Quantum phase transitions occur strictly at zero temperature and are accessed by varying a physical parameter such as a magnetic field or chemical potential. While these transitions themselves are experimentally inaccessible, the existence of a zero temperature quantum critical point has remarkable effects on the dynamical properties of interacting quantum many-body systems at finite temperatures. In this thesis, we study dynamics in four strongly interacting many-body systems near quantum critical points in the context of NMR relaxation, quantum quenches, many-body quantum chaos, and charge diffusion. In chapter 1, we begin by revisiting the issue of NMR relaxation in the quantum disordered phase of Ising spin chains. We find that the imaginary part of the spin susceptibility at low frequences is dominated by rare quantum processes which leads to an NMR relaxation rate that scales as $1/T_{1}\sim \exp(-\frac{2\Delta}{T})$ near the quantum critical point rather than the previously conjectured $1/T_{1}\sim \exp(-\frac{\Delta}{T})$. These results resolve certain discrepancies between the energy scales measured with different experimental probes in the quantum disordered paramagnetic phase of the Ising chain system $\text{CoNb}_{2}\text{O}_{6}$. In chapter 2, we study the non-equilibrium dynamics of Sachdev-Ye-Kitaev (SYK) models with $q$ body interactions after a quantum quench, considering a quench protocol which drives the system from an initial state with long-lived quasiparticle excitations to a final state lacking any long-lived quasiparticle excitations. For $q=4$, we find that the timescale for the system to locally thermalize $\tau_{eq}\sim\frac{\hbar}{k_{B}T}$ and for $q\rightarrow \infty$ we find that the system thermalizes instantaneously. In chapter 3, we study the real time dynamics of quantum electrodynamics in 2+1 dimensions with $N_{f}$ flavors of fermions. We focus on thermalization and the onset of many-body quantum chaos and compute the quantum Lyapunov exponent in a $\frac{1}{N_{f}}$ expansion. We briefly comment on chaos, locality, and gauge invariance. Finally, in Chapter 4 we consider whether the butterfly velocity - a speed at which quantum information propagates - may provide a fundamental bound on diffusion constants in dirty incoherent metals by computing the charge diffusion constant and the butterfly velocity in charge-neutral holographic matter with long wavelength ``hydrodynamic" disorder. In this limit, we find that the butterfly velocity does not set a sharp lower bound for the charge diffusion constant.
Quantum phase transitions occur strictly at zero temperature and are accessed by varying a physical parameter such as a magnetic field or chemical potential. While these transitions themselves are experimentally inaccessible, the existence of a zero temperature quantum critical point has remarkable effects on the dynamical properties of interacting quantum many-body systems at finite temperatures. In this thesis, we study dynamics in four strongly interacting many-body systems near quantum critical points in the context of NMR relaxation, quantum quenches, many-body quantum chaos, and charge diffusion. In chapter 1, we begin by revisiting the issue of NMR relaxation in the quantum disordered phase of Ising spin chains. We find that the imaginary part of the spin susceptibility at low frequences is dominated by rare quantum processes which leads to an NMR relaxation rate that scales as 1/T1∼exp(−T2Δ) near the quantum critical point rather than the previously conjectured 1/T1∼exp(−TΔ). These results resolve certain discrepancies between the energy scales measured with different experimental probes in the quantum disordered paramagnetic phase of the Ising chain system CoNb2O6. In chapter 2, we study the non-equilibrium dynamics of Sachdev-Ye-Kitaev (SYK) models with q body interactions after a quantum quench, considering a quench protocol which drives the system from an initial state with long-lived quasiparticle excitations to a final state lacking any long-lived quasiparticle excitations. For q=4, we find that the timescale for the system to locally thermalize τeq∼kBTℏ and for q→∞ we find that the system thermalizes instantaneously. In chapter 3, we study the real time dynamics of quantum electrodynamics in 2+1 dimensions with Nf flavors of fermions. We focus on thermalization and the onset of many-body quantum chaos and compute the quantum Lyapunov exponent in a Nf1 expansion. We briefly comment on chaos, locality, and gauge invariance. Finally, in Chapter 4 we consider whether the butterfly velocity - a speed at which quantum information propagates - may provide a fundamental bound on diffusion constants in dirty incoherent metals by computing the charge diffusion constant and the butterfly velocity in charge-neutral holographic matter with long wavelength ``hydrodynamic" disorder. In this limit, we find that the butterfly velocity does not set a sharp lower bound for the charge diffusion constant.
This dissertation is a study of various aspects of metals with strong interactions between electrons, with a particular emphasis on the problem of charge transport through them. We consider the physics of clean or weakly-disordered metals near some quantum critical points, and highlight novel transport regimes that could be relevant to experiments. We then develop a variety of exactly-solvable lattice models of strongly interacting non-Fermi liquid metals using novel non-perturbative techniques based on the Sachdev-Ye-Kitaev models, and relate their physics to that of the ubiquitous “strange metal” normal state of most correlated-electron superconductors, providing controlled theoretical insight into the possible mechanisms behind it. Finally, we use ideas from the field of quantum chaos to study mathematical quantities that can provide evidence for the existence of quasiparticles (or the lack thereof) in quantum many-body systems, in the context of metals with correlated electrons.
Understanding how quantum matter behaves when driven out of equilibrium is one of the key focuses in quantum physics. Thanks to impressive progress in the control and precision achieved in quantum synthetic matter over the past decades, the nonequilibrium quantum many-body physics has become one of the most active research areas today, especially after the experimental realization of Bose-Einstein condensates and optical lattices, which allows us to directly observe and study nonequilibrium quantum matter with great accuracy and controllability. In this dissertation, I explore the rich landscape of nonequilibrium quantum many-body physics and how quantum phase transitions, both symmetry-breaking and topological, can be extended to the nonequilibrium setting. In the first part of the dissertation, I focus on spinor Bose-Einstein condensates as an isolated quantum many-body system, and reveal their various dynamical behaviors, including quantum collapse and revivals, thermalization and nonthermal equilibration with no revival even though the system has finite degrees of freedom. In contrast to typical integrable systems, which usually do not thermalize, we find that spinor condensates have a parameter range in which the system thermalizes via the Eigenstate Thermalization Hypothesis (ETH). We show that this observation is linked to the presence of rare nonthermal states whose fraction vanishes with system size, and contributes to the notion of thermalization via weak ETH. Next, I explore a dynamical process that is complementary to thermalization in isolated quantum systems: information scrambling, which could be probed via out-of-time-order correlators (OTOC). I propose a nonintegrable, disordered and quasi-1D spin model, the ladder-XX model, for a feasible detection of information scrambling in a cold atom simulator. This chapter poses a fundamental question: "What are the signatures of quantum phases and phase transitions in isolated interacting systems driven out-of-equilibrium?" I study the ladder-XX model in both clean and disordered potentials, and characterize different nonequilibrium phases, i.e., ergodic and many-body localized, of the model based on the decay properties of OTOCs. Emergent light cone shows sublinear behavior, while the butterfly cones drastically differ from the light cone by demonstrating superlinear spread of information with a velocity that is bounded by the light cone velocity. In the second part of the dissertation, I continue to search for answers to the question posed above, however this time with a particular focus on symmetry-breaking and topological quantum phase transitions. I pin down a universal mechanism underlying the relation between information scrambling at any temperature and quantum phases at low temperatures. Our method points to key ingredients to dynamically detect long-range order in gapped phases through OTOCs for symmetry-breaking quantum phase transitions and Z2 topological order associated with Majorana zero modes localized at the edges. Our results pave the way to an intriguing observation that phases of quantum matter could protect the information from scrambling and thermalization, even when the system is interacting and nonintegrable. Finally, I explore and propose utilizing short-time transient temporal regimes and single-site probes to detect the phases and phase transitions in quantum matter. These studies reveal a dynamical crossover and a dynamical phase transition, respectively for periodic and open-boundary chains. In both cases, a nonequilibrium scaling law appears in the vicinity of the crossover/transition with associated exponents that differ from the analytical predictions for long times. Feasibility of detecting such dynamical criticality in experimental systems are discussed.
Recent experimental advances on ultracold atomic gases and trapped ions have made it possible to simulate exactly solvable quantum systems of interacting particles. In particular, the feasibility of making rapid changes, so-called quantum quenches, to such set-ups has allowed experimentalists to probe non-equilibrium phenomena in closed interacting quantum systems. This, in turn, has spurred a considerable theoretical interest in quantum many-body systems out of equilibrium. In this thesis, we study non-equilibrium properties of quantum many-body systems in the framework of exactly solvable quantum field theory in one spatial dimension. Specific systems include interacting fermions described by the Luttinger model and effective descriptions of spin chains using conformal field theory (CFT). Special emphasis is placed on heat and charge transport, studied from the point of view of quench dynamics, and, in particular, the effects of breaking conformal symmetries on transport properties. Examples include the Luttinger model with non-local interactions, breaking Lorentz and scale invariance, and inhomogeneous CFT, which generalizes standard CFT in that the usual propagation velocity v is replaced by a function v(x) that depends smoothly on the position x, breaking translation invariance. The quench dynamics studied here is for quantum quenches between, in general, different smooth inhomogeneous systems. An example of this is the so-called smooth-profile protocol, in which the initial state is defined by, e.g., smooth inhomogeneous profiles of inverse temperature and chemical potential, and the time evolution is governed by a homogeneous Hamiltonian. Using this protocol, we compute exact analytical results for the full time evolution of the systems mentioned above. In particular, we derive finite-time results that are universal in the sense that the same relations between the non-equilibrium dynamics and the initial profiles hold for any unitary CFT. These results also make clear that heat and charge transport in standard CFT are purely ballistic. Finally, we propose and study an inhomogeneous CFT model with v(x) given by a random function. We argue that this model naturally emerges as an effective description of one-dimensional quantum many-body systems with certain static random impurities. Using tools from wave propagation in random media, we show that such impurities lead to normal and anomalous diffusive contributions to heat transport on top of the ballistic one known from standard CFT.
Recent advances in theoretical physics have increasingly focused on the dynamics of quantum systems with many interacting degrees of freedom, while ultracold atom platforms now enable the realization of diverse theoretical models with precise control over system parameters and advanced monitoring techniques. A prominent example is cavity quantum electrodynamics (CQED), where large atomic or molecular ensembles are coupled to high-finesse optical cavities, enabling strong interaction with confined electromagnetic modes and leading to phenomena such as the superradiant phase transition, in which atoms and photons form a coherent state. Most theoretical studies of CQED have concentrated on regimes of spatially uniform atom–cavity coupling, where collective behavior allows a description in terms of the classical dynamics of a few macroscopic variables. However, experimental capabilities now permit exploration beyond this limit, though theoretical progress is hindered by the exponential computational complexity of simulating large quantum systems, particularly when environmental coupling is included. This thesis addresses such challenges by developing efficient approaches, within the Keldysh formalism of non-equilibrium quantum field theory, to study systems with strongly disordered interactions coupled to external reservoirs. Two representative models are considered: a disordered spin–boson model describing light–matter interactions with quenched disorder, relevant to recent CQED experiments in confocal cavities, and a fermion–phonon system governed by the Yukawa–Sachdev–Ye–Kitaev (Yukawa-SYK) model. Both systems are quantum critical, exhibiting a continuum of low-energy modes above their stationary states, yet disorder produces qualitatively distinct dynamical behaviors: in the spin–boson system it induces slow, glassy relaxation, whereas in the Yukawa-SYK model it leads to rapid thermalization. These contrasting outcomes reveal the non-trivial role of disorder in quantum many-body systems and motivate further investigation into its effects on non-equilibrium quantum dynamics.
The work presented in this thesis is divided into two main parts: strong zero modes in quantum spin chains with open boundaries and large deviations in classical spin systems. The results concerning the strong zero modes are presented in chapters 2 and 3, while chapter 4 contains the results about large deviations in systems of many, but independent, classical degrees of freedom. These two distinct classes of problems in spin chains are both about aspects of slow relaxation to equilibrium in many-body systems. Nowadays slow dynamics and non-ergodicity in many-body quantum systems are receiving much attention due to their notable technological potential for storing and processing, for very long times, the quantum information encoded in boundary degrees of freedom. In the first part of the work presented in this thesis we mainly focus on quantum spin chains with open boundaries, which can display coherence times for edge spins, that diverge with the system size, as a consequence of the emergence, in the thermodynamic limit, of conserved local quantities, called strong zero modes. First, we discuss the fate of these coherence times when dynamics becomes dissipative. Understanding the behavior of these long correlation times in open quantum systems, undergoing Markovian (memoryless) dynamics, would allow for the possibility of exploiting the protected information encoded in the boundary spins for applications in quantum devices in realistic non-equilibrium settings. Second, we study one possible simple generalization of the transverse field Ising model to a class of ladder spin systems with plaquette interactions in the presence of a transverse field. Also for these systems one can explicitly construct the strong zero mode operators and understand the behavior of the consequential long coherence times for the edge degrees of freedom under isolated (unitary) dynamics. This is possible because the models we consider, while appearing complex superficially, can be brought to simple forms by exploiting an extensive number of conserved quantities they possess. The results presented in chapters 2 and 3 are closely related, even if they focus on different models and investigate different aspects of their dynamics. Nevertheless, the underlying concept they are based on is the same one, that is, an eigenstate phase transition for the strong zero modes that has interesting consequences for the full energy spectrum. In the second part of the thesis we focus on a different type of phase transitions. Here we address the issue of dynamical large deviation phase transitions from a disordered phase to an ordered one, in classical systems which consist in a collection of independent Ising spins evolving stochastically. Surprisingly, by reweighing trajectories accordingly to a certain type of time-integrated observable, even a system of independently evolving spins can display some critical behavior, at the fluctuation level, in trajectory space in the large size and long time limit. By making use of the tilted generator techniques we study the statistics of two particular time-integrated observables. Their associated tilted generators have an exact Kramers-Wannier duality and they look like, up to a sign and an additive constant, some specific well known quantum Hamiltonians. In this sense, the dynamical large deviation phase transitions we observe in these classical stochastic systems translate in ground state quantum phase transitions taking place at the self dual point of the tilted generators we study.
The study of collective behaviour in many-body systems often explores fundamentally new ideas absent from the mere constituents of such a system. A paradigmatic model for these studies is the spin-1/2 XXZ chain and its fermionic equivalent. This thesis can be broadly divided into the study of two fundamental aspects of this model. Firstly, we discuss localisation phenomena in one dimensional lattices as often experimentally realised in cold atom systems. Secondly, we investigate how disorder and symmetry influence heat transport in spin chains. More specifically, in the first part we consider a system of non-interacting fermions in one dimension subject to a single-particle potential consisting of a strong optical lattice, a harmonic trap, and uncorrelated on-site disorder. We investigate a global inhomogeneous quantum quench and present numerical and analytical results for static and dynamical properties. We show that the approach to the non-thermal equilibrium state is extremely slow and that it implies a sensitivity to disorder parametrically stronger than that expected from Anderson localisation. We also consider the above system in a strong non-uniform electric field. In the non-interacting case, due to Wannier-Stark localisation, the single-particle wave functions are exponentially localised without quenched disorder. We show that this system remains localised in the presence of nearest-neighbour interactions and exhibits physics analogous to models of conventional many-body localisation. The second part explores the hydrodynamics of the disordered XYZ spin chain. Using time-evolving block decimation on open chains of up to 400 spins attached to thermal baths, we probe the energy transport of this system. Our principal findings are as follows. For weak disorder there is a stable diffusive region that persists up to a critical disorder strength that depends on the XY anisotropy. Then, for disorder strengths above this critical value energy transport becomes increasingly subdiffusive.