# Time-evolving a matrix product state with long-ranged interactions

@article{Zaletel2014TimeevolvingAM, title={Time-evolving a matrix product state with long-ranged interactions}, author={Michael P. Zaletel and Roger S. K. Mong and C. Karrasch and Joel E. Moore and F. Pollmann}, journal={Physical Review B}, year={2014}, volume={91}, pages={165112} }

We introduce a numerical algorithm to simulate the time evolution of a matrix product state under a long-ranged Hamiltonian in moderately entangled systems. In the effectively one-dimensional representation of a system by matrix product states, long-ranged interactions are necessary to simulate not just many physical interactions but also higher-dimensional problems with short-ranged interactions. Since our method overcomes the restriction to short-ranged Hamiltonians of most existing methods…

## 148 Citations

### Correlation-induced steady states and limit cycles in driven dissipative quantum systems

- Physics
- 2020

We study a driven-dissipative model of spins one-half (qubits) on a lattice with nearest-neighbor interactions. Focusing on the role of spatially extended spin-spin correlations in determining the…

### Matrix product state techniques for two-dimensional systems at finite temperature

- Physics
- 2017

The density matrix renormalization group is one of the most powerful numerical methods for computing ground-state properties of two-dimensional (2D) quantum lattice systems. Here we show its…

### Hybrid infinite time-evolving block decimation algorithm for long-range multidimensional quantum many-body systems

- Physics
- 2019

This work presents an algorithm based on a hybrid extension of iTEBD where finite blocks of a chain are first locally time-evolved before an iTE BD-like method combines these processes globally, which permits simulating the dynamics of many-body systems in the thermodynamic limit in $d\geq1$ dimensions including in the presence of long-range interactions.

### Phase diagram of the quantum Ising model with long-range interactions on an infinite-cylinder triangular lattice

- Physics
- 2018

Obtaining quantitative ground-state behavior for geometrically-frustrated quantum magnets with long-range interactions is challenging for numerical methods. Here, we demonstrate that the ground…

### A generalized phase space approach for solving quantum spin dynamics

- PhysicsNew Journal of Physics
- 2019

Numerical techniques to efficiently model out-of-equilibrium dynamics in interacting quantum many-body systems are key for advancing our capability to harness and understand complex quantum matter.…

### Numerical Methods for Many-Body Quantum Dynamics

- Physics
- 2019

A new truncation for matrix product operators is given, which reproduces local properties faithfully without reproducing non-local properties, and the utility of many-body localization as a medium for a thermodynamic engine is studied.

### Momentum-resolved time evolution with matrix product states

- PhysicsPhysical Review B
- 2022

We introduce a method based on matrix product states (MPS) for computing spectral functions of (quasi) one-dimensional spin chains, working directly in momentum space in the thermodynamic limit. We…

### One-dimensional many-body entangled open quantum systems with tensor network methods

- PhysicsQuantum Science and Technology
- 2018

We present a collection of methods to simulate entangled dynamics of open quantum systems governed by the Lindblad master equation with tensor network methods. Tensor network methods using matrix…

### Performance of the time-dependent variational principle for matrix product states in the long-time evolution of a pure state

- PhysicsPhysical Review B
- 2019

The projection of time-dependent variational principle (TDVP) for matrix product states enables us to perform long-time simulations of one-dimensional quantum systems with the conservation of the…

### Time-evolution methods for matrix-product states

- Computer ScienceAnnals of Physics
- 2019

## References

SHOWING 1-10 OF 42 REFERENCES

### Phys

- Rev. Lett. 93, 076401
- 2004

### Nature (London) 441

- 853
- 2006

### Phys

- Rev. Lett. 71, 4055
- 1993

### Phys

- Rev. Lett. 91, 147902
- 2003

### New Journal of Physics 12

- 025012
- 2010

### New J

- Phys. 12, 025012
- 2010

### Progress of Theoretical Physics Supplement 1

### Phys

- 130, 184111
- 2009