Related papers: Lowest Eigenvalues of Random Hamiltonians

In this paper we propose the recursive stochastic state selection method, an extension of the recently developed stochastic state selection method in Monte Carlo calculations for quantum spin systems. In this recursive method we use…

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…

We develop a bosonization scheme for the two-dimensional electron gas in the presence of an uniform magnetic field perpendicular to the two-dimensional system when the filling factor \nu = 1. We show that the elementary neutral excitations…

Some monotone increasing sequences of the lower bounds for the minimum eigenvalue of $M$-matrices are given. It is proved that these sequences are convergent and improve some existing results. Numerical examples show that these sequences…

We consider a finite number $N$ of interacting bosonic atoms at zero temperature confined in a one-dimensional double-well trap and study this system by using the two-site Bose-Hubbard (BH) Hamiltonian. For systems with $N=2$ and $N=3$, and…

Efficiently estimating energy expectation values of quantum lattice systems on quantum computers is a crucial subroutine for various quantum algorithms, which can lead to significant overhead due to the high measurement shot numbers…

We develop a new method to calculate eigenvalues in frustrated quantum spin models. It is based on the stochastic state selection (SSS) method, which is an unconventional Monte Carlo technique we have investigated in recent years. We…

Methods for calculating lower bounds to the exact energy using the variance of the upper bound energy are discussed and explored. All the matrix elements of the Hamiltonian squared are collected and considered, and those for which no known…

We present a general method to determine the energy minimum of spin Hamiltonians over separable states when the single-particle reduced density matrices are fixed. For ferromagnetic Ising and Ising-like models with nearest-neighbor…

General analytic energy bounds are derived for N-boson systems governed by ultrarelativistic Hamiltonians of the form H = sum_{i=1}^N||p_i|| + sum_{1=i<j}^N V(r_{ij}), where V(r) is a static attractive pair potential. It is proved that a…

We investigate the parameter dynamics of eigenvalues of Hamiltonians ('level dynamics') defined on symmetric spaces relevant for condensed matter and particle physics. In particular we: 1) identify appropriate reduced manifold on which the…

Through the introduction of auxiliary fermions, or an enlarged spin space, one can map local fermion Hamiltonians onto local spin Hamiltonians, at the expense of introducing a set of additional constraints. We present a variational…

For a gaussian interaction V(x,y)=\lambda e^{-(x^2+y^2)/r^2} with long range r>>l_B, l_B the magnetic length, we rigorously prove that the eigenvalues of the finite volume Hamiltonian H_{N,LL}=P_{LL} H_N P_{LL}, H_N=\sum_{i=1}^N [-i\hbar…

We review the properties of reduced density matrices for free fermionic or bosonic many-particle systems in their ground state. Their basic feature is that they have a thermal form and thus lead to a quasi-thermodynamic problem with a…

We investigate the entire family of multi-center point interaction Hamiltonians. We show that a large sub-family of these operators do not become either singular or trivial when the positions of two or more scattering centers tend to…

Understanding the mechanisms responsible for the equilibration of isolated quantum many-body systems is a long-standing open problem. In this work we obtain a statistical relationship between the equilibration properties of Hamiltonians and…

Predicting observables in equilibrium states is a central yet notoriously hard question in quantum many-body systems. In the physically relevant thermodynamic limit, certain mathematical formulations of this task have even been shown to…

Estimating the eigenstate properties of quantum systems is a long-standing, challenging problem for both classical and quantum computing. Existing universal quantum algorithms typically rely on ideal and efficient query models (e.g. time…

Manipulating Hamiltonians governing physical systems has found a broad range of applications, from quantum chemistry to semiconductor design. In this work, we provide a new way of manipulating Hamiltonians, by transforming their eigenvalues…

One of the most used approaches in simulating materials is the tight-binding approximation. When using this method in a material simulation, it is necessary to compute the eigenvalues and eigenvectors of the Hamiltonian describing the…