Local Disturbances Prevent Quantum Systems Reaching Stable Thermal States

Thermalisation does not necessarily occur even following a local quantum quench, challenging established understanding of how these systems evolve. Peter Reimann and Christian Eidecker-Dunkel at Bielefeld University present analytical and numerical evidence that this absence of thermalisation correlates with a sharp breakdown of the eigenstate thermalisation hypothesis (ETH), extending beyond weaker versions previously observed. Their work, focused on XX-spin-chain models with open boundary conditions and supported by observations in XXZ-models, reveals that introducing a single-spin impurity can disrupt the system’s path to equilibrium, particularly when the impurity is located at the chain’s end. This finding provides key insight into the fundamental principles governing non-equilibrium dynamics in many-body quantum systems

Localised quantum disturbances prevent thermalisation and strongly violate eigenstate thermalisation

An absence of thermalisation, previously unseen, has occurred following a local quantum quench, exceeding the performance of prior studies which focused on global quenches and typically only confirmed a weaker version of the eigenstate thermalization hypothesis (wETH). Analytical and numerical results reveal a strong violation of the eigenstate thermalization hypothesis (ETH), and consequently the wETH is also not fulfilled. This represents a significant departure from established understanding of how quantum systems reach equilibrium. XX-spin-chain models with open boundary conditions, and supporting evidence from XXZ-models, indicate that even minor, localised disturbances can prevent a system from settling into a predictable state, challenging the notion that large-scale disruption is necessary for non-equilibrium behaviour. Calculations and simulations revealed this absence of thermalisation even when the disturbance was limited to a single spin impurity positioned at either end or the centre of the chain. The significance of this lies in the established expectation that, given sufficient time, isolated quantum systems should reach a state of thermal equilibrium, characterised by a predictable distribution of energy amongst its many degrees of freedom. This expectation is deeply rooted in statistical mechanics and forms the basis for understanding a wide range of physical phenomena. The observed deviation from this behaviour, induced by a minimal perturbation, necessitates a re-evaluation of the conditions under which thermalisation occurs.

The team found a strong violation of the ETH, meaning even a weaker form, the wETH, was also not satisfied. The ETH posits that the matrix elements of physical observables in the energy eigenbasis of a quantum system are predictable and follow specific statistical distributions. A violation of this hypothesis implies that the system’s dynamics are not governed by the principles of thermalisation, and that the system retains memory of its initial conditions for extended periods. Further analysis of XXZ-models, a more general system incorporating anisotropic interactions, confirmed similar behaviour with end-impurity disturbances, though central placements yielded different results. The XXZ model introduces an additional interaction term, allowing for a more nuanced exploration of the interplay between interactions and thermalisation. These findings expand understanding of non-equilibrium dynamics beyond scenarios requiring large-scale perturbations, but current results do not yet extend to predicting behaviour in systems with more complex interactions or many interacting impurities. Future research will need to address these limitations to provide a more comprehensive picture of non-equilibrium behaviour in quantum systems.

Single spin alterations circumvent thermal equilibrium in a quantum chain

Establishing that thermalisation isn’t inevitable, even with minor disturbances, fundamentally alters expectations for quantum systems. Previously, a lack of equilibrium implied widespread disruption. Now, localised changes can suffice to prevent a system settling into a predictable state. This finding challenges the established eigenstate thermalisation hypothesis (ETH), a cornerstone of understanding how energy distributes within quantum systems. The ETH provides a framework for understanding how a quantum system evolves from an initial state to a thermal equilibrium state, and its breakdown suggests that the standard assumptions underlying this framework are not universally valid. It is important to acknowledge that these results rely on specific, simplified models, namely XX-spin chains with open boundary conditions and deliberately introduced imperfections. The XX-spin chain is a model system in quantum mechanics used to study many-body interactions, and the open boundary conditions allow for the investigation of edge effects and their influence on thermalisation.

A localised disturbance, such as altering a single ‘spin’ within a quantum system, can prevent the expected progression towards thermal equilibrium, a state of predictable energy distribution. This demonstrates a violation of the ETH, meaning even a weaker version of it is not fulfilled, yet the findings remain valuable as they identify the precise conditions under which standard assumptions break down. The concept of a ‘spin’ in this context refers to an intrinsic form of angular momentum possessed by quantum particles, and its alteration represents a localised change in the system’s Hamiltonian. Thermalisation, the process by which a quantum system settles into predictable energy distribution, isn’t always guaranteed. The timescale over which thermalisation is expected to occur depends on the strength of the interactions within the system and the size of the system itself. However, even in systems where thermalisation is expected to be rapid, the introduction of a localised disturbance can significantly delay or even prevent this process.

Large-scale disruption was previously considered necessary for a lack of thermalisation, the process by which a system settles into a predictable state, but altering a single component is now shown to be sufficient to prevent this balance. The absence of thermalisation is accompanied by a breakdown of the ETH, a key principle describing how energy distributes within quantum systems, and even its weaker form is invalidated. The Hamiltonian for the XXZ-chain model includes the term L^-1, which is significant in the calculations. This term represents the inverse of the system’s length and plays a crucial role in determining the energy spectrum and the dynamics of the system. The researchers employed numerical simulations based on time-evolving the system following the introduction of the impurity, and comparing the resulting dynamics to the predictions of the ETH. These simulations involved solving the time-dependent Schrödinger equation for the XX-spin and XXZ-chain models, and analysing the resulting wave function to determine the degree of thermalisation. The analytical results were obtained using perturbation theory and other mathematical techniques to derive expressions for the system’s energy levels and matrix elements.

The research demonstrates that thermalisation, the process by which a quantum system reaches a predictable energy distribution, can be prevented by altering just a single component of the system. This finding challenges the previous understanding that large-scale disruption was required to inhibit thermalisation and indicates a strong violation of the eigenstate thermalization hypothesis. Specifically, the study using XX-spin and XXZ-chain models showed that introducing a single-spin impurity, particularly at the end of the chain, was sufficient to disrupt the expected energy distribution. The authors detail analytical and numerical methods used to explore these dynamics and characterise the breakdown of established principles governing quantum systems.