Scars from protected zero modes and beyond in $U(1)$ quantum link and quantum dimer models

Abstract

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 $H={\mathcal{O}}_{\mathrm{kin}}+\lambda {\mathcal{O}}_{\mathrm{pot}}$ 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 $\lambda =0$ that are protected by an index theorem preventing any mixing with the nonzero modes at this coupling. We classify different types of scars for $|\lambda |\lesssim \mathcal{O}(1)$ 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 $\lambda$ 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.

arXiv commentVersion 3 addressing the comments of the Referees, slightly modified text, added references; 39 pages, 22 figures; Submission to SciPost Physics

References in corpus (73)

• Chaos and Quantum Thermalization
• Thermalization and its mechanism for generic isolated quantum systems
• Probing many-body dynamics on a 51-atom quantum simulator
• Many body localization and thermalization in quantum statistical mechanics
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Localization of interacting fermions at high temperature
• Many-body localization, thermalization, and entanglement
• The many-body localization phase transition
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Quantum many-body scars
• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Fractons
• Computational Studies of Quantum Spin Systems
• Quantum scarred eigenstates in a Rydberg atom chain: entanglement, breakdown of thermalization, and stability to perturbations
• Emergent SU(2) dynamics and perfect quantum many-body scars
• Entanglement of Exact Excited States of AKLT Models: Exact Results, Many-Body Scars and the Violation of Strong ETH
• Periodic orbits, entanglement and quantum many-body scars in constrained models: matrix product state approach
• Short-ranged RVB physics, quantum dimer models and Ising gauge theories
• Quantum Link Models: A Discrete Approach to Gauge Theories
• Observation of gauge invariance in a 71-site Bose-Hubbard quantum simulator
• Exact Quantum Many-Body Scar States in the Rydberg-Blockaded Atom Chain
• Weak Ergodicity Breaking and Quantum Many-Body Scars in Spin-1 XY Magnets
• Exact Excited States of Non-Integrable Models
• Lattice gauge theories and string dynamics in Rydberg atom quantum simulators
• Realizing a scalable building block of a U(1) gauge theory with cold atomic mixtures
• Mott insulators in strong electric fields
• Unified structure for exact towers of scar states in the AKLT and other models
• Onsager's Scars in Disordered Spin Chains
• Eta-Pairing in Hubbard Models: From Spectrum Generating Algebras to Quantum Many-Body Scars
• Quantum Ice : a quantum Monte Carlo study
• Nonthermal states arising from confinement in one and two dimensions
• Interacting Fibonacci anyons in a Rydberg gas
• Canonical Typicality of Energy Eigenstates of an Isolated Quantum System
• Subsystem ETH
• Collapse and revival of quantum many-body scars via Floquet engineering
• Quantum Many-Body Scars and Space-Time Crystalline Order from Magnon Condensation
• Field Theories With a Vector Global Symmetry
• Eta-pairing states as true scars in an extended Hubbard Model
• Quantum Many-Body Scars in Optical Lattices
• Towards Quantum Simulating QCD
• Signatures of rare states and thermalization in a theory with confinement
• Quantum scars from zero modes in an Abelian lattice gauge theory on ladders
• Dynamical scar states in driven fracton systems
• Quantum Many-Body Scar States in Two-Dimensional Rydberg Atom Arrays
• Quantum many-body scars from virtual entangled pairs
• Cyclic exchange, isolated states and spinon deconfinement in an XXZ Heisenberg model on the checkerboard lattice
• Entanglement of Exact Excited Eigenstates of the Hubbard Model in Arbitrary Dimension
• Exact localized and ballistic eigenstates in disordered chaotic spin ladders and the Fermi-Hubbard model
• Disorder-free localization in an interacting two-dimensional lattice gauge theory
• Connection between quantum-many-body scars and the AKLT model from the viewpoint of embedded Hamiltonians
• Dynamics of the vacuum state in a periodically driven Rydberg chain
• Quantum scars of bosons with correlated hopping
• Group theoretic approach to many-body scar states in fermionic lattice models
• Exact Floquet quantum many-body scars under Rydberg blockade
• Hilbert Space Fragmentation and Exact Scars of Generalized Fredkin Spin Chains
• Exact many-body scars and their stability in constrained quantum chains
• Minimal model for Hilbert space fragmentation with local constraints
• Anomalous hydrodynamics in a class of scarred frustration-free Hamiltonians
• Many-Body Spectral Reflection Symmetry and Protected Infinite-Temperature Degeneracy
• The (2+1)-d U(1) Quantum Link Model Masquerading as Deconfined Criticality
• Hilbert space fragmentation in a 2D quantum spin system with subsystem symmetries
• Many-body scar state intrinsic to periodically driven system: Rigorous results
• Restoring coherence via aperiodic drives in a many-body quantum system
• Chaos and quantum scars in Bose-Josephson junction coupled to a bosonic mode
• Exact Quantum Scars in the Chiral Non-Linear Luttinger Liquid
• Eigenstate thermalization hypothesis in quantum dimer models
• Area-law entangled eigenstates from nullspaces of local Hamiltonians
• Low-Energy Effective Theories of Quantum Link and Quantum Spin Models
• Multiple quantum scar states and emergent slow-thermalization in the flat-band system
• Topological Quantum Many-Body Scars in Quantum Dimer Models on the Kagome Lattice
• Periodically driven Rydberg chains with staggered detuning
• Quantum scarring in a spin-boson system: fundamental families of periodic orbits
• An algorithm to explore entanglement in small systems

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• Quantum Many-Body Scars: A Quasiparticle Perspective
• Weak Ergodicity Breaking in the Schwinger Model
• Prominent quantum many-body scars in a truncated Schwinger model
• Driving quantum many-body scars in the PXP model
• State Dependence of Krylov Complexity in $2d$ CFTs
• Quantum Many-Body Scars from Einstein-Podolsky-Rosen States in Bilayer Systems
• Exhaustive Characterization of Quantum Many-Body Scars using Commutant Algebras
• Prethermal fragmentation in a periodically driven Fermionic chain
• Asymptotic Quantum Many-Body Scars
• Strong Hilbert space fragmentation via emergent quantum drums in two dimensions
• Weak universality, quantum many-body scars and anomalous infinite-temperature autocorrelations in a one-dimensional spin model with duality
• Extracting Quantum Many-Body Scarred Eigenstates with Matrix Product States
• Tight-binding billiards
• Sublattice scars and beyond in two-dimensional $U(1)$ quantum link lattice gauge theories
• Robust quantum many-body scars in the one-dimensional spin-1 Kitaev model
• Emergent symmetries in prethermal phases of periodically driven quantum systems
• Mobility edges through inverted quantum many-body scarring
• Quantum Many-Body Scarring in a Non-Abelian Lattice Gauge Theory
• Classical route to ergodicity and scarring in collective quantum systems
• Stabilizer Scars
• Signatures of fragmentation for periodically driven fermions
• Exact volume-law entangled zero-energy eigenstates in a large class of spin models
• Scar-induced imbalance in staggered Rydberg ladders
• Remarks on effects of projective phase on eigenstate thermalization hypothesis
• Prethermalization in the PXP Model under Continuous Quasiperiodic Driving
• Quantum Scar States in Coupled Random Graph Models
• Crystalline phases and devil's staircase in qubit spin ice
• Mass-Assisted Local Deconfinement in a Confined ${\mathbb{Z}}_2$ Lattice Gauge Theory
• Geometric fragmentation and anomalous thermalization in cubic dimer model
• Jordan-Wigner composite-fermion liquids in 2D quantum spin-ice
• Quantum dimer model on fullerenes: resonance, scarring and confinement
• Disorder-Free Localization and Fragmentation in a Non-Abelian Lattice Gauge Theory
• Obstruction to Ergodicity from Locality and $U(1)$ Higher Symmetries on the Lattice
• Stable infinite-temperature eigenstates in SU(2)-symmetric nonintegrable models
• Counting gauge-invariant states with matter fields and finite gauge groups
• Additional quantum many-body scars of the spin-$1$ $XY$ model with Fock-space cages and commutant algebras