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Efficient simulation of one-dimensional quantum many-body systems
G. Vidal
TL;DR
Generic quantum many-body states require exponentially many parameters, while efficient simulation of time-dependent properties remains open in most non-perturbative cases. The paper presents a one-dimensional local-Hamiltonian simulation scheme based on slightly entangled state decompositions and reports efficient low-energy dynamics simulation using O(n) parameters.
Problem
Generic quantum many-body states require exponentially many parameters, and efficient simulation of time-dependent properties remains open in most non-perturbative cases.
Source: p. 1Method
The method decomposes slightly entangled states and efficiently updates the decomposition under one- or two-system unitary transformations for local Hamiltonian evolution.
Source: pp. 1–3Results
The scheme efficiently simulates low-energy dynamics in one-dimensional arrays using O(n) parameters, with small Schmidt-term truncations supported by roughly exponential coefficient decay.
Source: pp. 2, 4Takeaways & Limitations
The method can compute time-dependent properties of low-energy dynamics in sufficiently regular one-dimensional quantum systems with local interactions.
Source: p. 1The scheme's main errors arise from Schmidt-decomposition truncation and the Trotter expansion, and its efficiency depends on limited entanglement during the simulated evolution.
Source: pp. 1, 3
Abstract
from arXiv · showhide
We present a numerical method to simulate the time evolution, according to a Hamiltonian made of local interactions, of quantum spin chains and systems alike. The efficiency of the scheme depends on the amount of the entanglement involved in the simulated evolution. Numerical analysis indicate that this method can be used, for instance, to efficiently compute time-dependent properties of low-energy dynamics of sufficiently regular but otherwise arbitrary one-dimensional quantum many-body systems.