Researchers Reveal Hydrodynamic Limits in Quenched XY Spin Chains and Reduced Fidelities

The behaviour of quantum systems following a sudden change, or ‘quench’, remains a fundamental question in physics, and recent work by Gilles Parez from Laboratoire d’Annecy-le-Vieux de Physique Théorique, and Vincenzo Alba from the Università di Pisa, et al., sheds new light on this complex process. The researchers investigate how quickly a quantum system ‘forgets’ its initial state after a quench, using a measure called reduced fidelity, and reveal surprising connections between this ‘forgetting’ and the emergence of distinct quantum phases. Their findings demonstrate that the rate of change in this fidelity exhibits a unique ‘staircase’ pattern, indicative of quasiparticles moving at varying speeds, and even predict the possibility of ‘dynamical quantum phase transitions’, abrupt changes in behaviour without any change in external parameters. Importantly, this research also provides a theoretical framework for understanding the intriguing ‘Mpemba effect’, where, counterintuitively, a hot system can sometimes cool faster than a cold one, offering a novel quantum perspective on this long-standing puzzle.

Researchers investigate the time evolution of states within a subregion of a quantum system, specifically examining how closely the time-dependent state of that region resembles its initial state and its state at a very long time in the future. These measures, termed the reduced Loschmidt echo and the final-state fidelity, provide insights into how quickly the system loses memory of its initial conditions and evolves towards a new equilibrium. The study concentrates on quenches, sudden changes in the system’s parameters, within instances of the XY spin chain, a frequently used model in condensed matter physics.

Loschmidt Echo Detects Dynamical Quantum Transitions

This research details an investigation into dynamical quantum phase transitions and the quantum Mpemba effect, utilizing the Loschmidt echo to detect these transitions. The Loschmidt echo measures the overlap between the initial and time-evolved states after a quench; a sharp dip signals a phase transition. The study explores the connection between the echo, periodic revivals of the initial state, and the breakdown of the quasiparticle picture in interacting systems. It also delves into the quantum Mpemba effect, a counterintuitive phenomenon where a quantum system can reach equilibrium faster under certain conditions, analogous to the classical effect of hot water freezing faster than cold water.

Key findings reveal that the quantum Mpemba effect is linked to the initial state, the system’s symmetry, and the breakdown of the quasiparticle picture, representing a fundamentally different pathway to equilibrium. The research utilizes theoretical tools such as Rényi entropies and full counting statistics to quantify entanglement and fluctuations, and symmetry-resolved entanglement to understand the Mpemba effect. Recent experimental observations of the quantum Mpemba effect in quantum simulations and cold atom experiments provide evidence for the theoretical predictions. The research extends to dissipative systems, investigating how dissipation can either enhance or suppress the Mpemba effect.

Subregional Loschmidt Echo Reveals Memory Loss

Researchers investigated the out-of-equilibrium dynamics of quantum systems following a sudden change in their governing rules, known as a quantum quench. The team focused on quantifying how quickly a system loses memory of its initial state, using the reduced Loschmidt echo and the final-state fidelity. These quantities assess the overlap between the current state of a subsystem and its initial or final states, providing insights into the system’s evolution and potential phase transitions. The study extends the concept of the standard Loschmidt echo to focus on specific subregions within the system, offering a more experimentally accessible approach.

Experiments revealed that the reduced Loschmidt echo exhibits a complex structure, particularly when considering large systems and long timescales. For certain quenches, the echo features an infinite sequence of nested lightcones, indicating that entangled quasiparticles with a wide range of velocities influence the system’s evolution. This leads to a “staircase” pattern of sharp changes in the time-derivative of the fidelity, signaling significant shifts in the system’s behaviour. Interestingly, in a sub-hydrodynamic regime, the echo displays cusp-like singularities, reminiscent of dynamical quantum phase transitions.

Researchers propose criteria for identifying these transitions and predicting the specific times at which these singularities appear. Results demonstrate that the final-state fidelity provides a valuable tool for detecting the quantum Mpemba effect, offering a new way to study non-equilibrium dynamics. Data confirms that the quasiparticle picture accurately predicts the behaviour of entanglement and information after a quench, even in complex many-body systems.

Entanglement Spreads Via Nested Lightcones

This research investigates how quantum systems evolve after a sudden change in their governing rules, known as a quantum quench. The study focuses on quantum fidelities, which measure the overlap between the system’s initial and time-evolved states, and specifically examines the reduced Loschmidt echo and final-state fidelity. Results demonstrate that, under certain conditions, the dynamics of these fidelities can be understood through a quasiparticle picture, where entanglement spreads via the ballistic propagation of entangled quasiparticles. Interestingly, the researchers found that some quenches exhibit a complex structure in the time-derivative of the fidelity, featuring an infinite series of nested lightcones and cusp-like singularities, providing insight into the system’s response to the sudden change. Furthermore, the final-state fidelity proves to be a valuable tool for detecting the quantum Mpemba effect, a counterintuitive phenomenon where a system can reach equilibrium faster under certain conditions.