相关论文: Application of Bootstrap to $\theta$-term
Recently, a novel bootstrap method for numerical calculations in matrix models and quantum mechanical systems is proposed. We apply the method to certain quantum mechanical systems derived from some well-known local toric Calabi-Yau…
Determining the solvability of a given quantum mechanical system is generally challenging. We discuss that the numerical bootstrap method can help us to solve this question in one-dimensional quantum mechanics. We show that the bootstrap…
We study the quantum-mechanical bootstrap as it applies to the bound states of several central potentials in three dimensions. As part of this effort, we show how the bootstrap approach may be applied to ``non-algebraic'' potentials, such…
The bootstrap is a technique recently developed to get energy eigenvalues of bound states and correlation functions. There are three crucial steps - recursive equations, positivity constraints, search space. We calculate recursive equations…
We study the effectiveness of the numerical bootstrap techniques recently developed in arXiv:2004.10212 for quantum mechanical systems. We find that for a double well potential the bootstrap method correctly captures non-perturbative…
Bootstrap is a novel and ambitious paradigm for quantum physics. It aims to solve the target problems by exploiting theoretical constraints from general physical principles and self-consistency conditions. The bootstrap philosophy dates…
Periodic structures are ubiquitous in quantum many-body systems and quantum field theories, ranging from lattice models, compact spaces, to topological phenomena. However, previous bootstrap studies encountered technical challenges even for…
We show that for a particular model, the quantum mechanical bootstrap is capable of finding exact results. We consider a solvable system with Hamiltonian $H=SZ(1-Z)S$, where $Z$ and $S$ satisfy canonical commutation relations. While this…
Recently, an application of the numerical bootstrap method to quantum mechanics was proposed, and it successfully reproduces the eigenstates of various systems. However, it is unclear why this method works. In order to understand this…
Bootstrap methods, initially developed for solving statistical and quantum field theories, have recently been shown to capture the discrete spectrum of quantum mechanical problems, such as the single particle Schr\"odinger equation with an…
We test the bootstrap approach for determining the spectrum of one dimensional Hamiltonians, following the recent approach of Han, Hartnoll, and Kruthoff. We focus on comparing the bootstrap method data to known analytical predictions for…
In this review, we aim to utilize the bootstrap method to study models that have received significant interest in high energy theory and holography recently. Matrix bootstrap is proposed to determine the range of the solution up to an…
In the realm of contemporary physics, the bootstrap method is typically associated with an optimization-based approach to problem-solving. This method leverages our understanding of a specific physical problem, which is used as the…
General positivity constraints linking various powers of observables in energy eigenstates can be used to sharply locate acceptable regions for the energy eigenvalues, provided that efficient recursive methods are available to calculate the…
We consider matrix quantum mechanics with multiple bosonic matrices, including those obtained from dimensional reduction of Yang-Mills theories. Using the matrix bootstrap, we study simple observables like $\langle \mathop{tr} X^2 \rangle$…
The range of motion of a particle with certain energy $E$ confined in a potential is determined from the energy conservation law in classical mechanics. The counterpart of this question in quantum mechanics can be regarded as what the…
Recently, bootstrap methods from conformal field theory have been adapted for studying the energy spectrum of various quantum mechanical systems. In this paper, we consider the application of these methods in obtaining the spectrum from the…
Recently, the ``Bootstrap" technique was applied in Quantum Mechanics to solve the eigenspectra of Hermitian Hamiltonians and extended to non-Hermitian PT-symmetric systems. However, its application has been limited to real spectra. In this…
We point out that the bootstrap program in quantum mechanics proposed by Han et al reduces to a bootstrap study of a microcanonical ensemble of the same Hamiltonian in the $\hbar \to 0$ limit. In the limit, the quantum mechanical…
A numerical bootstrap method is proposed to provide rigorous and nontrivial bounds in general quantum many-body systems with locality. In particular, lower bounds on ground state energies of local lattice systems are obtained by imposing…