Related papers: Elementary example of exact effective-Hamiltonian …
We introduce a systematic framework to derive the effective Hamiltonian governing the coherent dynamics of non-Markovian open quantum systems. By applying the minimal dissipation principle, we uniquely isolate the coherent contribution to…
A potential approach for demonstrating quantum advantage is using quantum computers to simulate fermionic systems. Quantum algorithms for fermionic system simulation usually involve the Hamiltonian evolution and measurements. However, in…
We outline a procedure for applying Hamiltonian Truncation to Quantum Field Theories (QFTs) that have UV divergences. To do this, we derive a novel representation of an Effective Hamiltonian which makes manifest some of its important…
The $\mathbf{k}\cdot\mathbf{p}$ method, combined with group theory, is an efficient approach to obtain the low energy effective Hamiltonians of crystalline materials. Although the Hamiltonian coefficients are written as matrix elements of…
Exact unitary transformations play a central role in the analysis and simulation of many-body quantum systems, yet the conditions under which they can be carried out exactly and efficiently remain incompletely understood. We show that exact…
An approximate diagonalization method is proposed that combines exact diagonalization and perturbation expansion to calculate low energy eigenvalues and eigenfunctions of a Hamiltonian. The method involves deriving an effective Hamiltonian…
We consider the entropy and decoherence in fermionic quantum systems. By making a Gaussian Ansatz for the density operator of a collection of fermions we study statistical 2-point correlators and express the entropy of a system fermion in…
We describe a method for deriving effective low-energy theories of electronic interactions at graphene edges. Our method is applicable to general edges of honeycomb lattices (zigzag, chiral, and even disordered) as long as localized…
A method of exactly solving the master equation is presented in this letter. The explicit form of the solution is determined by the time evolution of a composite system including an auxiliary system and the open system in question. The…
We develop a new method that allows us to map models of interacting fermions onto bosonic models describing collective excitations in an arbitrary dimension. This mapping becomes exact in the thermodynamic continuous time limit. The boson…
We present a family of exactly-solvable generalizations of the Jaynes-Cummings model involving the interaction of an ensemble of SU(2) or SU(1,1) quasi-spins with a single boson field. They are obtained from the trigonometric…
We develop a numerical algorithm for computing the effective drift and diffusivity of the steady-state behavior of an overdamped particle driven by a periodic potential whose amplitude is modulated in time by multiplicative noise and forced…
We present a recursive formula for the computation of the static effective Hamiltonian of a system under a fast-oscillating drive. Our analytical result is well-suited to symbolic calculations performed by a computer and can be implemented…
We study the properties of heavy fermions in the vector-like representation of the electro-weak gauge group $SU(2)_W\times U(1)_Y$ with Yukawa couplings to the standard model (SM) Higgs boson. Using the renormalization group analysis, we…
The functional derivative of the effective action with respect to an external field is part of the equation of motion of this field if one-loop effects induced by quantum fluctuations or thermal fluctuations are included when minimizing the…
A construction of the Coulomb-Breit Hamiltonian for a pair of fermions, considered as a quantum two-body system, immersed in an arbitrary background gravitational field described by Einstein's General Relativity is presented. Working with…
James' effective Hamiltonian method has been extensively adopted to investigate largely detuned interacting quantum systems. This method is just corresponding to the second-order perturbation theory, and cannot be exploited to treat the…
By extending the mean-field Hamiltonian to include nonhermitian operators, the master equations for fermions and bosons can be derived. The derived equations reduce to the Markoff master equation in the low-density limit and to the…
Effective Hamiltonian methods are utilized to model the two-qubit cross-resonance gate for both the ideal two-qubit case and when higher levels are included. Analytic expressions are obtained in the qubit case and the higher-level model is…
In this work we present a novel quantum Monte-Carlo method for fermions, based on an exact decomposition of the Boltzmann operator $exp(-\beta H)$. It can be seen as a synthesis of several related methods. It has the advantage that it is…