Classical and quantum physics of strongly constrained systems

V. Pažma

Benjamin Everest

This thesis studies non-equilibrium open quantum systems where the dissipation is crucial to the achievement of novel physical regimes. We focus on atomic systems which allow for the coupling of a ground state to a Rydberg state, relying on the strong interactions between Rydberg atoms to produce the collective behaviour that we aim to investigate. For atoms in an optical lattice undergoing standard dissipation forms, e.g. loss and dephasing, we find these simple settings allow for the production of models contained in the non-equilibrium realm. \nWe start by looking at a system with engineered pair dissipation on a one-dimensional lattice. When the dissipation is strong relative to a tunnelling process it creates a quantum Zeno effect which projects the system onto a Zeno-subspace. This subspace is found to contain complexes which experience a binding due to the dissipation. The properties of these complexes are found to feature spin-orbit coupling and, in certain instances, a flat band. \nWe then study what kinetically constrained models (KCMs) can be reproduced in a lattice system. KCMs are models which typically feature trivial steady states, but a complex relaxation dynamics. These models appear in the fields of glasses and soft matter physics. We find a general framework for the consideration of a quantum Hamiltonian and a classical potential with strong dephasing noise. We then focus on a model mimicking volume excluded KCMs and find characteristic constrained behaviour, such as ergodicity breaking. \nWe apply this framework to the decay of a many-body localised state in an open system with interactions in which we find the decay to be classical in the two interaction limits. For weak interactions, it follows a stretched exponential form due to pair relaxation, while for strong interactions the decay follows a compressed exponential, now being modelled as an Avrami process due to the correlated relaxation. We also find that on-site loss only affects the strong interacting limit. \nWe then move on to the study of universal non-equilibrium behaviour in the directed percolation (DP) class. We consider on-site atomic loss and gain as a substitute for the standard decay channel. We show that this replaces the absorbing state with an enlarged absorbing space, leading to a loss of the DP transition at lower average densities. This class of DP-like systems has received little study, and we present a method of experimentally realising it in current set-ups. \nWe finish with a look at a quantum DP model, where we consider its quantum and classical limits. We find that the transition changes from first to second order as the system becomes more classical, featuring a bi-critical point. We then numerically demonstrate that the same transitions are visible in idealised and Rydberg models.

Singh, Shobhna

Constrained models play a pivotal role in condensed matter physics by capturing essential features of strongly interacting many-body systems. These models impose local or global restrictions that mirror real physical constraints, enabling the study of complex emergent behaviors. For instance, hard-core dimer models reflect physical systems with strong local constraints due to repulsive interactions. Similarly, loop models, vertex models, and height representations provide constrained frameworks that reveal rich phase structures and critical phenomena. In quantum systems, constraints often emerge naturally from microscopic Hamiltonian and lead to phenomena such as fractionalization and quantum spin liquids. Constrained models act as fertile grounds for theoretical insight, enabling exact solutions, mapping to field theories, and exploring universal behaviors. They also bridge condensed matter with disciplines like statistical mechanics, combinatorics, and computational complexity, offering a unified language to study order, disorder, and transitions in systems ranging from magnets to artificial spin ices and cold atomic gases. This thesis investigates critical phenomena, strongly correlated models, and optimization problems on aperiodic lattices, with a particular focus on NP-hard problems, dimer models, and their classical and quantum variants. Moving beyond periodic lattices like square and honeycomb structures, this research delves into the less understood area of aperiodic systems, such as quasicrystals, which exhibit long-range order without translational symmetry. These structures challenge traditional paradigms of condensed matter physics and open avenues for discovering new critical behaviors. I present original contributions that combine analytical methods and numerical algorithms to study constrained systems on quasicrystalline tilings. These include the solution of NP-hard optimization problems like the Hamiltonian cycle on Ammann-Beenker tilings, an energy-based worm algorithm for simulating classical dimers on random graphs and modified Penrose tilings, and the analytical solution of the dimer partition function on the newly discovered aperiodic Spectre tiling. I further extend the study to quantum systems by analytically investigating the quantum dimer model (QDM) on the Spectre tiling and numerically analyzing it on the Ammann-Beenker tiling, revealing distinctive ground-state properties and quantum phase transitions that arise due to aperiodicity and local tiling constraints. This work builds interdisciplinary bridges between condensed matter physics, graph theory, and computational complexity. It also sheds light on the feasibility and limitations of transferring universal results from periodic systems to aperiodic ones.

H Jensen, Heinz Koppe

Beatriz Olmos, Igor Lesanovsky, Juan P. Garrahan

We explore the relaxation dynamics of quantum many-body systems that undergo purely dissipative dynamics through non-classical jump operators that can establish quantum coherence. Our goal is to shed light on the differences in the relaxation dynamics that arise in comparison to systems evolving via classical rate equations. In particular, we focus on a scenario where both quantum and classical dissipative evolution lead to a stationary state with the same values of diagonal or "classical" observables. As a basis for illustrating our ideas we use spin systems whose dynamics becomes correlated and complex due to dynamical constraints, inspired by kinetically constrained models (KCMs) of classical glasses. We show that in the quantum case the relaxation can be orders of magnitude slower than the classical one due to the presence of quantum coherences. Aspects of these idealized quantum KCMs become manifest in a strongly interacting Rydberg gas under electromagnetically induced transparency (EIT) conditions in an appropriate limit. Beyond revealing a link between this Rydberg gas and the rather abstract dissipative KCMs of quantum glassy systems, our study sheds light on the limitations of the use of classical rate equations for capturing the non-equilibrium behavior of this many-body system.