Localization and universality in non-Hermitian many-body systems - PowerPoint PPT Presentation


 Localization and universality in 
 non-Hermitian many-body systems 
 Ryusuke Hamazaki R.H., K. Kawabata and M. Ueda. 
 Phys. Rev. Lett. 123, 090603 (2019) R.H., K. Kawabata, N. Kura and M. Ueda. 
 Phys. Rev. Research, to appear 
 Kohei Naoto Prof. Ueda [arXiv:1904.13082] iTHEMS QFT Seminar Sorry, this talk is *mainly based on numerical results *not about quantum field theory

Outline Introduction ・ Many-body localization in Hermitian systems ・ Non-Hermitian Hamiltonians Non-Hermitian many-body localization R.H., K. Kawabata and M. Ueda. 
 Phys. Rev. Lett. 123, 090603 (2019) Universality in non-Hermitian random matrices R.H., K. Kawabata, N. Kura and M. Ueda. 
 arXiv:1904.13082

Outline Introduction ・ Many-body localization in Hermitian systems ・ Non-Hermitian Hamiltonians Non-Hermitian many-body localization R.H., K. Kawabata and M. Ueda. 
 Phys. Rev. Lett. 123, 090603 (2019) Universality in non-Hermitian random matrices R.H., K. Kawabata, N. Kura and M. Ueda. 
 arXiv:1904.13082

unitary time evolution ? Thermalization of isolated quantum systems Deriving stat. mech. from quant. mech. microcanonical ensemble Dating back to J. von Neumann in 1929 Rapid development in these two decades Observation of thermalization dynamics 
 cf) with ultra cold atomic gases 
 S. Trotzky et al., Nature Physics (2012) (almost isolated, highly tunable systems)

<latexit sha1_base64="nkmDE2HqLhcTPRFGszsIJat9lkA=">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</latexit> Localization transition in quantum many-body systems Generic translation invariant systems thermalize unitary time evolution Possibility of two phases in disordered systems e.g.) (many-body localized) Delocalized (ergodic) phase: 
 MBL phase: 
 disorder 
 thermalization no thermalization strength many conserved 
 transition quantities

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 level-spacing statistics Level spacing distributions many-body eigenvalues MBL phase: 
 Delocalized phase: 
 thermalization no thermalization disorder 
 strength transition Poisson RMT Universality of random matrices: 
 uncorrelated eigenstates: 
 complexity of eigenstates many symmetry sectors

Outline Introduction ・ Many-body localization in Hermitian systems ・ Non-Hermitian Hamiltonians Non-Hermitian many-body localization R.H., K. Kawabata and M. Ueda. 
 Phys. Rev. Lett. 123, 090603 (2019) Threefold way in non-Hermitian random matrices R.H., K. Kawabata, N. Kura and M. Ueda. 
 arXiv:1904.13082