Related papers: Undecidability of the Spectral Gap (short version)
We develop a new adiabatic theorem for unique gapped ground states which does not require the gap for local Hamiltonians. We instead require a gap in the bulk and a smoothness of expectation values of sub-exponentially localized observables…
We study the stability with respect to a broad class of perturbations of gapped ground state phases of quantum spin systems defined by frustration-free Hamiltonians. The core result of this work is a proof using the…
There are several interacting spin systems which have a gap in their spin excitation spectrum. The gap does not occur due to anisotropies present in the system but is quantum mechanical in origin. We give a brief overview on the different…
A Schwinger boson mean field theory is developed for spin liquids in a symmetric spin-orbital model in higher dimensions. Spin, orbital and coupled spin-orbital operators are treated equally. We evaluate the dynamic correlation functions…
It has been unknown in kinetic theory whether the linearized Boltzmann or Landau equation with soft potentials admits a spectral gap in the spatially inhomogeneous setting. Most of existing works indicate a negative answer because the…
We study families H_n of 1D quantum spin systems, where n is the number of spins, which have a spectral gap \Delta E between the ground-state and first-excited state energy that scales, asymptotically, as a constant in n. We show that if…
We consider a general weak perturbation of a non-interacting quantum lattice system with a non-degenerate gapped ground state. We prove that the presence of isolated eigenvalues in the spectrum of the decoupled model leads to the existence…
In this paper we address the question of the existence of a spectral gap in a class of local Hamiltonians. These Hamiltonians have the following properties: their ground states are known exactly; all equal-time correlation functions of…
For the 1D quantum East model with open boundaries, we show that in the limit $s \to -\infty$, the ground state is accurately captured by a simple spin-coherent product state. We further identify a low-entanglement excited eigenstate that…
We present an exact solution of an experimentally realizable and strongly interacting one-dimensional spin system which is a limiting case of a quantum Ising model with long range interaction in a transverse and longitudinal field.…
In this paper, we consider the spectrum of a model in quantum electrodynamics with a spatial cutoff. It is proven that (1) the Hamiltonian is self-adjoint; (2) under the infrared regularity condition, the Hamiltonian has a unique ground…
For a class of Hamiltonians of $XXZ$ spin chains in a uniform external magnetic field that are small quantum perturbations of an Ising Hamiltonian, it is shown that the spectral gap above the ground-state energy remains strictly positive…
Having spectral correlations that, over small enough energy scales, are described by random matrix theory is regarded as the most general defining feature of quantum chaotic systems as it applies in the many-body setting and away from any…
We prove a new result on the spectral gap and mixing time of a Markov chain with Glauber dynamics on the space of Dyck paths (i.e., Catalan paths) and their generalization, which we call colored Dyck paths. The proof uses the comparison…
Non-adiabatic molecular phenomena, arising from the breakdown of the Born-Oppenheimer approximation, govern the fate of virtually all photo-physical and photochemical processes and limit the quantum efficiency of molecules and other…
For every Matrix Product State (MPS) one can always construct a so-called parent Hamiltonian. This is a local, frustration free, Hamiltonian which has the MPS as ground state and is gapped. Whenever that parent Hamiltonian has a degenerate…
Contrary to the conventional wisdom in Hermitian systems, a continuous quantum phase transition between gapped phases is shown to occur without closing the energy gap $\Delta$ in non-Hermitian quantum many-body systems. Here, the relevant…
The Cheeger inequalities give an upper and lower bound on the spectral gap of discrete Laplacians defined on a graph in terms of the geometric characteristics of the graph. We generalise this approach and we employ it to determine if a…
We study the quantum lattice gas model in one dimension introduced by Lesanovsky, who showed that the exact ground state and a couple of excited states can be obtained analytically. The Hamiltonian of the model depends solely on the…
Many physically interesting models show a quantum phase transition when a single parameter is varied through a critical point, where the ground state and the first excited state become degenerate. When this parameter appears as a coupling…