Zero-energy Quantum Many-Body Scar under Emergent Chiral Symmetry and Pseudo Hilbert Space Fragmentation

TL;DR

This paper uncovers a new type of quantum many-body scar at zero energy, arising from the interplay of chiral symmetry and pseudo Hilbert space fragmentation, leading to localized scar states with unusual dynamics.

Contribution

It demonstrates the emergence of zero-energy QMBS due to combined chiral symmetry and pseudo HSF, without requiring their direct intertwining, and characterizes their unique properties.

Findings

Zero-energy QMBS are highly localized and occur at even particle numbers.

Fidelity oscillates without decay, indicating unusual scarred dynamics.

Signature of QMBS can be observed in the original Hamiltonian.

Abstract

Hilbert space fragmentation (HSF) is a mechanism for generating quantum many-body scar (QMBS), which provides a route to weakly break ergodicity. The zero-energy QMBSs widely exist across various systems due to the intertwining of chiral symmetry and spatial inversion symmetry. In this work, we study the phenomenology of the zero-energy QMBS under the interplay between the chiral symmetry and pseudo HSF, where the Hilbert space is approximately fragmented into different blocks. We consider a model of tilted chain of interacting spinless fermions with periodically varying tunneling strength. At small tunneling strength and under resonance condition, the system is described by an effective model with chiral symmetry and pseudo HSF. We find that the interplay between the two gives rise to a highly localized zero-energy QMBS when the particle number is even. We identify a simple product state to signalize the zero-energy QMBS, which gives rise to unusual scarred dynamics. The fidelity oscillates around a fixed value without decaying instead of showing the usual collapse and revival in common scarred systems. We show that the signature of the zero-energy QMBS can also be captured by the original Hamiltonian. Our results uncover a new scar phenomenon and provide an example that does not need the intertwining of chiral and spatial symmetries to support zero-energy QMBS.