Related papers: Undecidability of the Spectral Gap (short version)
A quantum system subject to an external perturbation can experience leakage between uncoupled regions of its energy spectrum separated by a gap. To quantify this phenomenon, we present two complementary results. First, we establish…
Preparing the ground state of a given Hamiltonian and estimating its ground energy are important but computationally hard tasks. However, given some additional information, these problems can be solved efficiently on a quantum computer. We…
In the probabilistic approach to quantum many-body systems, the ground-state energy is the solution of a nonlinear scalar equation written either as a cumulant expansion or as an expectation with respect to a probability distribution of the…
The statistics of gap ratios between consecutive energy levels is a widely used tool, in particular in the context of many-body physics, to distinguish between chaotic and integrable systems, described respectively by Gaussian ensembles of…
Hastings established exponential decay of correlations for ground states of gapped quantum many-body systems. A ground state of a (geometrically) local Hamiltonian with spectral gap $\epsilon$ has correlation length $\xi$ upper bounded as…
The adiabatic theorem refers to a setup where an evolution equation contains a time-dependent parameter whose change is very slow, measured by a vanishing parameter $\epsilon$. Under suitable assumptions the solution of the…
Entanglement in the ground state of a many-body quantum system may arise when the local terms in the system Hamiltonian fail to commute with the interaction terms in the Hamiltonian. We quantify this phenomenon, demonstrating an analogy…
The energy spectrum of the Hofstadter model has a fractal structure with infinitely many gaps. We prove the persistence of each gap in presence of Hubbard interaction in the case of small transversal hopping, even when the coupling is much…
Towards better understanding of how to design efficient adiabatic quantum algorithms, we study how the adiabatic gap depends on the spectra of the initial and final Hamiltonians in a natural family of test-bed examples. We show that perhaps…
Quantum Mechanical ground states of many-body systems can be important resources for various investigations: for quantum sensing, as the initial state for nonequilibrium quantum dynamics following quenches, and the simulation of quantum…
Establishing the (non)existence of a spectral gap above the ground state in the thermodynamic limit is one of the fundamental steps for characterizing the topological phase of a quantum lattice model. This is particularly challenging when a…
We identify a structure in the spectra of 1d lattice models of interacting electrons, characterised by an anomalous gapped branch of elementary excitations. Focusing on a family of Bethe ansatz solvable models, where all excitations are…
We study gapless quantum spin chains with spin 1/2 and 1: the Fredkin and Motzkin models. Their entangled groundstates are known exactly but not their excitation spectra. We first express the groundstates in the continuum which allows for…
We consider a free quantum particle in one dimension whose mass profile exhibits jump discontinuities. The corresponding Hamiltonian is a self-adjoint realisation of the kinetic-energy operator, with the specific realisation determined by…
In this work, we make a connection between two seemingly different problems. The first problem involves characterizing the properties of entanglement in the ground state of gapped local Hamiltonians, which is a central topic in quantum…
In recent years, the entanglement spectra of quantum states have been identified to be highly valuable for improving our understanding on many problems in quantum physics, such as classification of topological phases, symmetry-breaking…
The nature of the low energy spectrum of frustrated quantum spin systems is investigated by means of a topological test introduced by Y. Hatsugai which enables to infer the possible existence or absence of a gap between the ground state and…
We study the ground state (GS) many-body quantum entanglement of two different transverse field models on a quasi-2D square lattice relevant to a Hydrogen-bonded crystal, i.e, squaric acid. We measure the genuine multipartite…
In the vast majority of many-body problems, it is the kinetic energy part of the Hamiltonian that is best known microscopically, and it is the detailed form of the interactions between the particles, the potential energy term, that is…
For a large class of finite-range quantum spin models with half-integer spins, we prove that uniqueness of the ground state implies the existence of a low-lying excited state. For systems of linear size L, of arbitrary finite dimension, we…