## Doctoral Dissertations

Dissertations that have an embargo placed on them will not be available to anyone until the embargo expires.

#### Author ORCID Identifier

https://orcid.org/0000-0002-0220-1223

#### AccessType

Open Access Dissertation

dissertation

#### Degree Name

Doctor of Philosophy (PhD)

Physics

2022

September

Romain Vasseur

#### Subject Categories

Condensed Matter Physics | Quantum Physics

#### Abstract

With the advent of the noisy-intermediate scale quantum (NISQ) era quantum computers are increasingly becoming a reality of the near future. Though universal computation still seems daunting, a great part of the excitement is about using quantum simulators to solve fundamental problems in fields ranging from quantum gravity to quantum many-body systems. This so-called second quantum revolution rests on two pillars. First, the ability to have precise control over experimental degrees of freedom is crucial for the realization of NISQ devices. Significant progress in the control and manipulation of qubits, atoms, and ions, as well as their interactions, has not only allowed for emulation of diverse range of physical systems but has also led to realization of quantum systems in non-conventional settings such as systems out-of-equilibrium, driven by oscillating fields, and with quasiperiodic (QP) modulation. These systems often show novel properties which not only provide an interesting testbed for NISQ devices but also an opportunity to exploit them for further development of quantum computing devices. Second, the study of dynamics of quantum information in quantum systems is essential for understanding and designing better quantum computers. In addition to their practical application as resource for quantum computation, quantum information has also become an essential element for our understanding of various physical problems, such as thermalization of isolated quantum many-body systems. This interplay between quantum information and computation, and quantum many-body systems is only expected to increase with time. In this thesis, we explore these topics in two parts, corresponding respectively to the two pillars mentioned above. In the first part, we study effects of quasiperiodicity on many-body quantum systems in low dimensions. QP systems are aperiodic but deterministic, so their behavior differs from that of clean systems and disordered ones as well. Moreover, these systems can be conveniently realized in an experimental setting where it is easier to isolate them from external decoherence. %Recent advancement in experimental techniques has made it easier to design and probe quantum systems with quasi-periodic modulations. We start with the easy-plane regime of the XXZ spin chain and show that the well-known fractal behavior of the spin Drude weight implies the divergence of the low-frequency conductivity for generic values of anisotropy. We tie this to the quasi-periodic structure in the Bethe ansatz solution resulting in different species of quasiparticles getting activated along the time evolution in a quasi-periodic pattern. We then study quantum critical systems under generic quasi-periodic modulations using real-space renormalization group (RSRG) procedure. In 1d, we show that the system flows to a new fixed point with the couplings following a discrete aperiodic sequence which allows us to analytically calculate the critical properties. We dub these new classes of quasi-periodic fixed points infinite-quasiperiodicity fixed points in line with the infinite-randomness fixed point observed in random quantum systems. We use this approach to analyze the quasiperiodic Heisenberg, Ising, and Potts spin chains. The RSRG is not analytically tractable in 2d, but numerically implementing it for the 2d quasi-periodic $q$-state quantum Potts model, we find that it is well controlled and becomes exact in the asymptotic limit. The critical behavior is shown to be largely independent of $q$ and is controlled by an infinite-quasiperiodicity fixed point. We also provide a heuristic argument for the correlation length exponent and the scaling of the energy gap. Moving on to the second part, we study monitored quantum circuits which have recently emerged as a powerful platform for exploring the dynamics of quantum information and errors in quantum systems. Unitary evolution generates entanglement between distant particles of the system. The dynamics of entanglement has been successfully studied by replacing the Hamiltonian evolution with random quantum circuits. Recently, the robustness of unitary evolution's ability to protect the entanglement against external projective measurements has received much attention. Entanglement is also a resource for quantum information, so its stability is directly related to the stability of a quantum computer against external noises. It has been observed that, in absence of any symmetry, there is a measurement induced phase transition (MIPT) in the behavior of bipartite entanglement that goes from volume law to area law as we tune the rate of measurements. Here we focus on monitored quantum circuits with U(1) symmetry which leads to the presence of a conserved charge density. These diffusive hydrodynamic modes scramble very differently than non-symmetric modes and we find that in addition to the entanglement transition, there is another transition \textit{inside} the volume phase which we call a charge sharpening'' transition. The sharpening transition is a transition in the ability/inability of the measurements to detect the global charge of the system. We study this sharpening transition in a variety of settings, including an effective field theory that predicts the transition to be in a modified Kosterlitz-Thouless universality class. We provide various numerical evidence to back our predictions.

#### DOI

https://doi.org/10.7275/30405986