Boundary Effects on Localization Transitions in a Disordered Non-Hermitian Interacting Fermionic Chain

Kernekoncepter

This study reveals that in a non-Hermitian disordered fermionic chain, boundary conditions significantly influence the system's spectral and localization properties, leading to distinct phases characterized by real or complex eigenspectra and varying degrees of localization.

Resumé

• Bibliographic Information: Suthar, K. (2024). Boundary-driven many-body phase transitions in a non-Hermitian disordered fermionic chain. arXiv preprint arXiv:2410.06160v1.
• Research Objective: To investigate the impact of boundary conditions on the spectral and localization properties of a one-dimensional non-Hermitian interacting fermionic chain in the presence of disorder.
• Methodology: The authors numerically study the Hatano-Nelson model with variable boundary terms. They analyze the complex energy spectrum, inverse participation ratio (IPR), level statistics, and quench dynamics of local particle density, population imbalance, and entanglement entropy.
• Key Findings:
  • The system exhibits boundary-driven spectral transitions from real to complex eigenspectra with increasing boundary coupling strength at weak disorder.
  • The localization properties, characterized by IPR and level statistics, are also sensitive to the boundary conditions, showing distinct behavior for open and periodic boundary conditions.
  • Strong disorder leads to a many-body localized (MBL) phase characterized by a real eigenspectrum, localized eigenstates, and logarithmic growth of entanglement entropy, irrespective of the boundary conditions.
• Main Conclusions:
  • Boundary conditions play a crucial role in determining the spectral and localization properties of non-Hermitian disordered systems.
  • The interplay of non-Hermiticity, disorder, and boundary effects leads to a rich phase diagram with distinct localized and extended phases.
• Significance: This study provides insights into the behavior of non-Hermitian systems, which are gaining increasing attention due to their relevance to open and dissipative quantum systems.
• Limitations and Future Research: The study focuses on a specific one-dimensional model. Exploring higher-dimensional systems and different types of non-Hermitian terms would be interesting avenues for future research.

Statistik

The critical disorder strength for the transition to the MBL phase is approximately Wc ≈ 4.
In the unidirectional hopping case (JL = 0) with open boundary conditions (δ = 0), the biorthogonal IPR (IB) approaches unity at an infinitesimal disorder strength.
The average complex level-spacing ratio (⟨r⟩) for the Gaussian orthogonal ensemble (GOE) distribution is 0.569, while for the Ginibre distribution, it is approximately 0.74.
In the strong disorder regime (W = 14), the entanglement entropy exhibits logarithmic growth, consistent with the characteristics of the MBL phase.

Citater

"The interplay of the effects of system size and boundary perturbations unveiled the sensitivity of the boundary for single-particle systems."
"The biorthogonal IPR includes the nonorthogonality of different eigenstates, thus captures the non-Hermitian effects of interacting disordered systems."
"The strong disorder suppresses the imaginary parts of the complex energies and dynamically stabilizes the system."
"The entanglement entropy of the initial wave-packet with non-reciprocal hopping does not spread as in the Hermitian case (in particular at weak disorder), rather slides as determined by the asymmetry in the hopping."

Vigtigste indsigter udtrukket fra

Boundary-driven many-body phase transitions in a non-Hermitian disordered fermionic chain

by Kuldeep Suth... kl. arxiv.org 10-10-2024

https://arxiv.org/pdf/2410.06160.pdf

Dybere Forespørgsler

How do these findings extend to higher-dimensional non-Hermitian systems, where the interplay of boundary effects and disorder can be even richer?

Extending these findings to higher dimensions presents exciting possibilities and challenges:
Amplified Complexity:

Boundary Geometry: In higher dimensions, the boundary is no longer just two end points but a surface (or higher-dimensional manifold). The shape and topology of this boundary become crucial, potentially leading to anisotropic skin effects and richer localization patterns.
Disorder Landscapes: Disorder in higher dimensions can be more intricate. We could have different types of disorder (e.g., correlated vs. uncorrelated) and varying disorder strengths in different spatial directions. This could result in complex localization landscapes with regions of varying localization lengths.
Potential New Phenomena:

Higher-Order Skin Effects: Theoretical studies suggest the possibility of higher-order skin effects in higher dimensions, where eigenstates localize not just at the boundary but in specific sub-regions of the boundary.
Topological Non-Hermitian Phases: The interplay of topology, non-Hermiticity, and disorder in higher dimensions could give rise to novel topological phases with unique edge states and transport properties.
Challenges:

Computational Cost: Numerical simulations become significantly more demanding in higher dimensions, limiting system sizes and the range of parameters that can be explored.
Analytical Approaches: Analytical solutions are often intractable in higher-dimensional disordered systems, making it challenging to develop a comprehensive theoretical understanding.
Research Directions:

Developing efficient numerical methods for studying higher-dimensional non-Hermitian disordered systems.
Exploring the role of boundary geometry and topology on localization transitions.
Investigating the interplay of different types of disorder with non-Hermiticity.
Searching for signatures of higher-order skin effects and novel topological phases.

Could the presence of interactions, which are known to be crucial for MBL in Hermitian systems, modify the observed boundary-driven transitions in the non-Hermitian case?

Yes, interactions can significantly modify the boundary-driven transitions in non-Hermitian systems:
Competition Between Localization Mechanisms:

NHSE vs. Interaction-Driven Localization: Interactions can compete with the non-Hermitian skin effect (NHSE). Strong interactions might suppress NHSE by promoting localization in the bulk, even at weak disorder. Conversely, strong non-Hermiticity might hinder the formation of a well-defined MBL phase.
Entanglement and Correlations: Interactions introduce entanglement and correlations between particles, which can alter the nature of localization. In Hermitian systems, interactions are essential for establishing MBL. In the non-Hermitian case, they might lead to new types of entangled localized states.
Potential Modifications to Transitions:

Shifted Critical Points: Interactions could shift the critical disorder strengths for the observed spectral and localization transitions.
New Phase Boundaries: The phase diagram might include new regions corresponding to phases dominated by interaction effects, such as an interaction-driven MBL phase coexisting with NHSE.
Modified Dynamics: The dynamics of entanglement growth and relaxation could be significantly altered due to the interplay of interactions and non-Hermiticity.
Investigating Interaction Effects:

Studying systems with varying interaction strengths to understand the competition between NHSE and interaction-driven localization.
Analyzing the entanglement structure of eigenstates to identify signatures of interaction-induced modifications to localization.
Exploring the dynamics of entanglement and other observables to characterize the interplay of interactions and non-Hermiticity.

What are the potential implications of these findings for understanding and controlling transport phenomena in open and dissipative quantum systems, which are often modeled using non-Hermitian Hamiltonians?

These findings have significant implications for transport in open and dissipative systems:
Boundary Engineering for Transport Control:

Selective Localization and Filtering: By tuning boundary parameters, we can potentially localize excitations in specific regions of a system, acting as a spatial filter for quantum information or energy.
Directional Transport: Non-reciprocal hopping, often present in non-Hermitian systems, can be exploited to achieve directional transport, where excitations flow preferentially in one direction. This has potential applications in quantum devices and energy harvesting.
Understanding Dissipation-Induced Phenomena:

Robustness of Transport: The interplay of disorder and non-Hermiticity can lead to robust transport channels that are protected against backscattering and localization. This is relevant for designing efficient energy or information transfer pathways in the presence of imperfections.
Dissipation-Driven Transitions: Dissipation, modeled by non-Hermiticity, can drive transitions between different transport regimes. Understanding these transitions is crucial for controlling the flow of excitations in open systems.
Applications in Various Fields:

Quantum Information Processing: Designing robust quantum memories or channels for transmitting quantum information in the presence of noise and dissipation.
Light Harvesting: Understanding and optimizing energy transfer processes in photosynthetic complexes, which are inherently open and dissipative systems.
Topological Photonics and Acoustics: Developing devices with robust and unidirectional transport properties for applications in optical communication and sensing.
Further Research:

Investigating the role of interactions in transport phenomena in non-Hermitian disordered systems.
Exploring the potential of boundary engineering for controlling the flow of excitations.
Developing theoretical frameworks to describe and predict transport properties in open and dissipative systems.