Decays in quantum hierarchical models

Amir, Ariel; Oreg, Yuval; Imry, Y.

doi:10.1103/physreva.77.050101

Cited by 16 publications

(15 citation statements)

References 21 publications

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“…A many-body wavefunction can be written as a superposition of the eigenstates of H eff . The eigenvalues of H eff are complex and have negative imaginary parts [32]. When the wavefunction is evolved using exp(−iH eff t), the imaginary parts of the eigenvalues cause the weight in each eigenstate to decrease over time [ Fig.…”

Section: Modelmentioning

confidence: 99%

Heralded Magnetism in Non-Hermitian Atomic Systems

2014

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Quantum phase transitions are usually studied in terms of Hermitian Hamiltonians. However, cold-atom experiments are intrinsically non-Hermitian because of spontaneous decay. Here, we show that nonHermitian systems exhibit quantum phase transitions that are beyond the paradigm of Hermitian physics. We consider the non-Hermitian XY model, which can be implemented using three-level atoms with spontaneous decay. We exactly solve the model in one dimension and show that there is a quantum phase transition from short-range order to quasi-long-range order despite the absence of a continuous symmetry in the Hamiltonian. The ordered phase has a frustrated spin pattern. The critical exponent ν can be 1 or 1=2. Our results can be seen experimentally with trapped ions, cavity QED, and atoms in optical lattices.

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Section: Modelmentioning

confidence: 99%

Heralded Magnetism in Non-Hermitian Atomic Systems

2014

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“…Many properties are strongly dependent on the openness of the system and the way the system interacting with the environment around it. In order to take the influences of the environment into account, the effective non-Hermitian Hamiltonian approach has been used extensively in treating open systems [1][2][3][4][5][6]. By introducing imaginary parts to the Hamiltonian to represent the physical gain and loss of the system, one can study the open systems in an consistent way by analyzing the complex eigenvalues of the effective Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

Anderson localization in the non-Hermitian Aubry-André-Harper model with physical gain and loss

2017

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We investigate the Anderson localization in non-Hermitian Aubry-André-Harper (AAH) models with imaginary potentials added to lattice sites to represent the physical gain and loss during the interacting processes between the system and environment. By checking the mean inverse participation ratio (MIPR) of the system, we find that different configurations of physical gain and loss have very different impacts on the localization phase transition in the system. In the case with balanced physical gain and loss added in an alternate way to the lattice sites, the critical region (in the case with p-wave superconducting pairing) and the critical value (both in the situations with and without p-wave pairing) for the Anderson localization phase transition will be significantly reduced, which implies an enhancement of the localization process. However, if the system is divided into two parts with one of them coupled to physical gain and the other coupled to the corresponding physical loss, the transition process will be impacted only in a very mild way. Besides, we also discuss the situations with imbalanced physical gain and loss and find that the existence of random imaginary potentials in the system will also affect the localization process while constant imaginary potentials will not.

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“…Thus, a consistent way to take the effect of the opening into account for arbitrary coupling strength between the system and the outside world is highly desirable. The effective non-Hermitian Hamiltonian approach to open quantum systems has been shown to be a very effective tool in addressing this issue [3,4,5,6,7,8].…”

Section: Introductionmentioning

confidence: 99%

Superradiance transition in one-dimensional nanostructures: An effective non-Hermitian Hamiltonian formalism

2009

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Using an energy-independent non-Hermitian Hamiltonian approach to open systems, we fully describe transport through a sequence of potential barriers as external barriers are varied. Analyzing the complex eigenvalues of the non-Hermitian Hamiltonian model, a transition to a superradiant regime is shown to occur. Transport properties undergo a strong change at the superradiance transition, where the transmission is maximized and a drastic change in the structure of resonances is demonstrated. Finally, we analyze the effect of the superradiance transition in the Anderson localized regime.

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Decays in quantum hierarchical models

Cited by 16 publications

References 21 publications

Heralded Magnetism in Non-Hermitian Atomic Systems

Heralded Magnetism in Non-Hermitian Atomic Systems

Anderson localization in the non-Hermitian Aubry-André-Harper model with physical gain and loss

Superradiance transition in one-dimensional nanostructures: An effective non-Hermitian Hamiltonian formalism

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