TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.17.5.128
TI  - Non-unitary quantum many-body dynamics using the Faber polynomial method
PY  - 2024/11/07
UR  - https://scipost.org/SciPostPhys.17.5.128
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 17
IS  - 5
SP  - 128
A1  - Diogo Soares, Rafael
AU  - Schirò, Marco
AB  - Efficient numerical methods are still lacking to probe the unconventional dynamics of quantum many-body systems under non-unitary evolution. In this work, we use Faber polynomials to numerically simulate both the dynamics of non-Hermitian systems and the quantum jumps unravelling of the Lindblad dynamics. We apply the method to the non-interacting and interacting Hatano-Nelson models evolving from two different setups: i) a Néel state, and ii) a domain wall. In the first case, we study how interactions preserve the initial magnetic order against the skin effect. In the second example, we present numerical evidence of the existence of an effective hydrodynamic description for the domain-wall melting problem in the non-interacting limit. Additionally, we investigate both the conditional and unconditional dynamics of the quantum jump unravelling in two quantum spin chains, which exhibit either the non-Hermitian or the Liouvillian skin effect. This numerical method inherently generalises the well-established method based on Chebyshev polynomials to accommodate non-Hermitian scenarios.
ER  -

@Article{10.21468/SciPostPhys.17.5.128,
	title={{Non-unitary quantum many-body dynamics using the Faber polynomial method}},
	author={Rafael Diogo Soares and Marco Schirò},
	journal={SciPost Phys.},
	volume={17},
	pages={128},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.17.5.128},
	url={https://scipost.org/10.21468/SciPostPhys.17.5.128},
}