Dephasing and weak localization in an interacting 1D system

Seth M. Davis

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.

Jürgen Brickmann, Peter Russegger

Seth M. Davis, Matthew S. Foster

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.

Yoshikazu Suzumura

Federica Cataldini, Frederik Møller, Mohammadamin Tajik +6 more

The relationship between many-body interactions and dimensionality is integral to numerous emergent quantum phenomena.A striking example is the Bose gas, which upon confinement to one dimension (1D) obeys an infinite set of conservation laws, prohibiting thermalization and constraining dynamics.In our experiment, we demonstrate that such a 1D behavior can extend much further into the dimensional crossover toward 3D than expected.Starting from a weakly interacting Bose gas trapped in a highly elongated potential, we perform a quench to instigate the dynamics of a single density mode.Employing the theory of generalized hydrodynamics, we identify the dominant relaxation mechanism as the 1D dephasing of the relevant collective excitations of the system, the rapidities.Surprisingly, the dephasing remains dominant even for temperatures far exceeding conventional limits of one dimensionality where thermalization should occur.We attribute our observations to an emergent Pauli blocking of transverse excitations caused by the rapidities assuming fermionic statistics, despite the gas being purely bosonic.Thus, our study suggests that 1D physics is less fragile than previously thought, as it can persist even in the presence of significant perturbations.More broadly, by employing the exact Bethe ansatz solutions of the many-body system, we facilitate an interpretation of how the emergent macroscopic behavior arises from the microscopic interactions.

Ch. Lonsky, P. Thomas, A. Weller