Speaker: Igor R. Klebanov (Princeton University)
Title: Group Invariant States as Many-Body Scars
Abstract: Quantum many-body scars have been an active area of research
in Condensed Matter Physics for several years. In some many-body
systems, the Hilbert space breaks up into a large ergodic sector and a
much smaller scar subspace. It has been suggested [K. Pakrouski et
al., Phys. Rev. Lett. 125 (2020) 230602] that the two sectors may be
distinguished by their transformation properties under a large group
whose rank grows with the system size (this group is not a symmetry of
the Hamiltonian). The scars are invariant under this group, while all
other states are not. We begin by reviewing some many-body systems
where group singlet states have special properties: the matrix quantum
mechanics and fermionic tensor models. We continue on to appropriately
deformed versions of the SU(2) Hubbard model and show that the scar
subsector is invariant under a large group, which acts on the lattice
sites. More generally, we apply this idea to lattice systems with N
sites that contain M Majorana fermions per site. The Hilbert space may
be decomposed under the action of the SO(N)xSO(M) group, and the scars
are the SO(N) singlets. For any even M, there are two families of
scars. One of them, which we call the eta-states, is symmetric under
the group O(N) that includes a reflection. The other, the zeta-states,
has the SO(N) invariance only. For M=4, where our construction reduces
to a deformed SU(2) Hubbard chain with local interactions, the former
family are the N+1 eta-pairing states, while the latter are the N+1
states of maximum spin. For M=6, we exhibit explicit formulae for the
scar states and calculate the bipartite entanglement entropy
analytically. For large N, it grows logarithmically with the region
size. In general, the energies of the scars within each family are not
equidistant. For M>6 we also find that, with local Hamiltonians, the
scars typically have certain degeneracies.
The latter part of the talk is based on the recent paper “Majorana
Scars as Group Singlets” by Zimo Sun, Fedor Popov, Igor Klebanov and
Kiryl Pakrouski, arXiv:2212.11914
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