• Corpus ID: 219573401

Quantum Many-body Bootstrap

@article{Han2020QuantumMB,
  title={Quantum Many-body Bootstrap},
  author={Xizhi Han},
  journal={arXiv: Strongly Correlated Electrons},
  year={2020}
}
  • Xizhi Han
  • Published 10 June 2020
  • Physics
  • arXiv: Strongly Correlated Electrons
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… 
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References

SHOWING 1-10 OF 25 REFERENCES
Rigorous bounds for ground-state properties of correlated Fermi systems.
TLDR
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
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.
TLDR
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.
TLDR
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
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.
  • White
  • Physics, Medicine
    Physical 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
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.
TLDR
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
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.
TLDR
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.
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