The existence of quantum many-body scars, which prevents thermalization from certain initial states after a long time, has been established across different quantum many-body systems. These include gauge theories corresponding to spin- 1 / 2 quantum link models. Establishing quantum scars in gauge theories with high spin is not accessible with existing numerical methods, which rely on exact diagonalization. We systematically identify scars for pure gauge theories with arbitrarily large integer spin S in 2 + 1 D , where the electric field is restricted to 2 S + 1 states per link. Through an explicit analytic construction, we show that the presence of scars is widespread in 2 + 1 D gauge theories for arbitrary integer spin. We confirm these findings numerically for small truncated spin and S = 1 quantum link models. Our analytic construction establishes the presence of scars far beyond volumes and spins that can be probed with existing numerical methods and can guide quantum simulation experiments toward interesting nonequilibrium phenomena, inaccessible otherwise. Published by the American Physical Society 2024
The existence of quantum many-body scars, which prevents thermalization from certain initial states after a long time, has been established across different quantum many-body systems. These include gauge theories corresponding to spin- 1 / 2 quantum link models. Establishing quantum scars in gauge theories with high spin is not accessible with existing numerical methods, which rely on exact diagonalization. We systematically identify scars for pure gauge theories with arbitrarily large integer spin S in 2 + 1 D , where the electric field is restricted to 2 S + 1 states per link. Through an explicit analytic construction, we show that the presence of scars is widespread in 2 + 1 D gauge theories for arbitrary integer spin. We confirm these findings numerically for small truncated spin and S = 1 quantum link models. Our analytic construction establishes the presence of scars far beyond volumes and spins that can be probed with existing numerical methods and can guide quantum simulation experiments toward interesting nonequilibrium phenomena, inaccessible otherwise. Published by the American Physical Society 2024
In this article, we elucidate the structure and properties of a class of anomalous high-energy states of matter-free U(1) quantum link gauge theory Hamiltonians using numerical and analytical methods. Such anomalous states, known as quantum many-body scars in the literature, have generated a lot of interest due to their athermal nature. Our starting Hamiltonian is H=Okin+λOpot , where λ is a real-valued coupling, and Okin ( Opot ) are summed local off-diagonal (diagonal) operators in the electric flux basis acting on the elementary plaquette □ . The spectrum of the model in its spin- 12 representation on Lx×Ly lattices reveal the existence of sublattice scars, |ψs⟩ , which satisfy Opot,□|ψs⟩=|ψs⟩ for all elementary plaquettes on one sublattice and Opot,□|ψs⟩=0 on the other, while being simultaneous zero modes or nonzero integer-valued eigenstates of Okin . We demonstrate a “triangle relation” connecting the sublattice scars with nonzero integer eigenvalues of Okin to particular sublattice scars with Okin=0 eigenvalues. A fraction of the sublattice scars have a simple description in terms of emergent short singlets, on which we place analytic bounds. We further construct a long-ranged parent Hamiltonian for which all sublattice scars in the null space of Okin become unique ground states and elucidate some of the properties of its spectrum. In particular, zero energy states of this parent Hamiltonian turn out to be exact scars of another U(1) quantum link model with a staggered short-ranged diagonal term. Published by the American Physical Society 2024
Quantum many-body scars are atypical energy eigenstates of chaotic quantum many-body systems that prevent certain special non-equilibrium initial conditions from thermalizing. We point out that quantum many-body scars exist for any nearest-neighbor spin-S XYZ quantum spin chain, and arise in the form of an infinite family of highly excited yet nonentangled product-state eigenstates, which define periodic textures in spin space. This set of scars, discovered originally by Granovskii and Zhedanov in 1985, encompasses both the experimentally relevant 'spin helices' for XXZ chains and more complicated helix-like states constructed from Jacobi elliptic functions for generic XYZ chains. An appealing feature of Granovskii-Zhedanov scars is that they are well-defined in the semiclassical limit S→∞, which allows for a systematic and analytical treatment of their dynamical instability to perturbations of the Hamiltonian. Using time-dependent spin-wave theory, we predict that upon perturbing along certain directions in Hamiltonian space, Granovskii-Zhedanov scars exhibit a dramatic asymmetry in their decay: depending on the sign of the perturbation, the decrease of their contrast is either slow and linear, or fast and exponential in time. This asymmetry can be traced to the absence (presence) of imaginarity in the spectrum of the Bogoliubov Hamiltonian governing quantum fluctuations about the scar, which corresponds to the absence (presence) of a non-zero Lyapunov exponent for the limiting classical trajectory. Numerical simulations using matrix product states (MPS) and infinite time-evolving block decimation (iTEBD) confirm that our prediction remains valid even far from the semiclassical limit. Our findings challenge existing theories of how quantum-many body scars relax.
We consider the spectrum of a U(1) quantum link model where gauge fields are realized as S=1/2 quantum spins and demonstrate a new mechanism for generating quantum many-body scars (high-energy eigenstates that violate the eigenstate thermalization hypothesis) in a constrained Hilbert space. Many-body dynamics with local constraints has attracted much attention due to the recent discovery of non-ergodic behavior in quantum simulators based on Rydberg atoms. Lattice gauge theories provide natural examples of constrained systems since physical states must be gauge-invariant. In our case, the Hamiltonian H=Okin+λOpot, where Opot (Okin) is diagonal (off-diagonal) in the electric flux basis, contains exact mid-spectrum zero modes at λ=0 whose number grows exponentially with system size. This massive degeneracy is lifted at any non-zero λ but some special linear combinations that simultaneously diagonalize Okin and Opot survive as quantum many-body scars, suggesting an order-by-disorder mechanism in the Hilbert space. We give evidence for such scars and show their dynamical consequences on ladders with up to 56 spins, which may be tested using available proposals of quantum simulators.
We consider the spectrum of a U(1) quantum link model where gauge fields are realized as S=1/2 spins and demonstrate a new mechanism for generating quantum many-body scars (high-energy eigenstates that violate the eigenstate thermalization hypothesis) in a constrained Hilbert space. Many-body dynamics with local constraints has attracted much attention due to the recent discovery of nonergodic behavior in quantum simulators based on Rydberg atoms. Lattice gauge theories provide natural examples of constrained systems since physical states must be gauge invariant. In our case, the Hamiltonian H=O_{kin}+λO_{pot}, where O_{pot} (O_{kin}) is diagonal (off-diagonal) in the electric flux basis, contains exact midspectrum zero modes at λ=0 whose number grows exponentially with system size. This massive degeneracy is lifted at any nonzero λ but some special linear combinations that simultaneously diagonalize O_{kin} and O_{pot} survive as quantum many-body scars, suggesting an "order-by-disorder" mechanism in the Hilbert space. We give evidence for such scars and show their dynamical consequences on two-leg ladders with up to 56 spins, which may be tested using available proposals of quantum simulators. Results on wider ladders point towards their presence in two dimensions as well.
Quantum many-body scarring (QMBS) has emerged as an intriguing paradigm of weak ergodicity breaking in nonintegrable quantum many-body models, particularly lattice gauge theories (LGTs) in 1 + 1 spacetime dimensions. However, an open question is whether QMBS has a true high-energy physics origin, and thus exists in higher-dimensional LGTs with dynamical matter. Given that nonergodic dynamics in d = 1 spatial dimension tend to vanish in d > 1 , it is important to probe this question. Using matrix product state techniques for both finite and infinite systems, we show that QMBS occurs in the 2 + 1 D U ( 1 ) quantum link model, as evidenced in persistent coherent oscillations in local observables, a marked slowdown in the growth of the bipartite entanglement entropy, and revivals in the fidelity. Interestingly, we see that QMBS is more robust when the matter degrees of freedom are bosonic rather than fermionic, which we argue is due to the strong nonlocality of the wave function in the latter case. Our results further shed light on the intimate connection between gauge symmetry and QMBS, and highlight the persistence of scarring in higher spatial dimensions. Our findings can be tested in near-term analog and digital quantum simulators, and we demonstrate their accessibility on a recently proposed cold-atom analog quantum simulator.
Non-equilibrium properties of strongly interacting gauge theories are often intractable with classical simulation methods. Due to recent developments of quantum simulations, studies of their properties in two spatial dimensions are becoming accessible. By demonstrating the existence of an approximate spectrum-generating algebra for a pure gauge plaquette ladder, we predict and verify the existence of Quantum Many-Body Scars in spin-1 Quantum Link Models. The analysis of the model is facilitated by a dualization process that maps the original gauge theory to a constrained spin chain. Was it not for the constraint, the system would have an exact spectrum-generating algebra. We propose a set of observables for diagnosing an approximate spectrum-generating algebra, which is expected to guide quantum simulators toward interesting physical regimes.