Article
Physics, Mathematical
Arman Babakhani, Parsa Bonderson
Summary: The universal properties of (2+1)D topological phases of matter enriched by a symmetry group G are described by G-crossed extensions of unitary modular tensor categories (UMTCs). These extensions capture the properties of the symmetry action, fractionalization, and defects arising from the interplay of the symmetry with the topological order. The relation between the G-crossed UMTC and the topological state spaces on general surfaces is described, and the projective representations of the mapping class groups are discussed.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2023)
Article
Materials Science, Multidisciplinary
Qing-Rui Wang, Meng Cheng
Summary: We propose a general construction method for 2D and 3D topological phases enriched by U(1) symmetry, with finite-dimensional Hilbert space per site. The construction starts from a commuting projector model and adds U(1) charges to achieve the desired topological phases. We demonstrate that all 2D U(1) symmetry-enriched topological phases with gapped boundaries can be realized using our construction, and we also construct a large class of 3D topological phases with U(1) symmetry fractionalized on particles or loop excitations.
Article
Quantum Science & Technology
Long Zhang, Xiong-Jun Liu
Summary: This research proposes a scheme to realize unconventional Floquet topological phases by engineering local band structures in particular momentum subspaces called bandinversion surfaces (BISs). By manipulating the BIS configuration, novel Floquet topological phases can be efficiently realized, manipulated, and detected.
Article
Physics, Multidisciplinary
Ruben Verresen, Ryan Thorngren, Nick G. Jones, Frank Pollmann
Summary: We introduce topological invariants for gapless systems and study the associated boundary phenomena, primarily focusing on the 1 + 1d case where the edge has a topological degeneracy with exponential or algebraic finite-size splitting. Symmetry properties of low-energy conformal field theory (CFT) provide discrete invariants establishing symmetry-enriched quantum criticality, with examples such as the Ising phase and cluster phases. The formalism unifies various examples previously studied in literature, including the classification of symmetry-enriched 1 + 1d Ising CFTs and the construction of topological invariants in higher dimensions.
Article
Materials Science, Multidisciplinary
Ryohei Kobayashi
Summary: In this paper, the authors provide state sum path integral definitions of exotic invertible topological phases proposed by Hsin, Ji, and Jian. These phases have time-reversal symmetry and depend on the choice of the Wu structure. The authors propose a lattice construction for the exotic phase based on the Wu structure, and also generalize the classification of G-SPT phases based on the Wu structure.
Article
Physics, Multidisciplinary
Tian-Shu Deng, Lei Pan, Yu Chen, Hui Zhai
Summary: This study investigates the stability of Kramers degeneracy and nontrivial topological states under time-reversal symmetry against coupling to the environment. The results show that dissipation can lead to splitting of spectral functions for degenerate states and induce backscattering between counterpropagating edge states, causing the absence of accurate quantization of conductance in the case of the quantum spin Hall effect. The findings have implications for interacting topological phases protected by time-reversal symmetry.
PHYSICAL REVIEW LETTERS
(2021)
Article
Physics, Multidisciplinary
Kai Li, Jiong-Hao Wang, Yan-Bin Yang, Yong Xu
Summary: Recent theoretical studies suggest that structural disorder can induce a topological insulator from a crystalline material, but experimental observation is challenging. With the experimentally realized randomly positioned Rydberg atoms, studying structural disorder induced topological phase transitions becomes feasible. The research reveals symmetry-protected topological amorphous insulators and structural disorder induced topological phase transition at a single-particle level in an experimentally accessible system.
PHYSICAL REVIEW LETTERS
(2021)
Article
Multidisciplinary Sciences
Vikash Mittal, Aswathy Raj, Sanjib Dey, Sandeep K. Goyal
Summary: The research shows that the topological phases of quantum walks remain relatively robust even in a lossy environment. In one-dimensional split-step quantum walks, the topological order persists as long as the Hamiltonian maintains exact PT-symmetry, while in two-dimensional quantum walks, PT-symmetry plays no role and losses may induce a topological phase transition.
SCIENTIFIC REPORTS
(2021)
Article
Optics
Ruey-Lin Chern, Yi-Ju Chou
Summary: This article investigates the photonic topological phases in Tellegen metamaterials. The research reveals the existence of two decoupled hybrid modes in the system, and the photonic system can be described using pseudospin states with spin-orbit Hamiltonians to determine the topological properties. Additionally, specific types of surface modes are found at the interface of Tellegen metamaterials, and their behavior is described through algebraic equations.
Article
Physics, Multidisciplinary
Abhishodh Prakash, Juven Wang
Summary: It has been proven that the boundaries of all nontrivial (1 + 1)-dimensional intrinsically fermionic symmetry-protected-topological phases, protected by finite on-site symmetries (unitary or antiunitary), are supersymmetric quantum mechanical systems. This supersymmetry arises as a consequence of the boundary 't Hooft anomaly that classifies the phase, and is distinct from other well-known degeneracies such as Kramers doublets.
PHYSICAL REVIEW LETTERS
(2021)
Article
Physics, Multidisciplinary
Yan Meng, Shuxin Lin, Bin-jie Shi, Bin Wei, Linyun Yang, Bei Yan, Zhenxiao Zhu, Xiang Xi, Yin Wang, Yong Ge, Shou-qi Yuan, Jingming Chen, Gui-Geng Liu, Hong-xiang Sun, Hongsheng Chen, Yihao Yang, Zhen Gao
Summary: For the classification of topological phases of matter, the consideration of whether a system is spinless or spinful is important. Recently, it has been theoretically realized that the algebraic structure of symmetries can be projectively represented in the presence of gauge symmetry, which enables the switch between spinless and spinful topological phases. In this study, spinful topological phases are experimentally demonstrated in spinless acoustic crystals with projective space-time inversion symmetry. This allows for the realization of a one-dimensional topologically gapped phase characterized by a 21 winding number, with double-degenerate bands in the entire Brillouin zone and two pairs of degenerate topological boundary modes.
PHYSICAL REVIEW LETTERS
(2023)
Article
Materials Science, Multidisciplinary
S. Sajad Dabiri, Hosein Cheraghchi
Summary: The effects of high-frequency electromagnetic fields on the emergence of quantum phases in thin topological insulators were investigated, with a focus on system parameters influencing the topological phases. It was demonstrated that altering system parameters could induce phase transitions between different types of insulators, which can be observed at low light intensities to avoid heating effects.
Article
Physics, Multidisciplinary
Helene Spring, Anton Akhmerov, Daniel Varjas
Summary: In amorphous topological materials, protection of topological surface states is improved due to continuous rotation symmetry, resulting in critical scaling of transport and protection of edge from localization in the topological phase.
Article
Physics, Particles & Fields
Yuting Hu, Zichang Huang, Ling-Yan Hung, Yidun Wan
Summary: In this paper, we establish the physical foundation of anyon condensation by building the effective Hamiltonian and the Hilbert space. We also generalize the Goldstone theorem to the case of anyon condensation and prove that the condensed phase is a symmetry enriched topological phase by constructing the corresponding symmetry transformations.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Condensed Matter
Ashley M. Cook
Summary: We introduce topological phases of matter defined by skyrmions in the ground state spin-or pseudospin-expectation value textures in the Brillouin zone. These phases are protected by a symmetry present in centrosymmetric superconductors. We consider a tight-binding model for spin-triplet superconductivity in transition metal oxides and find it realizes each of these topological skyrmion phases. We also find two types of topological phase transitions by which the skyrmion number can change.
JOURNAL OF PHYSICS-CONDENSED MATTER
(2023)
Article
Physics, Multidisciplinary
H. Polshyn, Y. Zhang, M. A. Kumar, T. Soejima, P. Ledwith, K. Watanabe, T. Taniguchi, A. Vishwanath, M. P. Zaletel, A. F. Young
Summary: Strong Coulomb interactions between electrons can lead to the emergence of topological gapped states in partially filled flat bands. Recent observations in twisted monolayer-bilayer graphene have shown insulators with Chern number C=1 at zero-magnetic-field limit, suggesting potential for further exploration of zero-magnetic-field phases with fractional statistics.
Article
Physics, Multidisciplinary
Junyeong Ahn, Guang-Yu Guo, Naoto Nagaosa, Ashvin Vishwanath
Summary: This study establishes a general theory of Riemannian geometry for resonant optical processes by identifying transition dipole moment matrix elements as tangent vectors, showing that optical responses can generally be thought of as manifestations of the Riemannian geometry of quantum states.
Article
Physics, Multidisciplinary
Patrick J. Ledwith, Ashvin Vishwanath, Eslam Khalaf
Summary: This study considers a family of twisted graphene multilayers and shows that they exhibit similar features to twisted bilayer graphene, including specific "magic angle" positions and ideal quantum geometry. Furthermore, it is found that ideal quantum geometry is closely related to the construction of fractional quantum Hall model wave functions.
PHYSICAL REVIEW LETTERS
(2022)
Article
Physics, Multidisciplinary
Onder Gul, Yuval Ronen, Si Young Lee, Hassan Shapourian, Jonathan Zauberman, Young Hee Lee, Kenji Watanabe, Takashi Taniguchi, Ashvin Vishwanath, Amir Yacoby, Philip Kim
Summary: Researchers have successfully constructed graphene-based van der Waals devices with narrow superconducting niobium nitride (NbN) electrodes. The study reveals the coexistence of superconductivity and a robust fractional quantum Hall (FQH) state in these devices. Additionally, the study identifies a possible signature for crossed Andreev reflection (CAR) across the superconductor, separating two FQH edges.
Article
Physics, Multidisciplinary
Nathanan Tantivasadakarn, Ashvin Vishwanath
Summary: Recent research has shown that clusterlike states can be used for measurement-based quantum computation and can be prepared in finite time while maintaining symmetry. By providing a Hamiltonian in higher dimensions, it was demonstrated that projective measurements along with feed-forward correction can recover the clusterlike state even in the presence of unwanted symmetric perturbations.
PHYSICAL REVIEW LETTERS
(2022)
Article
Multidisciplinary Sciences
Eslam Khalaf, Ashvin Vishwanath
Summary: This study predicts that spin polarons, bound states of an electron and a spin flip, can serve as charge carriers in the Chern-ferromagnet phase of twisted bilayer graphene. This exotic type of charge carrier has important implications in topological bands and may have potential experimental applications in materials like twisted bilayer graphene.
NATURE COMMUNICATIONS
(2022)
Article
Physics, Multidisciplinary
Xueda Wen, Yingfei Gu, Ashvin Vishwanath, Ruihua Fan
Summary: In this study, we investigate the properties of randomly driven (1 + 1) dimensional conformal field theories (CFTs), revealing the characteristics of non-equilibrium dynamical phases, including the heating phase and exceptional points. In most cases, random drivings lead to exponential growth of total energy and linear growth of subsystem entanglement entropy. However, at exceptional points, the subsystem entanglement entropy may grow as the square root of the number of driving steps, while the total energy still grows exponentially. Furthermore, we distinguish the heating phase from exceptional points by analyzing the distributions of operator evolution and energy density peaks.
Article
Chemistry, Physical
Cheng Shen, Patrick J. Ledwith, Kenji Watanabe, Takashi Taniguchi, Eslam Khalaf, Ashvin Vishwanath, Dmitri K. Efetov
Summary: Magic-angle twisted trilayer graphene (MATTG) has flat electronic bands and exhibits correlated quantum phases. A spectroscopy technique is demonstrated in this work to dissociate intertwined bands and quantify the energy gaps and Chern numbers C of the correlated states in MATTG. Hard correlated gaps with C = 0 at integer moiré unit cell fillings and charge density wave states originating from van Hove singularities at fractional fillings are uncovered. Displacement-field-driven first-order phase transitions at charge neutrality and v = 2 are also demonstrated. Overall, these properties establish a diverse electrically tunable phase diagram of MATTG.
Article
Physics, Multidisciplinary
Junkai Dong, Patrick J. Ledwith, Eslam Khalaf, Jong Yeon Lee, Ashvin Vishwanath
Summary: Motivated by higher Chern bands in twisted graphene multilayers, we investigate flat bands with arbitrary Chern number C and ideal quantum geometry. We find exact fractional Chern insulator (FCI) ground states for C > 1 bands with short-range interactions. By decomposing the higher Chern bands into separate bands with Chern number 1, we establish an SU(C) action combining real and momentum space translations and derive analytical constructions of FCI ground states. We confirm our predictions through numerical simulations and discuss implications for experimentally accessible systems such as monolayer graphene twisted relative to a Bernal bilayer.
PHYSICAL REVIEW RESEARCH
(2023)
Article
Materials Science, Multidisciplinary
Dan S. Borgnia, Ashvin Vishwanath, Robert-Jan Slager
Summary: We introduce the projected Green's function technique to study quasiperiodic systems and apply it to a few well-studied cases. By constructing an approximate sequence of transfer matrix equations, we can determine the existence of extended eigenfunctions. This technique proves to be flexible and effective in solving problems related to quasiperiodic systems.
Article
Materials Science, Multidisciplinary
Yi-Zhuang You, Ashvin Vishwanath
Summary: This study investigates the instability of ABC-stacked trilayer graphene metallic state to symmetry-breaking orders, revealing the preference for intervalley coherent order (IVC) as the ordering channel and examining the interaction between intervalley superconductivity and IVC fluctuations.
Article
Materials Science, Multidisciplinary
Ya-Hui Zhang, Ashvin Vishwanath
Summary: We report on the numerical discovery of a Luther-Emery liquid with pair-density-wave (PDW) correlations in doped spin-one Haldane chains or two-leg ladders. Our model, based on a generalized Kondo model, shows that a PDW with Q = ?? can emerge upon doping, regardless of the sign of the Kondo coupling JK. We also identify a composite order parameter for the superconductor, which can be experimentally realized in solid-state systems or fermionic cold atoms.
Article
Materials Science, Multidisciplinary
Eslam Khalaf, Patrick Ledwith, Ashvin Vishwanath
Summary: This study derives some general constraints on superconductivity in twisted bilayer graphene and shows the possibilities that the superconducting condensate must satisfy. The research reveals the influence of symmetry and pairing methods on the superconductivity in terms of energy bands and spin bands.
Article
Materials Science, Multidisciplinary
Xue-Yang Song, Ya-Hui Zhang, Ashvin Vishwanath
Summary: In this study, we theoretically explored the properties of twisted cuprate multilayers, a moire material family where the individual layers are strongly correlated. We found that at a specific twist angle, spontaneous time reversal breaking occurs, leading to a nearly gapless superconductor with spectroscopic features similar to monolayer cuprates. At smaller twist angles, driving an interlayer current can result in a gapped topological phase. The energy-phase relation of the interlayer Josephson junction displayed notable double-Cooper-pair tunneling dominant at approximately 45 degrees. The results were consistent with recent experiments, and the use of the moire structure as a probe of correlation physics, such as the pair density wave state, was discussed.
Article
Materials Science, Multidisciplinary
Zheng Zhu, D. N. Sheng, Ashvin Vishwanath
Summary: We investigate the evolution of Mott insulators in the triangular lattice Hubbard Model for different hole dopings in both strong and intermediate coupling limits. We find that at intermediate coupling, an unusual metallic state emerges with short ranged spin correlations but long ranged spin-chirality order. On the other hand, at strong coupling, the 120 degree magnetic order of the insulating magnet persists and produces hole pockets with a well-defined Fermi surface.