# A simple efficient algorithm in frustration-free one-dimensional gapped systems

@article{Huang2015ASE, title={A simple efficient algorithm in frustration-free one-dimensional gapped systems}, author={Yichen Huang}, journal={arXiv: Strongly Correlated Electrons}, year={2015} }

We propose an efficient algorithm for the ground state of frustration-free one-dimensional gapped
Hamiltonians. This algorithm is much simpler than the original one by Landau et al., and thus may
be easily accessible to a general audience in the community. We present all the details in two pages.

## 5 Citations

### Two-dimensional local Hamiltonian problem with area laws is QMA-complete

- MathematicsJ. Comput. Phys.
- 2021

It is shown that the two-dimensional (2D) local Hamiltonian problem with the constraint that the ground state obeys area laws is QMA-complete, and not all ground states of 2D local Hamiltonians with area laws have efficient classical representations that support efficient computation of local expectation values.

### Rigorous RG Algorithms and Area Laws for Low Energy Eigenstates in 1D

- Computer ScienceITCS
- 2017

A new algorithm is given, based on a rigorously justified RG type transformation, for finding low energy states for 1D Hamiltonians acting on a chain of n particles, which is natural and efficient.

### 2D Local Hamiltonian with Area Laws Is QMA-Complete

- Mathematics2020 IEEE International Symposium on Information Theory (ISIT)
- 2020

The 2D local Hamiltonian problem with the constraint that the ground state obeys area laws is QMA-complete and similar results are proved in 2D translation- invariant systems and for the 3D Heisenberg and Hubbard models with local magnetic fields.

### Entanglement Dynamics from Random Product States at Long Times

- Physics2021 IEEE International Symposium on Information Theory (ISIT)
- 2021

For any geometrically local Hamiltonian on a lattice, starting from a random product state the entanglement entropy almost never approaches the Page curve.

### Approximating local properties by tensor network states with constant bond dimension

- Computer Science
- 2019

In one dimension, it is proved that an area law for the Renyi entanglement entropy with index $\alpha<1$ implies a matrix product state representation with bond dimension $\mathrm{poly}(1/\delta)$.

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