Finite homological dimension and a derived equivalence

For a Cohen-Macaulay ring $R$, we exhibit the equivalence of the bounded derived categories of certain resolving subcategories, which, amongst other results, yields an equivalence of the bounded derived category of finite length and finite projective dimension modules with the bounded derived category of projective modules with finite length homologies. This yields isomorphisms of various generalized cohomology groups (like K-theory) and improves on terms of a spectral sequence and Gersten complexes.Comment: 23 pages : Some parts of the article changed, especially section 3, to add clarity. Other minor corrections mad

Higgs Inflation and General Initial Conditions

Higgs field of particle physics can play the role of the inflaton in the early universe, if it is non-minimally coupled to gravity. The Higgs inflation scenario predicts a small tensor to scalar ratio: $r\simeq 0.003$. Although this value is consistent with the upper bound $r < 0.12$ given by BICEP2/Keck Array and Planck data, but it is not at their maximum likelihood point: $r\simeq 0.05$. Inflationary observables depend not only on the inflationary models, but also depend on the initial conditions of inflation. Changing initial state of inflation can improve the value of $r$. In this work, we study the Higgs inflation model under general initial conditions and show that there is a subset of these general initial conditions which leads to enhancement of $r$. Then we show that this region of parameter space is consistent with non-Gaussianity bound.Comment: 13 pages, 2 figure

Spin-catalyzed hopping conductivity in disordered strongly interacting quantum wires

In one-dimensional electronic systems with strong repulsive interactions, charge excitations propagate much faster than spin excitations. Such systems therefore have an intermediate temperature range [termed the "spin-incoherent Luttinger liquid'" (SILL) regime] where charge excitations are "cold" (i.e., have low entropy) whereas spin excitations are "hot." We explore the effects of charge-sector disorder in the SILL regime in the absence of external sources of equilibration. We argue that the disorder localizes all charge-sector excitations; however, spin excitations are protected against full localization, and act as a heat bath facilitating charge and energy transport on asymptotically long timescales. The charge, spin, and energy conductivities are widely separated from one another. The dominant carriers of energy are neither charge nor spin excitations, but neutral "phonon" modes, which undergo an unconventional form of hopping transport that we discuss. We comment on the applicability of these ideas to experiments and numerical simulations.Comment: 14 pages, 6 figure

Instability of many-body localized systems as a phase transition in a nonstandard thermodynamic limit

The many-body localization (MBL) phase transition is not a conventional thermodynamic phase transition. Thus to define the phase transition one should allow the possibility of taking the limit of an infinite system in a way that is not the conventional thermodynamic limit. We explore this for the so-called "avalanche" instability due to rare thermalizing regions in the MBL phase for quenched-random systems in more than one spatial dimension, finding an unconventional way of scaling the systems so that they do have a type of phase transition. These arguments suggest that the MBL phase transition in systems with short-range interactions in more than one dimension is a transition where entanglement in the eigenstates begins to spread in to some typical regions: the transition is set by when the avalanches start. Once this entanglement gets started, the system does thermalize. From this point of view, the much-studied case of one-dimensional MBL with short-range interactions is a special case with a different, and in some ways more conventional, type of phase transition.Comment: 10 pages, 2 figure

Regimes of heating and dynamical response in driven many-body localized systems

We explore the response of many-body localized (MBL) systems to periodic driving of arbitrary amplitude, focusing on the rate at which they exchange energy with the drive. To this end, we introduce an infinite-temperature generalization of the effective "heating rate" in terms of the spread of a random walk in energy space. We compute this heating rate numerically and estimate it analytically in various regimes. When the drive amplitude is much smaller than the frequency, this effective heating rate is given by linear response theory with a coefficient that is proportional to the optical conductivity; in the opposite limit, the response is nonlinear and the heating rate is a nontrivial power-law of time. We discuss the mechanisms underlying this crossover in the MBL phase, and comment on its implications for the subdiffusive thermal phase near the MBL transition.Comment: 17 pages, 9 figure