Detection of an unbroken phase of a non-Hermitian system via a Hermitian factorization surface

Chandra, Lakkaraju, Leela Ganesh; Sen, Aditi

doi:10.1103/physreva.104.052222

Cited by 9 publications

(2 citation statements)

References 58 publications

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“…Additionally, some authors have used the PT -symmetric nature of non-hermitian hamiltonians to produce efficient algorithms to compute their spectra with arbitrarily high precision [49,50]. RT -symmetric bosonic and fermionic systems have been studied in various capacities ranging from exactly solvable models, to quantum batteries, detection of exceptional points through dynamics and unbroken phase through quantum-information-related techniques in [51][52][53][54][55][56]. Some authors have focused on solvable fermionic spin chains, for example in Refs.…”

Section: Introductionmentioning

confidence: 99%

Spectral crossover in non-hermitian spin chains: comparison with random matrix theory

Sarkar¹,

Sen²,

Kumar³

2023

Preprint

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We systematically study the short range spectral fluctuation properties of three non-hermitian spin chain hamiltonians using complex spacing ratios. In particular we focus on the non-hermitian version of the standard one-dimensional anisotropic XY model having intrinsic rotation-time-reversal (RT ) symmetry that has been explored analytically by Zhang and Song in [Phys.Rev.A 87, 012114 (2013)]. The corresponding hermitian counterpart is also exactly solvable and has been widely employed as a toy model in several condensed matter physics problems. We show that the presence of a random field along the x-direction together with the one along z facilitates integrability and RT -symmetry breaking leading to the emergence of quantum chaotic behaviour indicated by a spectral crossover resembling Poissonian to Ginibre unitary ensemble (GinUE) statistics of random matrix theory. Additionally, we consider two n × n dimensional phenomenological random matrix models in which, depending upon crossover parameters, the fluctuation properties measured by the complex spacing ratios show an interpolation between 1D-Poisson to GinUE and 2D-Poisson to GinUE behaviour. Here 1D and 2D Poisson correspond to real and complex uncorrelated levels, respectively.

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Section: Introductionmentioning

confidence: 99%

Spectral crossover in non-hermitian spin chains: comparison with random matrix theory

Sarkar¹,

Sen²,

Kumar³

2023

Preprint

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“…Therefore, we would wander whether the EUR can display some new phenomena in the non-Hermitian system. Second, recently several approaches have been proposed to detect and witness criticality in non-Hermitian systems such as the HSS [16], multiple quantum coherence [25], and the corresponding Hermitian factorization surface [26]. These quantities are sensitive to the quantum criticality, and often served as a signature of transition points in Hermitian systems.…”

Section: Introductionmentioning

confidence: 99%

Witnessing criticality in non-Hermitian systems via entopic uncertainty relation

Guo

Wang

2022

New J. Phys.

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Non-Hermitian systems with exceptional points lead to many intriguing phenomena due to the coalescence of both eigenvalues and corresponding eigenvectors, in comparison to Hermitian systems where only eigenvalues degenerate. In this paper, we propose an alternative proposal based on the entropy uncertainty relation (EUR) to detect the exceptional points and identify different phases of the non-Hermitian systems. We first investigate the EUR in a non-Hermitian system and then reveal a general connection between the EUR and the exceptional points of non-Hermitian system. Compared to the unitary Hermitian dynamics, the behaviors of EUR in the non-Hermitian system are well defined in two different ways depending on whether the system is located in unbroken or broken phase regimes. In unbroken phase regime where EUR undergoes an oscillatory behavior, while in broken phase regime where the oscillation of EUR breaks down. In the dynamical limit, we identify the critical phenomena of non-Hermitian systems in terms of the EUR. It is found that the EUR can exactly detect the critical points of non-Hermitian systems beyond PT-(anti-PT) symmetric systems. Finally, we comment on the possible experimental situation.

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Ground-state and thermal entanglements in non-Hermitian XY system with real and imaginary magnetic fields

Zhang

et al. 2023

Quantum Inf Process

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Detection of an unbroken phase of a non-Hermitian system via a Hermitian factorization surface

Cited by 9 publications

References 58 publications

Spectral crossover in non-hermitian spin chains: comparison with random matrix theory

Spectral crossover in non-hermitian spin chains: comparison with random matrix theory

Witnessing criticality in non-Hermitian systems via entopic uncertainty relation

Ground-state and thermal entanglements in non-Hermitian XY system with real and imaginary magnetic fields

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