相关论文: The diagonalization of quantum field Hamiltonians

Loop quantum cosmological methods are extended to homogeneous models in diagonalized form. It is shown that the diagonalization leads to a simplification of the volume operator such that its spectrum can be determined explicitly. This…

The so-called equation of motion method is useful to obtain the explicit form of the eigenvectors and eigenvalues of certain non self-adjoint bosonic Hamiltonians with real eigenvalues. These operators can be diagonalized when they are…

Using a Hamiltonian formulation of the spherically symmetric gravity-scalar field theory adapted to flat spatial slicing, we give a construction of the reduced Hamiltonian operator. This Hamiltonian, together with the null expansion…

We calculate the eigenvalues of some two-dimensional non-Hermitian Hamiltonians by means of a pseudospectral method and straightforward diagonalization of the Hamiltonian matrix in a suitable basis set. Both sets of results agree remarkably…

We develop an efficient and robust approach to Hamiltonian identification for multipartite quantum systems based on the method of compressed sensing. This work demonstrates that with only O(s log(d)) experimental configurations, consisting…

Development of exponentially scaling methods has seen great progress in tackling larger systems than previously thought possible. One such technique, full configuration interaction quantum Monte Carlo, is a useful algorithm that allows…

We explore the possibility of selecting a natural vacuum state for scalar and tensor gauge-invariant cosmological perturbations in the context of hybrid quantum cosmology, by identifying those variables for the description of the…

We present a non-perturbative framework for deriving effective Hamiltonians that describe low-energy excitations in quantum many-body systems. The method combines block diagonalization based on the Cederbaum--Schirmer--Meyer transformation…

Many promising quantum applications depend on the efficient quantum simulation of an exponentially large sparse Hamiltonian, a task known as sparse Hamiltonian simulation, which is fundamentally important in quantum computation. Although…

Loop quantum gravity in its Hamiltonian form relies on a connection formulation of the gravitational phase space with three key properties: 1.) a compact gauge group, 2.) real variables, and 3.) canonical Poisson brackets. In conjunction,…

We take the Bose-Hubbard model to illustrate exact diagonalization techniques in a pedagogical way. We follow the road of first generating all the basis vectors, then setting up the Hamiltonian matrix with respect to this basis, and finally…

Non-hermitian quantum graphs possessing real (i.e., in principle, observable) spectra are studied via their discretization. The discretized Hamiltonians are assigned, constructively, an elementary pseudometric and/or a more complicated…

A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few…

Within the framework of Quantum Reduced Loop Gravity we quantize the Hamiltonian for a gauge vector field. The regularization can be performed using tools analogous to the ones adopted in full Loop Quantum Gravity, while the matrix elements…

The performance of computational methods for many-body physics and chemistry is strongly dependent on the choice of basis used to cast the problem; hence, the search for better bases and similarity transformations is important for progress…

We propose a novel quantum Monte Carlo method in configuration space, which stochastically samples the contribution from a large secondary space to the effective Hamiltonian in the energy dependent partitioning of L\"owdin. The method…

We study random Hamiltonians on finite-size cubes and waveguide segments of increasing diameter. The number of random parameters determining the operator is proportional to the volume of the cube. In the asymptotic regime where the cube…

In this paper we discuss the utilization of Variational Quantum Solver (VQE) and recently introduced Generalized Unitary Coupled Cluster (GUCC) formalism for the diagonalization of downfolded/effective Hamiltonians in active spaces. In…

We describe a multi-scale resolution approach to analyzing problems in Quantum Mechanics using Daubechies wavelet basis. The expansion of the wavefunction of the quantum system in this basis allows a natural interpretation of each basis…

Computational chemistry at the atomic level has largely branched into two major fields, one based on quantum mechanics and the other on molecular mechanics using classical force fields. Because of high computational costs, quantum…