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Matrix product states for dynamical simulation of infinite chains.
M C Bañuls1, M B Hastings, F Verstraete
1Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany. banulsm@mpq.mpg.de
Physical Review Letters
|August 8, 2009
Summary
We present a novel tensor network method for infinite chains, enabling accurate ground state and time evolution calculations without finite size extrapolation. This approach allows for longer simulation times and analysis of non-invariant systems, including impurity models.
Area of Science:
- Condensed Matter Physics
- Quantum Many-Body Systems
- Computational Physics
Background:
- Accurate computation of ground state properties and time evolution for infinite quantum systems is computationally challenging.
- Existing methods often require finite size extrapolation or suffer from limitations in simulation time due to bond dimension truncation.
Purpose of the Study:
- To introduce a new tensor network contraction method for efficient and accurate calculations on infinite chains.
- To overcome limitations of existing methods regarding finite size extrapolation and simulation time.
Main Methods:
- A transverse contraction of the tensor network is employed.
- The tensor network is folded in the time direction before contraction.
- The method avoids explicit truncation of the bond dimension during time evolution.
Main Results:
- The proposed method accurately computes ground state properties and time evolution of infinite chains.
- It enables computation of time-dependent expectation values and dynamic correlation functions for significantly longer evolution times.
- The algorithm is applicable to non-invariant infinite chains, including impurity models.
Conclusions:
- This novel tensor network contraction method offers a significant advancement for studying infinite quantum systems.
- The technique provides a more efficient and accurate approach to simulating quantum dynamics and static properties.
- It opens new possibilities for investigating complex systems like impurity models that were previously intractable.
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