Quantum Spin Model Exhibits Localisation Transition with Logarithmic Disorder Growth.

Research demonstrates the Sun model, a Hamiltonian system of interacting spins on a half-line, exhibits localisation for coupling strengths less than a critical value. This confirms it as a genuine one-dimensional model where disorder grows logarithmically with system size, impacting spectral statistics which become Poissonian.

The behaviour of quantum systems when subjected to disorder remains a central question in condensed matter physics, with implications for understanding materials exhibiting unusual electronic properties. Recent research focuses on the phenomenon of many-body localisation (MBL), where interactions between particles can halt the spread of quantum information, even in systems that would normally exhibit chaotic behaviour. Wojciech De Roeck and Amirali Hannani, both from the Institute for Theoretical Physics at KU Leuven, investigate this in their paper, ‘Many-body Localization and Poisson statistics in the Quantum Sun model’. Their work provides rigorous mathematical proof of localisation and a specific statistical signature, namely Poisson statistics, within a simplified, yet representative, model known as the Quantum Sun model. This model, characterised by interacting spins arranged along a half-line and coupled to an external environment, is particularly interesting because the amount of disorder it contains scales modestly with system size, allowing for more tractable theoretical analysis.

Many-body localisation (MBL) consistently emerges as a central theme within the study of disordered quantum systems, prompting ongoing investigation into the precise conditions governing its emergence and persistence. Disordered systems, characterised by a lack of translational symmetry, present unique challenges to conventional understandings of quantum behaviour, and MBL represents a departure from the expectation of thermalisation in interacting systems. Thermalisation, in this context, refers to the process by which a quantum system reaches equilibrium and its properties become predictable based on temperature. Scientists investigate the interplay between disorder, interactions and quantum many-body effects to understand how localisation can arise and be sustained, offering insights into the fundamental principles governing complex quantum phenomena.

A significant portion of this research utilises random matrix theory, a mathematical framework employing random matrices to model the statistical properties of complex systems, to understand the behaviour of these systems. This approach allows researchers to analyse the energy levels and wavefunctions of disordered systems without needing to solve the full quantum mechanical problem, providing valuable insights into their properties.

The foundational work on localisation, particularly Anderson localisation, provides a crucial basis for understanding MBL. Anderson localisation, discovered in 1958, describes the localisation of non-interacting electrons in a disordered potential. Researchers investigate the effects of interactions on the localisation length – a measure of how far a quantum particle can travel before being localised – and the critical behaviour of disordered systems, revealing the complex interplay between disorder and interactions in determining the fate of quantum states. Critical behaviour refers to the system’s response near a phase transition, where small changes in parameters can lead to dramatic changes in its properties.

Scientists explore the use of MBL to create robust quantum memories, protecting quantum information from decoherence and enabling long-distance quantum communication. Decoherence, the loss of quantum information due to interaction with the environment, is a major obstacle to building practical quantum technologies. They investigate the use of localised states as qubits – the quantum analogue of classical bits – demonstrating that MBL can provide a natural mechanism for protecting quantum information from environmental noise.

Scientists explore the use of MBL to design novel materials with unique properties, such as enhanced conductivity or magnetism, recognising the potential of localised quantum states to enable new functionalities. They investigate the use of MBL to create materials with tailored electronic and magnetic properties, potentially leading to advancements in areas such as energy storage and spintronics.

Researchers investigate the relationship between MBL and the absence of thermalisation, revealing the fundamental principles governing the behaviour of interacting quantum systems. They explore the role of integrability – a property of systems with an infinite number of conserved quantities – and the absence of quasiparticle excitations – emergent particles that simplify the description of complex systems – in stabilising localised states and preventing thermalisation. This relationship extends to the absence of ergodicity – the property of a system exploring all accessible states – and diffusion, further solidifying the unique characteristics of MBL systems.

Scientists explore the use of MBL to create robust quantum sensors, protecting quantum information from environmental noise and enabling high-precision measurements. By leveraging the stability of localised states, these sensors could achieve unprecedented sensitivity and accuracy in applications such as medical imaging and materials science.

Researchers investigate the effects of dimensionality on the stability of MBL, revealing the challenges of maintaining localisation in higher dimensions due to the increased availability of phase space. They explore the role of long-range interactions and correlations in stabilising localised states in higher dimensions, potentially extending the applicability of MBL to a wider range of systems.

Scientists explore the use of MBL to design novel materials with enhanced optical properties, such as strong light absorption or emission, recognising the potential of localised quantum states to enable new functionalities. They investigate the use of localised states as building blocks for creating materials with tailored optical properties, potentially leading to advancements in areas such as solar energy harvesting and optoelectronics.

Scientists explore the effects of different types of disorder on the stability of MBL, revealing the sensitivity of MBL to the specific details of the disorder. They investigate the effects of long-range correlations, quasiperiodic potentials – disorder with a specific mathematical structure – and random matrix potentials on the localisation length and the critical behaviour of disordered systems.