Joint ICTP/SISSA Condensed Matter Seminar, 2 May at 11:00am, Ivan Khaymovich

[CMSP Seminars Secretariat]

---------------------------------------
  Joint ICTP/SISSA Condensed Matter Seminar
---------------------------------------

** * * Tuesday**, 2 May 2023, 11:00**am ***(CET)** * **
In person: *Luigi Stasi Seminar Room **(Leonardo Building, second floor)***
**
/Zoom: 
https://zoom.us/meeting/register/tJYrceqsqjgtHtf6zzYWD1A6lEHGqh7QoIHk/<https://zoom.us/meeting/register/tJIsfuuhqjsrE9EZY2loNxNobg8Lf39NUVHJ>

Speaker: *Ivan Khaymovich *(Stockholm University)

Title: *Localization enhancement in gain-loss non-Hermitian disordered 
models

*
Abstract:
Recently the interest to non-Hermitian disordered models has been 
revived, due to the claims of instability of a many-body localization to 
a coupling to a bath.
To describe such open quantum systems, one often focuses on an energy 
leakage to a bath, using effective non-Hermitian Hamiltonians. A 
well-known Hatano-Nelson model [1], being a 1d Anderson localization 
(AL) model, with different hopping amplitudes to the right/left, shows 
AL breakdown, as non-Hermiticity suppresses the interference.
Unlike this, we consider models with the complex gain-loss disorder and 
show that in general these systems tend to localization due to 
non-Hermiticity.
First, we focus on a non-Hermitian version [2] of a Rosenzweig-Porter 
model [3], known to carry a fractal phase [4] along with the AL and 
ergodic ones.
We show that ergodic and localized phases are stable against the 
non-Hermitian matrix entries, while the fractal phase, intact to 
non-Hermiticity of off-diagonal terms, gives a way to AL in a gain-loss 
disorder.
The understanding of this counterintuitive phenomenon is given in terms 
of the cavity method and in addition in simple hand-waving terms from 
the Fermi's golden rule, applicable, strictly speaking, to a Hermitian 
RP model. The main effect in this model is given by the fact that the 
generally complex diagonal potential forms an effectively 2d (complex) 
distribution, which parametrically increases the bare level spacing and 
suppresses the resonances.
Next, we consider a power-law random banded matrix ensemble (PLRBM) [5], 
known to show AL transition (ALT) at the power of the power-law hopping 
decay a=d equal to the dimension d. In [6], we show that a non-Hermitian 
gain-loss disorder in PLRBM shifts ALT to smaller values 
$d/2<a_{AT}(W)<d$, dependent on the disorder on-site W.
A similar effect of the reduced critical disorder due to the gain-loss 
complex-valued disorder has been recently observed by us numerically [7].
In order to analytically explain the above numerical results, we derive 
an effective non-Hermitian resonance counting and show that the 
delocalization transition is driven by so-called "bad resonances", 
  which cannot be removed by the wave-function hybridization (e.g., in 
the renormalization group approach), while the usual "Hermitian" 
resonances are suppressed in the same way as in the non-Hermitian RP model.

[1] N. Hatano, D. R. Nelson, "Localization Transitions in Non-Hermitian 
Quantum Mechanics", PRL 77, 570 (1996).
[2] G. De Tomasi, I. M. K. "Non-Hermitian Rosenzweig-Porter 
random-matrix ensemble: Obstruction to the fractal phase", Phys. Rev. B, 
106, 094204 (2022).
[3] N. Rosenzweig and C. E. Porter, “Repulsion of energy levels” in 
complex atomic spectra,” Phys. Rev. B 120, 1698 (1960).
[4] V. E. Kravtsov, I. M. K., E. Cuevas, and M. Amini, “A random matrix 
model with localization and ergodic transitions,” New J. Phys. 17, 
122002 (2015).
[5] A. D. Mirlin, Y. V. Fyodorov, F.-M. Dittes, J. Quezada, and T. H. 
Seligman, “Transition from localized to extended eigenstates in the 
ensemble of power-law random banded matrices,” Phys. Rev. E 54, 
3221–3230 (1996).
[6] G. De Tomasi, I. M. K. "Non-Hermitian resonance counting in 
gain-loss power law random banded matrices", in preparation.
[7] L. S. Levitov "Absence of localization of vibrational modes due to 
dipole-dipole interaction", EPL 9, 83 (1989).
[8] G. De Tomasi, I. M. K. "Enhancement of many-body localization in 
non-Hermitian systems", in preparation.