Periodic Reporting for period 4 - LoCoMacro (Local Control of Macroscopic Properties in Isolated Many-body Quantum Systems)
Periodo di rendicontazione: 2023-07-01 al 2024-10-31
A fascinating principle underlies our understanding of how large systems behave: despite being made up of countless tiny particles, the overall properties of many systems, like gases, liquids, or solids, can often be described using just a few basic parameters, such as temperature. By adjusting these parameters, one can change how a material behaves and even switch it between different phases, like turning water into ice.
Usually, achieving such changes requires influencing the entire system. But in some special cases, a small, localized disturbance can have a big impact. A common example is supercooled water, which can stay liquid even below freezing point, until it touches a tiny piece of ice, which causes the whole thing to suddenly freeze. This shows how a small local change can trigger a global transformation.
Things get much more complex when we look at systems that are not in equilibrium. If interactions with their surroundings can be neglected, these systems evolve purely according to the laws of quantum mechanics. Even though they cannot fully settle into a traditional equilibrium state, it was found that they often behave as if they are in an exotic or "effective" equilibrium, especially when observed locally.
One well-studied case is the so-called quantum quench, where a system is suddenly changed (like flipping a switch on some global setting) and then allowed to evolve. In homogeneous one-dimensional systems, the long-term behavior after a quench is now fairly well understood.
LoCoMacro took this a step further. It asked: What happens if the disturbance is not global, but highly localized? Can small, local changes still affect the system as a whole when it is out of equilibrium?
Through this lens, LoCoMacro explored how inhomogeneities (small irregularities or local perturbations) can influence the large-scale behavior of quantum systems over time. The project’s key achievements include:
- Showing new ways to create exotic quantum states of matter.
- Designing methods to locally control large-scale behavior in out-of-equilibrium systems.
- Discovering conditions where large-scale entanglement (a core feature of quantum mechanics) can emerge, potentially useful for future technologies like quantum computing.
The project focused on answering several key questions:
(a) What does the system look like at late times after introducing inhomogeneities?
(b) Can we calculate exactly how properties like correlations and entanglement evolve over time?
(c) Which physical quantities remain conserved and shape the system's long-term behavior?
(d) How and when do quantum systems reach thermal-like states, or fail to?
(e) What role do symmetries play in how the system evolves?
(f) How do quantum measurements affect what we observe locally in such systems?
(g) Can subsystems become multipartite entangled in isolated many-body systems?
By addressing these questions, LoCoMacro has helped deepen our understanding of how local actions can influence entire quantum systems, offering not only fundamental insights into quantum physics but also opening doors to potential applications in quantum technologies.
Usually, achieving such changes requires influencing the entire system. But in some special cases, a small, localized disturbance can have a big impact. A common example is supercooled water, which can stay liquid even below freezing point, until it touches a tiny piece of ice, which causes the whole thing to suddenly freeze. This shows how a small local change can trigger a global transformation.
Things get much more complex when we look at systems that are not in equilibrium. If interactions with their surroundings can be neglected, these systems evolve purely according to the laws of quantum mechanics. Even though they cannot fully settle into a traditional equilibrium state, it was found that they often behave as if they are in an exotic or "effective" equilibrium, especially when observed locally.
One well-studied case is the so-called quantum quench, where a system is suddenly changed (like flipping a switch on some global setting) and then allowed to evolve. In homogeneous one-dimensional systems, the long-term behavior after a quench is now fairly well understood.
LoCoMacro took this a step further. It asked: What happens if the disturbance is not global, but highly localized? Can small, local changes still affect the system as a whole when it is out of equilibrium?
Through this lens, LoCoMacro explored how inhomogeneities (small irregularities or local perturbations) can influence the large-scale behavior of quantum systems over time. The project’s key achievements include:
- Showing new ways to create exotic quantum states of matter.
- Designing methods to locally control large-scale behavior in out-of-equilibrium systems.
- Discovering conditions where large-scale entanglement (a core feature of quantum mechanics) can emerge, potentially useful for future technologies like quantum computing.
The project focused on answering several key questions:
(a) What does the system look like at late times after introducing inhomogeneities?
(b) Can we calculate exactly how properties like correlations and entanglement evolve over time?
(c) Which physical quantities remain conserved and shape the system's long-term behavior?
(d) How and when do quantum systems reach thermal-like states, or fail to?
(e) What role do symmetries play in how the system evolves?
(f) How do quantum measurements affect what we observe locally in such systems?
(g) Can subsystems become multipartite entangled in isolated many-body systems?
By addressing these questions, LoCoMacro has helped deepen our understanding of how local actions can influence entire quantum systems, offering not only fundamental insights into quantum physics but also opening doors to potential applications in quantum technologies.
LoCoMacro made several important breakthroughs, particularly in understanding how local changes affect global behavior in quantum systems:
- It developed a new phase-space formulation of quantum mechanics for a particular class of isolated spin systems.
- It introduced and solved a novel interacting model showing quantum jamming, where particles become immobile due to internal constraints.
- It uncovered purely quantum features of this jamming and revealed semilocal conservation laws, a new type of constraint influencing how information spreads.
- It identified scenarios where local perturbations have lasting, macroscopic effects.
- It showed that long-range correlations can persist and that macroscopic quantum states (not explainable as simple sums of microscopic effects) can naturally emerge.
LoCoMacro focused on one-dimensional quantum systems, exploring how different kinds of inhomogeneities (local irregularities) affect them. The project studied three key scenarios:
(1) Joining two different states (bipartitioning protocols).
-Identified invariant subspaces in non-interacting systems, allowing an exact formulation of generalized hydrodynamics including quantum effects.
-In interacting systems, models like the dual folded XXZ chain revealed how kinetic constraints create discontinuities in physical quantities.
-Explored systems with different initial temperatures, showing that the interface between ordered and disordered regions remains highly correlated, a universal feature across models.
(2) Local perturbations in homogeneous systems.
-Found that even brief local changes can cause permanent effects far from the disturbance.
-Linked this to semilocal conserved charges, leading to new forms of statistical models and challenging standard thermalization theories.
- Observed similar behavior in quantum scars, exotic states that resist thermal equilibrium.
(3) local perturbations in jammed quantum states
- Studied systems in jammed quantum states, where particle motion is constrained.
- Showed that local perturbations trigger macroscopic effects, which can be explained by kinetic constraints amplifying quantum behavior at large scales.
In addition to dynamics, LoCoMacro also investigated unusual states that remain stable over time:
(a) Rare Area-Law States. Classified Hamiltonians by their ability to host excited states with low entanglement (area-law scaling). These are rare and vanish under certain conditions, implying the absence of local conserved charges with energy gaps.
(b) Highly entangled states with universal behavior. Identified states with high entropy and robust tripartite information, a measure of complex entanglement that remains nonzero even when traditional expectations suggest it should vanish.
(c) Energy-Filtered States. Studied effectively stationary states with low energy variance and non-clustering correlations, properties reminiscent of quantum scars.
- It developed a new phase-space formulation of quantum mechanics for a particular class of isolated spin systems.
- It introduced and solved a novel interacting model showing quantum jamming, where particles become immobile due to internal constraints.
- It uncovered purely quantum features of this jamming and revealed semilocal conservation laws, a new type of constraint influencing how information spreads.
- It identified scenarios where local perturbations have lasting, macroscopic effects.
- It showed that long-range correlations can persist and that macroscopic quantum states (not explainable as simple sums of microscopic effects) can naturally emerge.
LoCoMacro focused on one-dimensional quantum systems, exploring how different kinds of inhomogeneities (local irregularities) affect them. The project studied three key scenarios:
(1) Joining two different states (bipartitioning protocols).
-Identified invariant subspaces in non-interacting systems, allowing an exact formulation of generalized hydrodynamics including quantum effects.
-In interacting systems, models like the dual folded XXZ chain revealed how kinetic constraints create discontinuities in physical quantities.
-Explored systems with different initial temperatures, showing that the interface between ordered and disordered regions remains highly correlated, a universal feature across models.
(2) Local perturbations in homogeneous systems.
-Found that even brief local changes can cause permanent effects far from the disturbance.
-Linked this to semilocal conserved charges, leading to new forms of statistical models and challenging standard thermalization theories.
- Observed similar behavior in quantum scars, exotic states that resist thermal equilibrium.
(3) local perturbations in jammed quantum states
- Studied systems in jammed quantum states, where particle motion is constrained.
- Showed that local perturbations trigger macroscopic effects, which can be explained by kinetic constraints amplifying quantum behavior at large scales.
In addition to dynamics, LoCoMacro also investigated unusual states that remain stable over time:
(a) Rare Area-Law States. Classified Hamiltonians by their ability to host excited states with low entanglement (area-law scaling). These are rare and vanish under certain conditions, implying the absence of local conserved charges with energy gaps.
(b) Highly entangled states with universal behavior. Identified states with high entropy and robust tripartite information, a measure of complex entanglement that remains nonzero even when traditional expectations suggest it should vanish.
(c) Energy-Filtered States. Studied effectively stationary states with low energy variance and non-clustering correlations, properties reminiscent of quantum scars.
Even after the official conclusion of the LoCoMacro project, several research efforts, either recently completed or still underway, continue to build on its foundation. Some of the most important of these are focused on a fascinating phenomenon: the breakdown of clustering, a principle in physics that usually says distant parts of a system become uncorrelated.
In one line of research, we are exploring interacting integrable systems, quantum systems where the long-term behavior is usually well described by a powerful framework known as generalized hydrodynamics. This theory works by tracking certain mathematical quantities called root densities. However, our findings suggest that in some cases, this approach isn’t enough to fully capture what is going on. These exceptions may point to deeper and still undiscovered physical principles.
In another study, we looked at what happens when a localized disturbance is introduced into a system that starts in a symmetry-breaking ground state, which is a highly ordered state where the system "chooses" one of many possible equivalent configurations. We found that quantum correlations behave in unexpected ways, indicating that even small local actions can disrupt or reshape the entire structure of the system’s correlations.
In one line of research, we are exploring interacting integrable systems, quantum systems where the long-term behavior is usually well described by a powerful framework known as generalized hydrodynamics. This theory works by tracking certain mathematical quantities called root densities. However, our findings suggest that in some cases, this approach isn’t enough to fully capture what is going on. These exceptions may point to deeper and still undiscovered physical principles.
In another study, we looked at what happens when a localized disturbance is introduced into a system that starts in a symmetry-breaking ground state, which is a highly ordered state where the system "chooses" one of many possible equivalent configurations. We found that quantum correlations behave in unexpected ways, indicating that even small local actions can disrupt or reshape the entire structure of the system’s correlations.