Related papers: Different Bootstrap Matrices in Many QM Systems
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…
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…
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…
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…
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…
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…
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…
Large $N$ matrix quantum mechanics is central to holographic duality but not solvable in the most interesting cases. We show that the spectrum and simple expectation values in these theories can be obtained numerically via a `bootstrap'…
We implement a bootstrap method that combines stationary state conditions, thermal inequalities, and semidefinite relaxations of matrix logarithm in the ungauged one-matrix quantum mechanics, at finite rank N as well as in the large N…
Recently, novel numerical computation on quantum mechanics by using a bootstrap method was proposed by Han, Hartnoll, and Kruthoff. We consider whether this method works in systems with a $\theta$-term, where the standard Monte-Carlo…
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…
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 $\langle \mathop{tr} X^2 \rangle$…
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…
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 work we report on a new bootstrap method for quantum mechanical problems that closely mirrors the setup from conformal field theory (CFT). We use the equations of motion to develop an analogue of the conformal block expansion for…
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…
In this paper, we employ the bootstrap method, a technique that relies on consistency relations instead of direct diagonalization, to determine the expectation values in quantum many-body systems. We then use these values to assess the…
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 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…
Matrix quantum mechanics plays various important roles in theoretical physics, such as a holographic description of quantum black holes. Understanding quantum black holes and the role of entanglement in a holographic setup is of paramount…