We present a class of Hamiltonians $H$ for which a sector of the Hilbert space invariant under a Lie group $G$, which is not a symmetry of $H$, possesses the essential properties of many-body scar states. These include the absence of thermalization and the "revivals" of special initial states in time evolution. Some of the scar states found in earlier work may be viewed as special cases of our construction. A particular class of examples concerns interacting spin-1/2 fermions on a lattice consisting of $N$ sites (it includes deformations of the Fermi-Hubbard model as special cases), and we show that it contains two families of $N+1$ scar states. One of these families, which was found in recent literature, is comprised of the well-known $η$-pairing states. We find another family of scar states which is $U(N)$ invariant. Both families and most of the group-invariant scar states produced by our construction in general, give rise to the off-diagonal long range order which survives at high temperatures and is insensitive to the details of the dynamics. Such states could be used for reliable quantum information processing because the information is stored non-locally, and thus cannot be easily erased by local perturbations. In contrast, other scar states we find are product states which could be easily prepared experimentally. The dimension of scar subspace is directly controlled by the choice of group $G$ and can be made exponentially large.
In this work, based on the Fredkin spin chain, we introduce a family of spin-$1/2$ many-body Hamiltonians with a three-site interaction featuring a fragmented Hilbert space with coexisting quantum many-body scars. The fragmentation results from an emergent kinetic constraint resembling the conserved spin configuration in the 1D Fermi-Hubbard model in the infinite onsite repulsion limit. To demonstrate the many-body scars, we construct an exact eigenstate that is in the middle of the spectrum within each fractured sub-sector displaying either logarithmic or area-law entanglement entropy. The in…
Following the recent observation of wave function revivals in large Rydberg atom quantum simulators, much effort has focused on understanding the emergence of many-body scars in non-integrable quantum systems. Here we explore the origin of scarred wavefunction revivals in a family of models obtained by deforming the graph adjacency matrix of the PXP model - the effective model of Rydberg atoms in the strong Rydberg blockade regime. We consider deformations that either enhance the Rydberg constraint, ultimately resulting in an effective tight-binding model of two hypercubes joined at a single v…
The discovery of Quantum Many-Body Scars (QMBS) both in Rydberg atom simulators and in the Affleck-Kennedy-Lieb-Tasaki (AKLT) spin-1 chain model, have shown that a weak violation of ergodicity can still lead to rich experimental and theoretical physics. In this review, we provide a pedagogical introduction to and an overview of the exact results on weak ergodicity breaking via QMBS in isolated quantum systems with the help of simple examples such as the fermionic Hubbard model. We also discuss various mechanisms and unifying formalisms that have been proposed to encompass the plethora of syste…
Certain wave functions of non-interacting quantum chaotic systems can exhibit "scars" in the fabric of their real-space density profile. Quantum scarred wave functions concentrate in the vicinity of unstable periodic classical trajectories. We introduce the notion of many-body quantum scars which reflect the existence of a subset of special many-body eigenstates concentrated in certain parts of the Hilbert space. We demonstrate the existence of scars in the Fibonacci chain -- the one- dimensional model with a constrained local Hilbert space realized in the 51 Rydberg atom quantum simulator [H.…
Motivated by recent observations of ergodicity breaking due to Hilbert space fragmentation in 1D Fermi-Hubbard chains with a tilted potential [Scherg et al., arXiv:2010.12965], we show that the same system also hosts quantum many-body scars in a regime $U\approx Δ\gg J$ at electronic filling factor $ν=1$. We numerically demonstrate that the scarring phenomenology in this model is similar to other known realisations such as Rydberg atom chains, including persistent dynamical revivals and ergodicity-breaking many-body eigenstates. At the same time, we show that the mechanism of scarring in the F…
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 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 Hamilton…
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）
We propose a class of non-integrable quantum spin chain models that exhibit quantum many-body scars even in the presence of disorder. With the use of the so-called Onsager symmetry, we construct such scarred models for arbitrary spin quantum number $ S $. There are two types of scar states, namely, coherent states associated to an Onsager-algebra element and one-magnon scar states. While both of them are highly-excited states, they have area-law entanglement and can be written as a matrix product state. Therefore, they explicitly violate the eigenstate thermalization hypothesis. We also invest…
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 …
A quantum many-body scar system usually contains a special non-thermal subspace (approximately) decoupled from the rest of the Hilbert space. In this work, we propose a general structure called deformed symmetric spaces for the decoupled subspaces hosting quantum many-body scars, which are irreducible sectors of simple Lie groups transformed by matrix-product operators (or projected entangled pair operators), of which the entanglement entropies are proved to obey sub-volume-law scaling and thus violate the eigenstate thermalization hypothesis. A deformed symmetric space, in general, is require…
Motivated by recent experimental observations of coherent many-body revivals in a constrained Rydberg atom chain, we construct a weak quasi-local deformation of the Rydberg blockade Hamiltonian, which makes the revivals virtually perfect. Our analysis suggests the existence of an underlying non-integrable Hamiltonian which supports an emergent SU(2)-spin dynamics within a small subspace of the many-body Hilbert space. We show that such perfect dynamics necessitates the existence of atypical, nonergodic energy eigenstates - quantum many-body scars. Furthermore, using these insights, we construc…
Aspects of Hilbert space fragmentation in the quantum East model: fragmentation, subspace-restricted quantum scars, and effects of density-density interactions
本文解析刻画量子 East 模型的 Hilbert 空间碎裂与子空间受限量子伤疤，并揭示密度–密度相互作用导致的谱学转变及无限耦合可积极限。
We discuss quantum dynamics in the transverse field Ising model in two spatial dimensions. We show that, up to a prethermal timescale, which we quantify, the Hilbert space 'shatters' into dynamically disconnected subsectors. We identify this shattering as originating from the interplay of a $\mathrm{U}(1)$ conservation law and a one-form $\mathbb{Z}_2$ constraint. We show that the number of dynamically disconnected sectors is exponential in system volume, and includes a subspace exponential in system volume within which the dynamics is exactly localized, even in the absence of quenched disorde…
Exact group invariant scar towers in two dimensional gauge theories
CERN（欧洲核子研究中心）；Institute for Theoretical Physics, ETH Zurich（苏黎世联邦理工学院理论物理研究所）；Department of Physics, University of the Basque Country UPV/EHU（巴斯克大学物理系）；IKERBASQUE, Basque Foundation for Science（伊克尔巴斯科奎，巴斯克科学基金会）
We study a kinetically constrained pair hopping model that arises within a Landau level in the quantum Hall effect. At filling $ν= 1/3$, the model exactly maps onto the so-called "PXP model", a constrained model for the Rydberg atom chain that is numerically known to exhibit ETH-violating states in the middle of the spectrum or quantum many-body scars. Indeed, particular charge density wave configurations exhibit the same revivals seen in the PXP model. We generalize the mapping to fillings factors $ν= p/(2p+1)$, and show that the model is equivalent to non-integrable spin-chains within partic…
The Hilbert space of a quantum system with internal global symmetry $G$ decomposes into sectors labelled by irreducible representations of $G$. If the system is chaotic, the energies in each sector should separately resemble ordinary random matrix theory. We show that such "sector-wise" random matrix ensembles arise as the boundary dual of two-dimensional gravity with a $G$ gauge field in the bulk. Within each sector, the eigenvalue density is enhanced by a nontrivial factor of the dimension of the representation, and the ground state energy is determined by the quadratic Casimir. We study the…
To provide a physical example of quantum scars, we study the many-body scars in the spin-1 Kitaev chain where the so-called PXP Hamiltonian is exactly embedded in the spectra. Regarding the conserved quantities, the Hilbert space is fragmented into disconnected subspaces and we explore the associated constrained dynamics. The continuous revivals of the fidelity and the entanglement entropy when the initial state is prepared in $\vert\mathbb{Z}_k\rangle$ ($k=2,3$) state illustrate the essential physics of the PXP model. We study the quantum phase transitions in the one-dimensional spin-1 Kitaev…
The concept of geometrical frustration has led to rich insights into condensed matter physics, especially as a mechansim to produce exotic low energy states of matter. Here we show that frustration provides a natural vehicle to generate models exhibiting anomalous thermalization of various types within high energy states. We consider three classes of non-integrable frustrated spin models: (I) systems with local conserved quantities where the number of symmetry sectors grows exponentially with the system size but more slowly than the Hilbert space dimension, (II) systems with exact eigenstates …
