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Continuous Phase Transition without Gap Closing in Non-Hermitian Quantum Many-Body Systems.
Norifumi Matsumoto1, Kohei Kawabata1, Yuto Ashida1,2
1Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan.
Physical Review Letters
|January 15, 2021
Summary
Quantum phase transitions in non-Hermitian systems can occur without closing the energy gap. This is driven by the breakdown of the Lieb-Robinson bound, leading to a diverging length scale and unique phase transition phenomena.
Area of Science:
- Quantum Many-Body Physics
- Non-Hermitian Systems
- Condensed Matter Theory
Background:
- Conventional quantum phase transitions in Hermitian systems typically involve closing the energy gap.
- Non-Hermitian systems exhibit unique phenomena not observed in their Hermitian counterparts.
Purpose of the Study:
- To investigate continuous quantum phase transitions in non-Hermitian quantum many-body systems.
- To explore the conditions under which phase transitions can occur without closing the energy gap.
Main Methods:
- Theoretical analysis of non-Hermitian quantum many-body systems.
- Investigation of the Lieb-Robinson bound and its breakdown.
- Development of an exactly solvable generalized Kitaev toric-code model.
Main Results:
- A continuous quantum phase transition between gapped phases occurs without closing the energy gap (Δ).
- The characteristic length scale (ξ) diverges due to the breakdown of the Lieb-Robinson bound (unbounded v_{LR}), not a vanishing gap.
- System parameter susceptibility shows a singularity arising from eigenstate nonorthogonality.
Conclusions:
- Non-Hermitian physics allows for novel quantum phase transitions distinct from Hermitian systems.
- The breakdown of fundamental bounds like Lieb-Robinson is a key mechanism for these new transitions.
- The generalized toric-code model provides a concrete platform for studying these non-Hermitian phenomena.
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