We demonstrate the presence of anomalous high-energy eigenstates, or many-body scars, in $U(1)$ quantum link and quantum dimer models on square and rectangular lattices. In particular, we consider the paradigmatic Rokhsar-Kivelson Hamiltonian $H=\mathcal{O}_{\mathrm{kin}} + λ\mathcal{O}_{\mathrm{pot}}$ where $\mathcal{O}_{\mathrm{pot}}$ ($\mathcal{O}_{\mathrm{kin}}$) is defined as a sum of terms on elementary plaquettes that are diagonal (off-diagonal) in the computational basis. Both these interacting models possess an exponentially large number of mid-spectrum zero modes in system size at $λ=0$ that are protected by an index theorem preventing any mixing with the nonzero modes at this coupling. We classify different types of scars for $|λ| \lesssim \mathcal{O}(1)$ both at zero and finite winding number sectors complementing and significantly generalizing our previous work [Banerjee and Sen, Phys. Rev. Lett. 126, 220601 (2021)]. The scars at finite $λ$ show a rich variety with those that are composed solely from the zero modes of $\mathcal{O}_{\mathrm{kin}}$, those that contain an admixture of both the zero and the nonzero modes of $\mathcal{O}_{\mathrm{kin}}$, and finally those composed solely from the nonzero modes of $\mathcal{O}_{\mathrm{kin}}$. We give analytic expressions for certain "lego scars" for the quantum dimer model on rectangular lattices where one of the linear dimensions can be made arbitrarily large, with the building blocks (legos) being composed of emergent singlets and other more complicated entangled structures.
We present a class of quantum dimer models on the kagome lattice with full translational invariance that feature a quantum many-body scar state of analytically known entanglement properties within their spectra. Using exact diagonalization on lattices of up to 60 sites, we show that non-scar states conform to the eigenstate thermalization hypothesis. Specifically, we show that energies are distributed according to the Gaussian ensemble expected of their respective symmetry sector, illustrate the existence of the scar from bipartite entanglement properties, and demonstrate revival phenomena in …
Symmetry protected quantum many body scars through half-gauging
Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学）；National Tsing Hua University（国立清华大学）；National Center for Theoretical Sciences（国家理论科学中心）；Academia Sinica（中央研究院）
Dressed Floquet scars from protected zero modes in a Rydberg chain
Indian Association for the Cultivation of Science（印度科学文化促进协会）；University of Hyderabad（海得拉巴大学）；S. N. Bose National Centre for Basic Sciences（S.N. 玻色基础科学国家中心）
Symmetry-protected topological phases and transition in a frustrated spin-$\frac{1}{2}$ XXZ chain
受抑的自旋$1/2$ XXZ锯齿形链相关的Rb $_2$铜$_2$钼$_3$ O $_{12}$的重新审视，在光的拓扑保护（SPT）阶段。使用密度矩阵重整化群方法的无限系统，我们确定投影表示为四个不同的时间反演不变的SPT阶段，两个宇称对称的二聚体阶段附近的海森堡和XX限制和两个宇称破缺的矢量手征（VC）二聚体之间的阶段。最近邻铁磁交换耦合中的小的键交替引起两个不同的VC二聚体相之间的直接SPT转变。数值计算还发现，两个Berezinskiii-Kosterlitz无带隙VC相到两个不同带隙VC相的跃迁在与SU（2）对称情形相同的Tomonaga-Luttinger参数值的高斯临界点相遇.
The earliest known examples of quantum superposition were found in organic chemistry -- in molecules that `resonate' among multiple arrangements of $π$-bonds. Small molecules such as benzene resonate among a few bond arrangements. In contrast, a large system that stretches over a macroscopic lattice may resonate among an extensive number of configurations. This is analogous to a quantum spin liquid as described by Anderson's resonating valence bond (RVB) picture. In this article, we study the intermediate case of somewhat large molecules, the C$_{20}$ and C$_{60}$ fullerenes. We build a minima…
Formation of quantum scars in many-body systems provides a novel mechanism for enhancing coherence of weakly entangled states. At the same time, coherence of edge modes in certain symmetry protected topological (SPT) phases can persist away from the ground state. In this work we show the existence of many-body scars and their implications on bulk coherence in such an SPT phase. To this end, we study the eigenstate properties and the dynamics of an interacting spin-$1/2$ chain with three-site "cluster" terms hosting a $\mathbb{Z}_2 \times \mathbb{Z}_2$ SPT phase. Focusing on the weakly interact…
Ground-State Phase Diagram of the Bond-Alternating $S=2$ Quantum Spin Chain with the $XXZ$ and On-Site Anisotropies -- Symmetry Protected Topological Phase versus Trivial Phase
We discuss physical constructions, and the boundary properties of various symmetry protected topological phases that involve 1-form symmetries, from one spatial dimension (1d) to four spatial dimensions (4d). For example, the prototype 3d boundary state of 4d SPT states involving 1-form symmetries can be either a gapless photon phase (quantum electrodynamics) or gapped topological order enriched by 1-form symmetries, namely the loop excitations of these topological orders carry nontrivial 1-form symmetry charges. This study also serves the purpose of diagnosing anomaly of 3d states of matter. …
Detecting underlying symmetry-protected topological phases via strange correlators and edge engineering
Beijing Normal University（北京师范大学）；Westlake University（西湖大学）；Westlake Institute for Advanced Study（西湖高等研究院）；The Hong Kong University of Science and Technology（香港科技大学）；Beihang University（北京航空航天大学）；Tianmushan Laboratory（天目山实验室）
Duality places an important constraint on the renormalization group flows and the phase diagrams. For self-dual theories, the self-duality can be promoted as a symmetry, this leads to the multi-criticalities. This work investigates a description of the deconfined quantum criticality, the $N_f=2$ QED$_3$, as an example of self-dual theories and its multi-critical behavior under perturbative deformations. The multi-criticality is described by the theory with Gross-Neveu couplings and falls in a different universality class than the standard deconfined quantum criticality. We systematically calcu…
Systematic construction of quantum many-body scars in frustrated Rydberg arrays
Institute of Science and Technology Austria (ISTA)（奥地利科学与技术研究所）；Physics Department, Technical University of Munich, TUM School of Natural Sciences（慕尼黑工业大学自然科学学院物理系）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）
Predictions of localized Majorana modes, and ideas for manipulating these degrees of freedom, are the two key ingredients in proposals for physical platforms for Majorana quantum computation. Several proposals envisage a scalable network of such Majorana modes coupled bilinearly to each other by quantum-mechanical mixing amplitudes. Here, we develop a theoretical framework for characterizing collective topologically protected zero-energy Majorana fermion excitations of such networks of localized Majorana modes. A key ingredient in our work is the Gallai-Edmonds decomposition of a general graph…
We study the phase diagram of the $SO_q(3)$ quantum group invariant spin-1 bilinear-biquadratic spin chain for real values of $q>1$. Numerical computations suggest that the chain has at least three clearly distinguished phases: A chiral analogue of the Haldane phase, a dimerized phase and a ferromagnetic phase. In contrast, the counterpart of the extended critical region that is known to exist for $q=1$ remains elusive. Our results show that the Haldane phase fails to exhibit a two-fold degeneracy in the entanglement spectrum but that the degeneracy is restored upon a suitable $q$-deformation …
Additional quantum many-body scars of the spin-$1$ $XY$ model with Fock-space cages and commutant algebras
Institute of Mathematical Sciences（马哈拉施特拉数学科学研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Technische Universität München (TUM)（慕尼黑工业大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）
