Quantum Many-Body Scars: A Quasiparticle Perspective

Abstract

Weakly interacting quasiparticles play a central role in the low-energy description of many phases of quantum matter. At higher energies, however, quasiparticles cease to be well-defined in generic many-body systems due to a proliferation of decay channels. In this review, we discuss the phenomenon of quantum many-body scars, which can give rise to certain species of stable quasiparticles throughout the energy spectrum. This goes along with a set of unusual non-equilibrium phenomena including many-body revivals and non-thermal stationary states. We provide a pedagogical exposition of this physics via a simple yet comprehensive example, that of a spin-1 XY model. We place our discussion in the broader context of symmetry-based constructions of many-body scar states, projector embeddings, and Hilbert space fragmentation. We conclude with a summary of experimental progress and theoretical puzzles.

Ergodicity breaking provably robust to arbitrary perturbations

“…Illustration of the unit vectors n𝑖 ( 𝑝) that appear in the lattice divergence in Eq. (7). Left: The colors represent the sign that accompanies 𝑍 𝑖 𝑍 𝑗 for neighboring sites 𝑖 and 𝑗 after summing all contributions to Eq.…”

“…Left: The colors represent the sign that accompanies 𝑍 𝑖 𝑍 𝑗 for neighboring sites 𝑖 and 𝑗 after summing all contributions to Eq. (7). Right: These contributions can be regrouped to show that the divergence vanishes as a consequence of Eq.…”

“…'Traditional' answers have included integrable [1] and manybody localized [2,3] systems, both of which have extensively many conserved quantities. A more recent answer involves many-body scars [4][5][6][7], whereby typical initial conditions thermalize, but there exist special (low-entanglement) initial conditions that do not. More recently still, it was observed that the interplay of (finitely many) conservation laws can break ergodicity [8], a phenomenon that was later understood as arising from Hilbert space fragmentation (aka shattering) [9,10], whereby the unitary time evolution matrix block diagonalizes into exponentially many subsectors, with the dynamics unable to connect different subsectors [11][12][13][14][15][16][17].…”

Quantum many-body scars of spinless fermions with density-assisted hopping in higher dimensions

“…This is an unexpected behavior given the nonintegrability of the system and offers another example of a quantum many-body system that evades thermalization. This nonthermalizing dynamics is attributed to the existence of atypical eigenstates dubbed quantum many-body scars (QMBS) [10][11][12][13], which have nonthermal properties, and hence violate the ETH. These QMBS have a sub-volume-law entanglement scaling even though they are in the middle of the energy spectrum.…”

Mobility edges through inverted quantum many-body scarring

“…A weaker violation of the eigenstate thermalization hypothesis occurs in systems with quantum many-body scars [9][10][11]. Conventionally, scarred states are weakly entangled with subthermal scaling of the entanglement entropy [12][13][14][15][16][17][18], and procedures to embed these special states in the bulk of an otherwise thermal spectrum have been developed [19].…”