider a purification of the mixed state density matrix, which…

Quantum Physics · Physics 2025-07-09 Sakura Schafer-Nameki , Apoorv Tiwari , Alison Warman , Carolyn Zhang

Mixed-state phases have recently attracted significant attention as a generalization beyond their pure-state counterparts. Prominent examples include mixed-state symmetry-protected topological (mSPT) phases and the strong-to-weak symmetry…

Strongly Correlated Electrons · Physics 2026-03-05 Aswin Parayil Mana , Zijian Song , Fei Yan , Tzu-Chieh Wei

Sliding bilayers are systems that exploit the possibility of relatively translating two monolayers along a specific direction in real space, such that different stackings could be implemented in the process. This simple approach allows for…

Mesoscale and Nanoscale Physics · Physics 2024-05-06 Sergio Bravo , P. A. Orellana , L. Rosales

Topological orders can be understood as spontaneous symmetry breaking of higher-form symmetries. In the non-Abelian case, the broken higher-form symmetries are notably non-invertible. In this work, we extend this framework to mixed states,…

Quantum Physics · Physics 2026-04-17 Zijian Song , Jian-Hao Zhang

We employ ab-initio electronic structure calculations to investigate the charge-density waves and periodic lattice distortions in bilayer 2H-NbSe$_2$. We demonstrate that the vertical stacking can give rise to a variety of patterns that may…

Strongly Correlated Electrons · Physics 2024-11-08 Fabrizio Cossu , Dhani Nafday , Krisztian Palotás , Mehdi Biderang , Heung-Sik Kim , Alireza Akbari , Igor Di Marco

Twisted bilayer graphene offers a unique bilayer two-dimensional-electron system where the layer separation is only in sub-nanometer scale. Unlike Bernal-stacked bilayer, the layer degree of freedom is disentangled from spin and valley,…

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