Weak ergodicity breaking from quantum many-body scars

Abstract

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 onedimensional model with a constrained local Hilbert space realized in the 51 Rydberg atom quantum simulator [H. Bernien et al., arXiv:1707.04344]. The quantum scarred eigenstates are embedded throughout the thermalizing many-body spectrum, but surprisingly lead to direct experimental signatures such as robust oscillations following a quench from a charge-density wave state found in experiment. We develop a model based on a single particle hopping on the Hilbert space graph, which quantitatively captures the scarred wave functions up to large systems of L = 32 atoms. Our results suggest that scarred many-body bands give rise to a new universality class of quantum dynamics, which opens up opportunities for creating and manipulating novel states with long-lived coherence in systems that are now amenable to experimental study.

Dynamics and level statistics of interacting fermions in the lowest Landau level

“…Such eigenstate branches appear to be common in overlap distributions, e.g.in figure 5(a) of [138] and in figure 3(a) of [140]. In the present case, states in this branch have much smaller overlaps than the dominant eigenstates, and hence do not play any noticeable role in the dynamics, unlike the case of [140]. Figure 9.…”

“…The dynamics of a quantum state is governed by the eigenstates of Hamiltonian with which the state has significant overlap. The distribution of overlaps-the overlaps with eigenstates as a function of corresponding eigenenergies, thus has been examined in the non-equilibrium literature for various Hamiltonians and initial states [75,86,[132][133][134][135][136][137][138][139][140].…”

Exact Quantum Many-Body Scar States in the Rydberg-Blockaded Atom Chain

“…The apparent Wigner-Dyson statistics suggests that the Hamiltonian is not integrable. Note that, as shown in the inset, the density of states has a peak at E = 0; this degeneracy is protected by particle-hole and lattice symmetries [10,11,16]. In addition, the density of states exhibits peaks around some integer-valued energies.…”

Transportless equilibration in isolated many-body quantum systems

“…Closely related further generalizations of the above local equilibration paradigm are the concepts of hindered equilibrium, quasi-equilibrium, metastability, and, above all, prethermalization [1,[32][33][34][35][36]. The first three concepts play a crucial role for instance in chemical reactions with long-lived intermediates, or in quantum systems exhibiting 'glassy behavior' [37,38], while the concept of prethermalization refers, e.g. to a fast but only partial thermalization of a certain subset of modes, (quasi-) particles 4 , or other generalized degrees of freedom [14].…”

“…Similarly, (56) takes the form . G(t) may be viewed as a survival probability (of the initial state) or return probability (of the time evolved state), sometimes also denoted as (quantum) fidelity.Mathematically speaking,(38) and (69) immediately imply that…”