We consider three topics, all concerning the confluence of dynamics, disorder, and interactions in low-dimensional quantum many-body systems of interest for the potential manipulation of quantum matter. Particle fractionalization is believed to orchestrate the physics of many strongly correlated systems, yet its direct experimental detection remains a challenge. We propose a measurement for an ultracold matter system, in which correlations in initially decoupled 1D chains are imprinted via quantum quench upon two-dimensional Dirac fermions. Coupling fractionalized initial states launches relativistic "fractionalization waves'' along the chains, while coupling noninteracting chains induces perpendicular dispersion. These could be easily distinguished in an ultracold gas experiment. As a potential window on transitions out of the ergodic phase of weakly disordered, quasi-one-dimensional fermion systems, we study dephasing due to a diffusive noise bath generated by inelastic scattering due to short-ranged interactions. We calculate the dephasing of weak localization perturbatively through second order in the bath coupling and discover a failure of the self-consistent Born approximation. We also consider a many-channel quantum wire where short-ranged, spin-exchange interactions coexist with screened Coulomb interactions. We calculate the dephasing rate, treating the short-ranged interaction perturbatively and the Coulomb interaction exactly, giving the first controlled calculation of quasi-1D dephasing due to diffusive noise. Our results are relevant to the search for precursors to the many-body localization transition. They also link dephasing to the enhancement of the spin-triplet interaction near a metal-insulator transition, providing for the amplification of dephasing at low temperatures in spin SU(2)-symmetric quantum wires. The physics of massless, 2D Dirac fermions with a spatially modulated Dirac cone could have important applications in low-dimensional superconductivity and other Dirac materials. This is mathematically identical to a theory of massless fermions on a certain class of curved spacetime manifolds. We study these manifolds, which are dominated by curvature singularities, and find that isotropic and nematic fluctuations have profound yet different effects on the spacetime geometry. We present analytical results on geodesic geometry, give some exact solutions for some highly-symmetric toy models, and speculate about the role of induced one-dimensionality for such bound orbits in the physics of 2D dirty d-wave superconductivity.
We consider three topics, all concerning the confluence of dynamics, disorder, and interactions in low-dimensional quantum many-body systems of interest for the potential manipulation of quantum matter. Particle fractionalization is believed to orchestrate the physics of many strongly correlated systems, yet its direct experimental detection remains a challenge. We propose a measurement for an ultracold matter system, in which correlations in initially decoupled 1D chains are imprinted via quantum quench upon two-dimensional Dirac fermions. Coupling fractionalized initial states launches relativistic "fractionalization waves'' along the chains, while coupling noninteracting chains induces perpendicular dispersion. These could be easily distinguished in an ultracold gas experiment. As a potential window on transitions out of the ergodic phase of weakly disordered, quasi-one-dimensional fermion systems, we study dephasing due to a diffusive noise bath generated by inelastic scattering due to short-ranged interactions. We calculate the dephasing of weak localization perturbatively through second order in the bath coupling and discover a failure of the self-consistent Born approximation. We also consider a many-channel quantum wire where short-ranged, spin-exchange interactions coexist with screened Coulomb interactions. We calculate the dephasing rate, treating the short-ranged interaction perturbatively and the Coulomb interaction exactly, giving the first controlled calculation of quasi-1D dephasing due to diffusive noise. Our results are relevant to the search for precursors to the many-body localization transition. They also link dephasing to the enhancement of the spin-triplet interaction near a metal-insulator transition, providing for the amplification of dephasing at low temperatures in spin SU(2)-symmetric quantum wires. The physics of massless, 2D Dirac fermions with a spatially modulated Dirac cone could have important applications in low-dimensional superconductivity and other Dirac materials. This is mathematically identical to a theory of massless fermions on a certain class of curved spacetime manifolds. We study these manifolds, which are dominated by curvature singularities, and find that isotropic and nematic fluctuations have profound yet different effects on the spacetime geometry. We present analytical results on geodesic geometry, give some exact solutions for some highly-symmetric toy models, and speculate about the role of induced one-dimensionality for such bound orbits in the physics of 2D dirty d-wave superconductivity.
As a potential window on transitions out of the ergodic, many-body-delocalized phase, we study the dephasing of weakly disordered, quasi-one-dimensional fermion systems due to a diffusive, non-Markovian noise bath. Such a bath is self-generated by the fermions, via inelastic scattering mediated by short-ranged interactions. The ergodic phase can be defined by the nonzero dephasing rate, which makes transport incoherent and classical on long length scales. We calculate the dephasing of weak localization perturbatively through second order in the bath coupling, obtaining a short-time expansion. However, no well-defined dephasing rate can be identified, and the expansion breaks down at long times. This perturbative expansion is not stabilized by including a mean-field cooperon ``mass'' (decay rate), signaling a failure of the self-consistent Born approximation. We also consider a many-channel quantum wire where short-ranged, spin-exchange interactions coexist with screened Coulomb interactions. We calculate the dephasing rate, treating the short-ranged interactions perturbatively and the Coulomb interaction exactly. The latter provides a physical infrared regularization that stabilizes perturbation theory at long times, giving the first controlled calculation of quasi-1D dephasing due to diffusive noise. At first order in the diffusive bath coupling, we find an enhancement of the dephasing rate, but at second order, we find a rephasing contribution. Our results differ qualitatively from those obtained via self-consistent calculations commonly employed in higher dimensions. Our results are relevant in two different contexts: first, in the search for precursors to many-body localization in the ergodic phase of an isolated many-fermion system. Second, our results provide a mechanism for the enhancement of dephasing at low temperatures in spin SU(2)-symmetric quantum wires, beyond the Altshuler-Aronov-Khmelnitsky result. The enhancement is possible due to the amplification of the triplet-channel interaction strength and provides an additional physical mechanism that could contribute to the experimentally observed low-temperature saturation of the dephasing time.
Particle fractionalization is believed to orchestrate the physics of many strongly correlated systems, yet its direct experimental detection remains a challenge. We propose a simple measurement for an ultracold matter system, in which correlations in initially decoupled 1D chains are imprinted via quantum quench upon two-dimensional Dirac fermions. Luttinger liquid correlations launch relativistic "fractionalization waves" along the chains, while coupling noninteracting chains induces perpendicular dispersion. These could be easily distinguished in an ultracold gas experiment.
In this thesis, we consider two topics that involve strong spatial or temporal fluctuations in interacting quantum many-body systems. We first consider far-from equilibrium quantum hydrodynamics in light-driven helical edge states of a 2D topological insulator. We then consider the enhancement of superconducting and magnetic instabilities in fermion systems with random or structured inhomogeneity, driven by the nesting of fractal wave functions. In the first part, we study quantum quenches of helical edge liquids with spin-flip inelastic scattering. Counterpropagating charge packets in helical edges can be created by an ultrashort electric pulse applied across a 2D topological insulator. Localized “hot spots” that form due to scattering enable two types of strongly nonlinear wave dynamics. First, propagating packets develop self-focusing shock fronts. Second, colliding packets with opposite charge can exhibit near-perfect retroreflection, despite strong dissipation. This leads to an interaction-mediated frequency doubling that could be detected experimentally from emitted terahertz radiation. In the second part, we study the enhanced correlation effects in many-fermion systems induced by structured or random inhomogeneities. We consider the interplay of superconductivity and a wide spectrum of critical (multifractal) wave functions (“spectrum-wide quantum criticality,” SWQC) in the one-dimensional Aubry-Andr ́e and power-law random-banded matrix models (PRBMs) with attractive interactions, using self-consistent BCS theory. We find that SWQC survives the incorporation of attractive interactions at the Anderson localization transition, whereas the pairing amplitude is maximized near this transition in both models. Although increasing inhomogeneity always depletes the superfluid stiffness, we find that superconductivity is still controlled by the fractal-enhanced amplitude near the Anderson transition. Our results suggest that SWQC, recently discovered in two-dimensional topological surface-state and nodal superconductor models, can robustly enhance superconductivity. We also study the interplay of magnetic ordering and the spectrum-wide quantum critical wave functions in PRBMs with repulsive Hubbard interaction. We employ self-consistent Hartree-Fock numerics and analytical field theory calculations using a Keldysh Finkel’stein nonlinear sigma model. We find that weak interactions delocalize the system, while strong interaction localizes the system. Ferromagnetism sets in near the Anderson transition, where the ferromagnetic spin susceptibility is also shown to peak. This indicates that ferromagnetic ordering is enhanced by the fractal wave functions. Using the sigma model, we calculate the quantum corrections to the conductance and spin susceptibility. We find that the analytical and numerical results are mutually consistent.
Metallic phases have been observed in several disordered two-dimensional (2D) systems, including thin films near superconductor-insulator transitions and quantum Hall systems near plateau transitions. The existence of 2D metallic phases at zero temperature generally requires an interplay of disorder and interaction effects. Consequently, experimental observations of 2D metallic behavior have largely defied explanation. We formulate a general stability criterion for strongly interacting, massless Dirac fermions against disorder, which describe metallic ground states with vanishing density of states. We show that (2+1)-dimensional quantum electrodynamics (QED3) with a large, even number of fermion flavors remains metallic in the presence of weak scalar potential disorder due to the dynamic screening of disorder by gauge fluctuations. We also show that QED3 with weak mass disorder exhibits a stable, dirty metallic phase in which both interactions and disorder play important roles.
A central goal in the study of modern condensed matter physics is the characterization of the dynamical properties of quantum systems. Many decades of effort towards this goal, studying a diverse range of (near-equilibrium) quantum matter, from Fermi liquids, to quantum two-level systems, to interacting spin models, and more, has revealed a remarkable pervasiveness of the simple dynamical description of these complex systems in terms of quasi-particles that carry spin, charge, and heat, and that are generally able to equilibrate systems. \n\nThis thesis is an examination of some exceptions to this rule. Specifically, we study a number of instances of quantum matter where equilibration phenomena happens at rather long time scales, or does not occur at all. Particular emphasis is laid on the role of dimensionality, disorder, and dissipation in engendering such novel dynamical behavior.\n\nFirst, we consider non-equilibrium dynamics in one-dimensional quasi-condensates. Low dimensionality inhibits scattering in these systems, and low-energy excitations are long-lived phase fluctuations that exhibit an enriched conformal symmetry. Utilizing this symmetry, we generalize sudden quenches typically used to study non-equilibrium dynamics to quenches along general relativistic and conformal trajectories. Gases never truly equilibrate after such a quench; instead, they evolve into a `prethermal' state with thermal-looking correlations and a chiral asymmetry. \n\nWe then study the problem of the dynamical transition driven by disorder, from an ergodic to a non-ergodic phase, in one-dimensional quantum spin chains. In particular, in XXZ chains with on-site disorder, we find a unique intermediate phase straddling the boundary of the dynamical phase transition, wherein rare-region effects lead to long-time tails in equilibration and vanishing DC conduction before the onset of non-ergodicity. We propose generalizations of such `Griffiths' behavior to arbitrary dimensions. We also study the dynamics of random-bond Heisenberg chains by developing a strong-disorder renormalization group protocol for these systems. We discuss how magnetic noise from such disordered systems contains signatures of their anomalous dynamical properties. \n\nNext, we re-examine the phenomenological theory of two-level systems in amorphous materials in the light of new experimental evidence that these states have large electric/magnetic dipole moments. We propose and justify an interpretation of the model as one of tunneling electrons slowed down by a large phonon drag and discuss the dynamical consequences of such polaronic effects. \n\nFinally, we discuss how magnetic noise measurements can be used to non-invasively access the anomalous properties of systems such as those discussed above. In particular, we examine how scattering properties of isolated magnetic impurities and non-local transport in a variety of two-dimensional materials can be probed experimentally using NV centers as noise magnetometers.
Quasi-one-dimensional quantum models are ideal for theoretically exploring the physical phenomena associated with strong correlations. In this thesis we study three examples where strong correlations play an important role in the static or dynamic properties of the system. Firstly, we examine the behaviour of a doped fermionic two-leg ladder in which umklapp interactions are present. Such interactions arise at special band fillings and can be induced by the formation of charge density wave order in an array of two-leg ladders with long-range (three-dimensional) interactions. For the umklapp which arises from the half-filling of one of the bands, we show that the low-energy theory has a number of phases, including a strong coupling regime in which the dominant fluctuations are superconducting in nature. These superconducting fluctuations carry a finite wave vector – they are the one-dimensional analogue of Fulde-Ferrell-Larkin-Ovchinnikov superconductivity. In a second example, we consider a quantum spin model which captures the essential one-dimensional physics of CoNb2O6, a quasi-one-dimensional Ising ferromagnet. Motivated by high-resolution inelastic neutron scattering experiments, we calculate the dynamical structure in the paramagnetic phase and show that a small misalignment of the transverse field can lead to quasi-particle breakdown – a surprising broadening in the single particle mode observed in experiment. Finally, we study the out-of-equilibrium dynamics of a model with tuneable integrability breaking. When integrability is broken by the presence of weak interactions, we show that the system relaxes to a non-thermal state on intermediate time scales, the so-called “prethermalization plateau”. We describe the approximately stationary behaviour in this regime by constructing a generalised Gibbs ensemble with charges deformed to leading order in perturbation theory. Expectation values of these charges are time-independent, but interestingly the charges do not commute with the Hamiltonian to leading order in perturbation theory. Increasing the strength of the integrability breaking interactions leads to behaviour compatible with thermalisation. In each case we use a combination of perturbative analytical calculations and non-perturbative numerical computations to study the problem at hand.