Related papers: Seniority-zero Linear Canonical Transformation The…
In this paper we introduce an alternative approach to studying the evolution of a quantum harmonic oscillator subject to an arbitrary time dependent force. With the purpose of finding the evolution operator, certain unitary transformations…
A new representation for electrons is introduced, in which the electron operators are written in terms of a spinless fermion and the Pauli operators. This representation is canonical, invertible and constraint-free. Importantly, it…
In this work, the benefits of the phase fitting technique are embedded in high order discrete Lagrangian integrators. The proposed methodology creates integrators with zero phase lag in a test Lagrangian in a similar way used in phase…
It is shown how to adapt the non-perturbative coupled cluster method of many-body theory so that it may be successfully applied to Hamiltonian lattice $SU(N)$ gauge theories. The procedure involves first writing the wavefunctions for the…
A time-dependent unitary (canonical) transformation is found which maps the Hamiltonian for a harmonic oscillator with time-dependent real mass and real frequency to that of a generalized harmonic oscillator with time-dependent real mass…
Continuous unitary transformations are a powerful tool to extract valuable information out of quantum many-body Hamiltonians, in which the so-called flow equation transforms the Hamiltonian to a diagonal or block-diagonal form in second…
In this note we study inverse spectral problems for canonical Hamiltonian systems, which encompass a broad class of second order differential equations on a half-line. Our goal is to extend the classical resultss developed in the work of…
H\"uckel molecular orbital (HMO) theory provides a semi-empirical treatment of the electronic structure in conjugated {\pi}-electronic systems. A scalable system-agnostic execution of HMO theory on a quantum computer is reported here based…
This paper develops a systematic strong coupling spin wave expansion of itinerant Kondo lattice magnets, magnets in which local moment spins are Kondo coupled to itinerant charge degrees of freedom. The strong coupling expansion is based on…
Unknown unitary inversion is a fundamental primitive in quantum computing and physics. Although recent work has demonstrated that quantum algorithms can invert arbitrary unknown unitaries without accessing their classical descriptions,…
Two-level boson systems displaying a quantum phase transition from a spherical (symmetric) to a deformed (broken) phase are studied. A formalism to diagonalize Hamiltonians with $O(2L+1)$ symmetry for large number of bosons is worked out.…
The supersymmetric structure of a generalized non-Hermitian driven two-level system is demonstrated. A unitary rotation turns the Hamiltonian into a more convenient form. After decoupling a set of differential equations, the supersymmetric…
We present efficient algorithms for obtaining the Hamiltonian in Lightcone Conformal Truncation (LCT) for a 2d scalar field with a generic potential. We apply this method to the sine-Gordon and sinh-Gordon models in $1+1d$, and find precise…
This paper derives master equations for an atomic two-level system for a large set of unitarily equivalent Hamiltonians without employing the rotating wave and certain Markovian approximations. Each Hamiltonian refers to physically…
A full coupled-cluster expansion suitable for sparse algebraic operations is developed by expanding the commutators of the Baker-Campbell-Hausdorff series explicitly for cluster operators in binary representations. A full coupled-cluster…
This report discusses two new ideas for using perturbation methods to solve the time-independent Schr\"odinger equation. The first concept begins with rewriting the perturbation equations in a form that is closely related to matrix…
A novel canonical transformation is offered as the mean for studying properties of a system of strongly correlated electrons. As an example of the utility of the transformation, it is used to demonstrate the existence of a quantum phase…
Seniority-zero wavefunctions describe bond-breaking processes qualitatively. As eigenvectors of a model Hamiltonian, Richardson-Gaudin states provide a clear physical picture and allow for systematic improvement via standard single…
Hamilton-Jacobi theory is a fundamental subject of classical mechanics and has also an important role in the development of quantum mechanics. Its conceptual framework results from the advantages of transformation theory and, for this…
We present a finite-temperature canonical-ensemble determinant quantum Monte Carlo algorithm that enforces an exact fermion number and enables stable simulations of correlated lattice fermions. We propose a stabilized QR update that reduces…