Localization with non-Hermitian off-diagonal disorder

In this work we discuss a non-Hermitian system described via a one-dimensional single-particle tight-binding model, where the non-Hermiticity is governed by a random nearest-neighbor tunnellings, such that the left-to-right and right-to-left hopping strengths are unequal. A physical situation of completely real eigenspectrum arises owing to the Hamiltonian's tridiagonal matrix structure under a simple \emph {sign conservation} of the product of the conjugate nearest-neighbor tunnelling terms. The off-diagonal disorder leads the non-Hermitian system to a localization-delocalization transition. The emergent nature of the transition is recognized through a finite-size spectral analysis. A comprehensive scaling theorem is then developed for characterizing the criticality. We perform careful analysis of localization length, inverse participation ratio, and energy splitting for reporting the scaling exponents, which turns out to be different from the ones in the conventional Anderson localization.Comment: 10 Pages, 5 Figure

Spontaneous magnetization of quantum XYXY spin model in joint presence of quenched and annealed disorder

We investigate equilibrium statistical properties of the quantum XY spin-1/2 model in an external magnetic field when the interaction and field parts are subjected to quenched or/and annealed disorder. The randomness present in the system are termed annealed or quenched depending on the relation between two different time scales - the time scale associated with the equilibriation of the randomness and the time of observation. Within a mean-field framework, we study the effects of disorders on spontaneous magnetization, both by perturbative and numerical techniques. Our primary interest is to understand the differences between quenched and annealed cases, and also to investigate the interplay when both of them are present in a system. We observe in particular that when interaction and field terms are respectively quenched and annealed, critical temperature for the system to magnetize in the direction parallel to the applied field does not depend on any of the disorders. Further, an annealed disordered interaction neither affects the magnetizations nor the critical temperatures. We carry out a comparative study of the different combinations of the disorders in the interaction and field terms, and point out their generic features.Comment: 9 pages, 2 figures, 1 tabl

Adiabatic freezing of long-range quantum correlations in spin chains

We consider a process to create quasi long-range quantum discord between the non-interacting end spins of a quantum spin chain, with the end spins weakly coupled to the bulk of the chain. The process is not only capable of creating long-range quantum correlation but the latter remains frozen, when certain weak end-couplings are adiabatically varied below certain thresholds. We term this phenomenon as adiabatic freezing of quantum correlation. We observe that the freezing is robust to moderate thermal fluctuations and is intrinsically related to the cooperative properties of the quantum spin chain. In particular, we find that the energy gap of the system remains frozen for these adiabatic variations, and moreover, considering the end spins as probes, we show that the interval of freezing can detect the anisotropy transition in quantum XY spin chains. Importantly, the adiabatic freezing of long-range quantum correlations can be simulated with contemporary experimental techniques.Comment: Main text (6 pages, 6 figures) and Supplemental material (4 pages, 4 figures), REVTeX 4-

Trends of information backflow in disordered spin chains

We investigate the trends of information backflow associated with the dynamics of a sub-part of a disordered spin-1/2 transverse field Heisenberg chain for different regimes of the Hamiltonian. Towards this aim, the decay profile of bipartite entanglement shared between a probe-qubit and a system-qubit (sub-part) of the chain is monitored in time. A clear shift in the trends of the decay profiles of the bipartite entanglement from monotonic in the low-disorder limit to non-monotonic in the moderately large disorder limit occurs due to strong information backflow from the environment (complementary-part) to the system-qubit. A connection between environmental interruption caused by the information backflow and the disorder strength is established by examining the entanglement revival frequencies. The growth patterns of the revival frequencies in the localized phase play an instrumental role to effectively distinguish an interacting system (many-body localized) from its non-interacting (Anderson localized) counterpart.Comment: 7 pages, 4 figures, close to the published versio