Simulating fermionic lattice models with qubits requires mapping fermionic degrees of freedom to qubits. The simplest method for this task, the Jordan-Wigner transformation, yields strings of Pauli operators acting on an extensive number of qubits. This overhead can be a hindrance to implementation of qubit-based quantum simulators, especially in the analog context. Here we thus review and anal...

on utilizing the spectral representation of selfadjoint operators in hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in hilbert spaces via a taylor's type expansion are given.

We present a canonical mapping transforming physical boson operators into quadratic products of cluster composite bosons that preserves matrix elements of operators when a physical constraint is enforced. We map the 2D lattice Bose-Hubbard Hamiltonian into 2×2 composite bosons and solve it within a generalized Hartree-Bogoliubov approximation. The resulting Mott insulator-superfluid phase diagr...

We propose a quantum-classical hybrid scheme for implementing the nonunitary Gutzwiller factor using discrete Hubbard-Stratonovich transformation, which allows us to express as linear combination of unitary operators involving only single-qubit rotations, at cost sum over auxiliary fields. To perform fields, we introduce two approaches that have complementary features. The first approach employ...

We develop the quantum inverse scattering method for the one-dimensional Hubbard model on the infinite interval at zero density. R-matrix and monodromy matrix are obtained as limits from their known counterparts on the finite interval. The R-matrix greatly simplifies in the considered limit. The new R-matrix contains a submatrix which turns into the rational R-matrix of the XXX-chain by an appr...

We develop the quantum inverse scattering method for the one-dimensional Hubbard model on the innnite line at zero density. This enables us to diagonalize the Hamiltonian algebraically. The eigenstates can be classiied as scattering states of particles, bound pairs of particles and bound states of pairs. We obtain the corresponding creation and annihilation operators and calculate the S-matrix....

We construct entanglement witnesses using fundamental quantum operators of spin models which contain two-particle interactions and have a certain symmetry. By choosing the Hamiltonian as such an operator, our method can be used for detecting entanglement by energy measurement. We apply this method to the Heisenberg model in a cubic lattice with a magnetic field, the XY model and other familiar ...

With the success of dynamical mean-field theories, solvers for quantum-impurity problems have become an important tool for the numerical study of strongly correlated systems. Continuous-time quantum Monte Carlo sampling of the expansion in powers of the hybridization between the “impurity” and the bath provides a powerful solver when interactions are strong. Here we show that the usual updates ...

We present an analytic study of the phase diagram of the one-dimensional t − J model and a couple of its cousins. To deal with the interactions induced by the no double occupancy constraints, we introduce a deformation of the Hubbard operators. When the deformation parameter ∆ is small, the induced interactions are softened, accessible by perturbation theory. We combine bososnization with renor...

By means of a diagram technique for Hubbard operators, we show the existence of a spin-dependent renormalization of the localized levels in an interacting region, e.g., quantum dot, modeled by the Anderson Hamiltonian with two conduction bands. It is shown that the renormalization of the levels with a given spin direction is due to kinematic interactions with the conduction subbands of the oppo...