Aspects of low-dimensional quantum systems in and out-of-equilibrium

Abstract

The classification of novel phases of matter beyond the Landau paradigm has been comprehensively explored over the past decade. In this context, one-dimensional quantum systems are particularly promising, as they host unconventional phases of matter missing in their higher-dimensional counterparts. Venturing further in this direction, quantum systems far from equilibrium have been intensively studied recently as a subject which lies at the interface between quantum information and many-body quantum physics and provides novel non-equilibrium universal behaviors ranging from approach to thermal equilibrium to the arrest of thermalization. These universal behaviors are distinctively quantum, although quantum phase coherence can easily get obliterated at high temperatures. Additionally, the advent of analog quantum simulators, such as ultracold atoms, atoms with tunable long-range interactions with Rydberg excitations and trapped atomic ions enable us to obtain in-depth insight into these phases, due to their greater degree of control and highly coherent Hamiltonian dynamics.

Embarking in this direction, the inclusion of generalized statistics provides the possibility of yielding an intriguing phase diagram in low-dimensional quantum systems. Looking at this potential, we will first uncover a rich phase diagram of a one-dimensional model with generalized statistics comprising four Fermi points. Our analysis utilizes two powerful analytical approaches, namely bosonization and Bethe Ansatz, which allows us to unravel various facets of the low-energy properties exclusive to this model.

The dynamical phase transitions far from equilibrium has been widely explored over the years, which cannot be comprehended within the framework of paradigmatic equilibrium statistical phase transitions. The familiar notion of such phase transitions involves the non-analytic properties of observables as a function of time; this further transpires on transient time scales. Contrary to that, we will demonstrate in our work an alternate notion of dynamical phase transition by investigating the relaxation behavior of correlators at late times in a specific class of Floquet quantum systems. Our study unveils that this phase transition is closely intertwined with the symmetry property and saddle point structure of the Floquet energy spectrum, unlike the non-analyticity associated with the observables.

Periodically driven systems often suffer from the issue of undesirable heating, where no non-trivial order can be sustained; this issue further leads the systems towards a featureless infinite-temperature thermal fixed point. To stabilize such drive-induced states, several mechanisms have been scrutinized over the years, ranging from Floquet many-body localization to Floquet prethermalization. In this work, we will study an alternate mechanism to bypass the heating issue, which concerns the interplay between dynamical localization, interactions, and resonances. Focusing on a specific class of Floquet systems, we will demonstrate that this interplay can lead to several intriguing ergodicity-breaking mechanisms, from emergent integrability to Hilbert space fragmentation, which are unique to this non-equilibrium setup.

The advent of quantum simulators has unlocked the exploration of multiple novel ergodicity-breaking mechanisms, which furnish powerful tools for storing and manipulating quantum information. This exploration recently led us to a new ergodicity-breaking mechanism, dubbed Hilbert space fragmentation. However, the analytical understanding of such a fragmented Hilbert space remains quite challenging as it does not follow the conventional symmetry structures. In this work, we explore this mechanism in a one-dimensional correlated hopping model utilizing an analytical construct called irreducible strings. This construct helps us to unveil various attributes of this fragmented Hilbert space. Additionally, we will discuss a novel thermalization property of this fragmented quantum system, termed "subspace-restricted thermalization", which impacts the static and dynamic measures of thermalization studied in this model.