Zero-energy quantum many-body scar under emergent chiral symmetry and pseudo Hilbert space fragmentation

Abstract

Hilbert space fragmentation (HSF) is a mechanism for generating quantum many-body scar (QMBS), which provides a route to weakly break ergodicity. Many scarred systems possess an exponentially large number of zero-energy states due to the chiral symmetry induced bipartition of the Hilbert space. In this work, we study the QMBS phenomenology 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, we analytically derive the resonance conditions under which 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. This zero-energy QMBS induces an unusual scarred dynamical phenomenon. Specifically, the fidelity from a simple initial state oscillates around a finite fixed value without decaying, instead of showing the typical decaying collapse and revival observed when the particle number is odd and in common scarred systems. We show that the signature of the unusual scarred dynamical behaviour can also be detected in the original driven system by measuring local observables. Our findings enrich the scar phenomenon and deepen the understanding of the relation between Hilbert space structure and QMBS.

Graphical abstract

Keywords

quantum thermalization / quantum many-body scars / Hilbert space fragmentation / Floquet systems

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Declarations

The authors declare that they have no competing interests and there are no conflicts.

Acknowledgements

This study was supported by the National Natural Science Foundation of China (Grant Nos. 12025509 and 12305048), Shenzhen Fundamental Research Project (Grant No. JCYJ20230808105009018), the National Key Research and Development Program of China (Grant No. 2022YFA1404104), and Guangdong Provincial Quantum Science Strategic Initiative (No. GDZX2305006). Y.K. is supported by the National Natural Science Foundation of China (Grant No. 12275365) and the Natural Science Foundation of Guangdong (Grant No. 2023A1515012099).

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