Quantum many-body scars from virtual entangled pairs

Abstract

We study weak ergodicity breaking in a one-dimensional, nonintegrable spin-1 XY model. We construct for it an exact, highly excited eigenstate, which despite its large energy density, can be represented analytically by a finite bond-dimension matrix product state (MPS) with area-law entanglement. Upon a quench to a finite Zeeman field, the state undergoes periodic dynamics with perfect many-body revivals, in stark contrast to other generic initial states which instead rapidly thermalize. This dynamics can be completely understood in terms of the evolution of entangled virtual spin-1/2 degrees of freedom, which in turn underpin the presence of an extensive tower of strong-eigenstate thermalization hypothesis (ETH)-violating many-body eigenstates. The resulting quantum many-body scars are therefore of novel origin. Our results provide important analytical insights into the nature and entanglement structure of quantum many-body scars.

η -pairing states as true scars in an extended Hubbard model

“…To systematically construct Hamiltonians that make the η-pairing states scarry, we first understand scarring in spin-1 systems. In particular, the spin-1 XY model [31,32] is known to contain an exact tower of scar states, which are analogous to the η-pairing states in the Hubbard model. We first construct scarred models in the simpler spin-1 setting, then show how these results translate to electronic models.…”

“…The spin-1 XY model is one of the simplest models known to have an exact tower of scar states [31,32]. In Ref.…”

“…to break a special nonlocal SU(2) symmetry present in sectors with even magnetization [32,77]. On hypercubic lattices, the scar tower |S N is formed by the operator Q † :…”

“…Conversely, there are nonintegrable systems with exactly known scar states, such as the Affleck-Kennedy-Lieb-Tasaki (AKLT) model [28][29][30], the spin-1 XY model [31,32], and a spin-1/2 domain-wall-conserving model [33,34], among others [35][36][37][38][39][40][41][42][43], including a framework to make target states as scars in nonintegrable models [35,36]; there is also a growing number of examples of scars in the Floquet setting [41,[44][45][46][47][48].…”

Weak-ergodicity-breaking via lattice supersymmetry

“…Quantum scars have been linked to anomalously slow dynamics observed in laser-dressed Rydberg atom ensembles [11], and have attracted a considerable theoretical effort [10,[12][13][14][15][16][17][18][19][20]. While a number of models supporting quantum many-body scars have recently been found [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35], the general conditions (if any) for stabilizing ETH-violating states are still unknown, and the role of symmetries in this context stands as an open question. Some of the recent works in this direction link the presence of quantum scars to signatures of integrability [13], to semiclassical trajectories [15,19], to quasiparticle excitations [16,17] and to the emergence of an algebraic structure [14].…”