Ergodicity breaking in the Spin-1 U(1) Quantum Link Model
(2025) PHYM01 20251Mathematical Physics
Department of Physics
- Abstract
- Classical and quantum mechanics describe particle interactions fundamentally differently, yet isolated many-body systems generally thermalise in both descriptions. Recent studies using quantum simulators have observed exceptions to this, where the memory of special initial states is retained through anomalously long-lived revivals. The non-ergodic findings could be explained by Quantum Many-Body Scars, and furthermore, the isolated system first exhibiting such behaviour could be described by a model relevant to high-energy physics, namely the spin-1/2 U(1) Quantum Link Model. In addition to scars, this model exhibits Hilbert Space Fragmentation, a related instance of ergodicity breaking. As the electrostatic potential is irrelevant for... (More)
- Classical and quantum mechanics describe particle interactions fundamentally differently, yet isolated many-body systems generally thermalise in both descriptions. Recent studies using quantum simulators have observed exceptions to this, where the memory of special initial states is retained through anomalously long-lived revivals. The non-ergodic findings could be explained by Quantum Many-Body Scars, and furthermore, the isolated system first exhibiting such behaviour could be described by a model relevant to high-energy physics, namely the spin-1/2 U(1) Quantum Link Model. In addition to scars, this model exhibits Hilbert Space Fragmentation, a related instance of ergodicity breaking. As the electrostatic potential is irrelevant for spin-1/2, this thesis aims to unveil its impact as the phase diagram is laid out for spin-1. The dynamics are found to be similar for S=1/2 and S=1; with scarring in the ergodic regime and an array of effective models emerging with fragmentation for large mass μ and electrostatic potential g. These phases of ergodicity breaking provide a potential testing ground for experiments aimed at probing lattice gauge theories with analogue quantum simulators. (Less)
- Popular Abstract
- The earth persistent orbit around the sun and a magnet's constant magnetism are two examples of the fact that most interacting systems reach an equilibrium. In this thesis, however, non-equilibrium phenomena are found in a quantum system.
For most initial trajectories, a single particle bouncing around in a box will cover almost all of the space after a long time. However, for some starting trajectories, the particle bounces around in a perfectly periodic orbit. A window's logo consistently bumping on the boundary centres of the computer screen is one example of such an orbit. If one adds many particles with different initial trajectories, the periodicity is, nonetheless, no longer to be found as particles bounce and scatter all around,... (More) - The earth persistent orbit around the sun and a magnet's constant magnetism are two examples of the fact that most interacting systems reach an equilibrium. In this thesis, however, non-equilibrium phenomena are found in a quantum system.
For most initial trajectories, a single particle bouncing around in a box will cover almost all of the space after a long time. However, for some starting trajectories, the particle bounces around in a perfectly periodic orbit. A window's logo consistently bumping on the boundary centres of the computer screen is one example of such an orbit. If one adds many particles with different initial trajectories, the periodicity is, nonetheless, no longer to be found as particles bounce and scatter all around, causing them to spread evenly in space. Particle configurations can be assumed equally probable, and the speeds at which they travel are only governed by the system's temperature, i.e. energy.
In quantum mechanics, a moving particle is described by an advancing wave peak where the top corresponds to the high probability of finding the particle at that location. In contrast to classical non-linear and deterministic motion, probabilistic quantum systems are governed by linear equations. Nonetheless, for many interacting particles, the assumption of equally probable configurations generally holds for isolated systems in both descriptions. However, not always. It has been found that there exist many-body systems exhibiting periodic trajectories. This periodicity prevents the system from locally reaching an equilibrium. Furthermore, such systems retain a memory of the initial state, as its periodicity makes it more probable than non-periodic states with equal energy.
This emergence of a non-uniform probability is called breaking of ergodicity, and two such phenomena, dubbed Quantum Many-Body Scarring and Hilbert Space Fragmentation, are investigated in the following thesis. Their existence in the model of interest has been recorded using simulations on a classical computer, but could correspondingly have been conducted experimentally on an isolated quantum system by the usage of lasers and gases or, in other words, by the usage of an analogue quantum simulator.
Being able to keep a memory of an initially prepared state is fundamental to the development of quantum simulation. So that one can observe and control how a given state changes in time. But foremost, the study of ergodicity breaking is a study on the nature of particle interaction and systems reaching or not reaching an equilibrium. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/9198471
- author
- Nygren, Lothar LU
- supervisor
- organization
- alternative title
- Icke-jämviktsdynamik i en spinmodell – Kvantärr och Hilbertrumsfragmentering
- course
- PHYM01 20251
- year
- 2025
- type
- H2 - Master's Degree (Two Years)
- subject
- keywords
- Ergodicity breaking, Non-equilibrium dynamics, Quantum Many-Body Scars, Hilbert Space Fragmentation, Many-body physics
- language
- English
- id
- 9198471
- date added to LUP
- 2025-06-17 16:03:08
- date last changed
- 2025-06-17 16:03:08
@misc{9198471,
abstract = {{Classical and quantum mechanics describe particle interactions fundamentally differently, yet isolated many-body systems generally thermalise in both descriptions. Recent studies using quantum simulators have observed exceptions to this, where the memory of special initial states is retained through anomalously long-lived revivals. The non-ergodic findings could be explained by Quantum Many-Body Scars, and furthermore, the isolated system first exhibiting such behaviour could be described by a model relevant to high-energy physics, namely the spin-1/2 U(1) Quantum Link Model. In addition to scars, this model exhibits Hilbert Space Fragmentation, a related instance of ergodicity breaking. As the electrostatic potential is irrelevant for spin-1/2, this thesis aims to unveil its impact as the phase diagram is laid out for spin-1. The dynamics are found to be similar for S=1/2 and S=1; with scarring in the ergodic regime and an array of effective models emerging with fragmentation for large mass μ and electrostatic potential g. These phases of ergodicity breaking provide a potential testing ground for experiments aimed at probing lattice gauge theories with analogue quantum simulators.}},
author = {{Nygren, Lothar}},
language = {{eng}},
note = {{Student Paper}},
title = {{Ergodicity breaking in the Spin-1 U(1) Quantum Link Model}},
year = {{2025}},
}