# Quantum Many-body Bootstrap

@article{Han2020QuantumMB, title={Quantum Many-body Bootstrap}, author={Xizhi Han}, journal={arXiv: Strongly Correlated Electrons}, year={2020} }

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 positivity constraints on certain operator expectation values. Complemented with variational upper bounds, ground state observables are constrained to be within a narrow range. The method is demonstrated with the Hubbard model in one and two dimensions, and…

## One Citation

Bootstrapping Bloch bands

- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2021

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…

## References

SHOWING 1-10 OF 25 REFERENCES

Rigorous bounds for ground-state properties of correlated Fermi systems.

- Physics, MedicinePhysical review. B, Condensed matter
- 1991

It is shown that upper and lower bounds on the ground-state energy of models describing correlated Fermi systems may be combined to produce bounds onThe ground- state magnetization and chemical potential, and ways of improving these bounds are discussed, including the use of kinetic frustration, nonuniform clusters, and averaging over boundary conditions.

Lower bounds for ground states of condensed matter systems

- Physics
- 2012

Standard variational methods tend to obtain upper bounds on the ground state energy of quantum many-body systems. Here we study a complementary method that determines lower bounds on the ground state…

Bootstrapping Matrix Quantum Mechanics.

- Physics, MedicinePhysical review letters
- 2020

It is shown that the spectrum and simple expectation values in these theories can be obtained numerically via a "bootstrap" methodology, where operator expectation values are related by symmetries and bounded with certain positivity constraints.

Enhanced Constraints for Accurate Lower Bounds on Many-Electron Quantum Energies from Variational Two-Electron Reduced Density Matrix Theory.

- Physics, MedicinePhysical review letters
- 2016

An orders-of-magnitude improvement in the accuracy of 2-RDM calculations without an increase in their computational cost is presented.

Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms

- Physics
- 2015

Numerical results for ground-state and excited-state properties (energies, double occupancies, and Matsubara-axis self-energies) of the single-orbital Hubbard model on a two-dimensional square…

Density matrix formulation for quantum renormalization groups.

- Physics, MedicinePhysical review letters
- 1992

A generalization of the numerical renormalization-group procedure used first by Wilson for the Kondo problem is presented. It is shown that this formulation is optimal in a certain sense. As a…

Ground-state phase diagram of the square lattice Hubbard model from density matrix embedding theory

- Physics
- 2016

We compute the ground-state phase diagram of the Hubbard and frustrated Hubbard models on the square lattice with density matrix embedding theory using clusters of up to 16 sites. We provide an error…

Density matrix embedding: a simple alternative to dynamical mean-field theory.

- Medicine, PhysicsPhysical review letters
- 2012

Frequency independence and the minimal bath make DMET a computationally simple and efficient method and compared to benchmark data, total energies, correlation functions, and metal-insulator transitions are well reproduced, at a tiny computational cost.

The Conformal Bootstrap: Theory, Numerical Techniques, and Applications

- Physics
- 2019

Conformal field theories have been long known to describe the fascinating universal physics of scale invariant critical points. They describe continuous phase transitions in fluids, magnets, and…

Variational reduced density matrix method in the doubly-occupied configuration interaction space using four-particle N-representability conditions: Application to the XXZ model of quantum magnetism.

- Medicine, PhysicsThe Journal of chemical physics
- 2019

The different approximations are applied to the one-dimensional XXZ model of quantum magnetism, which has a rich phase diagram with one critical phase and constitutes a stringent test for the method and shows the usefulness of the treatment to achieve a high degree of accuracy.