We investigate various topics in theoretical quantum condensed matter physics.
First, we show that a one-dimensional quantum wire with as few as 2 channels of interacting fermions can host metallic Luttinger liquid states of matter that are stable against all perturbations up to $q^\text{th}$-order in fermion creation/annihilation operators for any fixed finite $q$.
The leading relevant perturbations are thus complicated operators that are expected to modify the physics only at very low energies, below accessible temperatures.
The stability of these Luttinger liquid fixed points is due to strong interactions between the channels, which can (but need not) be chosen to be purely repulsive.
Our results might enable elementary physical realizations of these phases, and may also serve as a useful paradigm for thinking about higher-dimensional non-Fermi liquids.
Separately, we present an elementary but general description of relaxation to gaussian and equilibrium generalized Gibbs states in lattice models of fermions or bosons with quadratic hamiltonians. Our analysis applies to arbitrary initial states that satisfy a mild condition on clustering of correlations.
We obtain quantitive, model-independent predictions for how quickly local quantities relax in such systems.
These predictions can be tested in near-term quantum gas experiments.
Finally, we study chaotic many-body quantum systems that obey the eigenstate thermalization hypothesis (ETH).
We show that a known bound on the growth rate of the out-of-time-order four-point correlator in such systems follows directly from the general ETH structure of operator matrix elements.
This ties together two key paradigms of thermal behavior in isolated many-body quantum systems.
We also consider a bipartition of the system, and study the entanglement properties of an energy eigenstate with nonzero energy density.
When the two subsystems have nearly equal volumes, we find a universal correction to the entanglement entropy that is proportional to the square root of the system's heat capacity (or a sum of capacities, if there are conserved quantities in addition to energy).
