Related papers: Renormalization Analysis for Degenerate Ground Sta…
We consider Hamiltonians of models describing non-relativistic quantum mechanical matter coupled to a relativistic field of bosons. If the free Hamiltonian has an eigenvalue, we show that this eigenvalue persists also for nonzero coupling.…
Nonrelativistic Hamiltonians with large, even infinite, ground-state degeneracy are studied by connecting the degeneracy to the property of a Dirac operator. We then identify a special class of Hamiltonians, for which the full space of…
We consider the transformation of Hamilton operators under various sets of quantum operations acting simultaneously on all adjacent pairs of particles. We find mappings between Hamilton operators analogous to duality transformations as well…
We prove that the Hamiltonian of the model describing a spin which is linearly coupled to a field of relativistic and massless bosons, also known as the spin-boson model, admits a ground state for small values of the coupling constant…
In this paper, we develop a wave function renormalization scheme for models of non-relativistic quantum particles interacting with a quantized relativistic field, in the Hamiltonian formalism of quantum field theory. We construct the…
For a large class of quantum mechanical models of matter and radiation we develop an analytic perturbation theory for non-degenerate ground states. This theory is applicable, for example, to models of matter with static nuclei and…
If a local Hamiltonian eigenstate is mapped to another state by local operators commuting with the Hamiltonian terms, the latter is also an eigenstate. This basic observation implies a no-go result for both being a unique ground state and…
We study the renormalized Nelson model for a scalar matter particle in a continuous confining potential interacting with a possibly massless quantized radiation field. When the radiation field is massless we impose a mild infrared…
We prove the existence, uniqueness, and strict positivity of ground states of the possibly massless renormalized Nelson operator under an infrared regularity condition and for Kato decomposable electrostatic potentials fulfilling a binding…
We construct a set of exact ground states with a localized ferromagnetic domain wall and an extended spiral structure in a quasi-one-dimensional deformed flat-band Hubbard model. In the case of quarter filling, we show the uniqueness of the…
We study a system of qubits that are coupled to each other via only one degree of freedom represented, e.g., by $\sigma_z$-operators. We prove that, if by changing the Hamiltonian parameters, a non-degenerate ground state of the system is…
A degenerate variant of mean field perturbation theory for the on-site Bose-Hubbard Hamiltonian is presented. We split the perturbation into two terms and perform exact diagonalization in the two-dimensional subspace corresponding to the…
We consider a model for a massive uncharged non-relativistic particle interacting with a massless bosonic field, widely referred to as the Nelson model. It is well known, that an ultraviolet renormalized Hamilton operator exists in this…
We study the performance of the D-Wave 2X quantum annealing machine on systems with well-controlled ground-state degeneracy. While obtaining the ground state of a spin-glass benchmark instance represents a difficult task, the gold standard…
Quadratic operators are used in transforming the model Hamiltonian (H) of one correlated and dispersive band in an unique positive semidefinite form coopting both the kinetic and interacting part of H. The expression is used in deducing…
Ultraviolet (UV) renormalization of the Nelson model in quantum field theory is considered. A relationship between a ultraviolet renormalization term and the ground state energy of the Hamiltonian with total momentum zero is studied by…
The one-dimensional quantum spin-1/2 model with nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic interaction is considered. The Hamiltonian is first bosonized by using the linear spin wave approximation, and then…
In applications where multiple optimal solutions are needed, transverse-field quantum annealing (QA) is known to sample degenerate ground states in a strongly biased manner. Despite extensive empirical observations, it remains unclear which…
Starting from the study of one-dimensional potentials in quantum mechanics having a small distance behavior described by a harmonic oscillator, we extend this way of analysis to models where such a behavior is not generally expected. In…
A two-level atom coupled to the radiation field is studied. First principles in physics suggest that the coupling function, representing the interaction between the atom and the radiation field, behaves like $\vert k \vert^{- 1/2}$, as the…