Entanglement and correlations in one-dimensional quantum many-body systems

Iztok Pižorn

We show that the entanglement entropy of single quasiparticle excitations of one dimensional systems exceeds the ground state entanglement entropy for log(2), if the correlation length of the system is finite. For quadratic fermion systems we show that the excess of entanglement is related to the number of quasiparticles in the excited state. This observation is confirmed by numerical examples of one dimensional quantum many-body systems, including nonintegrable. Tensor network methods to describe quasiparticle excitations are discussed.

Xhek Turkeshi

Ping Xu, Yang Shen, Yuan-Yao He +1 more

In this work, we study the correlation between entanglement and the negative sign problem in quantum Monte Carlo for the simulation of low-dimensional strongly correlated quantum many body systems. Entanglement entropy characterizes the difficulty of many-body simulation with tensor network state related methods, while the average sign measures the difficulty in many-body simulation for a variety of quantum Monte Carlo methods. Although there exist cases where one type of method works better than the other, it is desirable to find the possible correlation between entanglement and average sign for general hard strongly correlated systems regarding computational complexity. We take the doped two-dimensional Hubbard model as an example and numerically calculate the doping evolution of both the entanglement in the ground state with Density Matrix Renormalization Group and the average sign in the Auxiliary Field Quantum Monte Carlo simulation at low temperature. The results show that they are indeed correlated. The entanglement entropy (average sign) shows a peak (dip) around 20% doping, indicating that it is the difficult region for both methods. The vicinity of 20% doping is also the most intriguing region in both the Hubbard model and cuprate high-Tc superconductors where competing states with close energy intertwine with each other. Recognizing the correlation between entanglement and average sign provides new insight into our understanding of the difficulty in the simulation of strongly correlated quantum many-body systems.

Anubhav Kumar Srivastava, Guillem Müller-Rigat, Maciej Lewenstein +1 more

Alexander Streltsov

Christopher Eltschka, Jens Siewert

The existence of correlations between the parts of a quantum system on the one hand, and entanglement between them on the other, are different properties. Yet, one intuitively would identify strong N -party correlations with N -party entanglement in an N -partite quantum state. If the local systems are qubits, this intuition is confirmed: The state with the strongest N -party correlations is the Greenberger-Horne-Zeilinger (GHZ) state, which does have genuine multipartite entanglement. However, for high-dimensional local systems the state with strongest N -party correlations may be a tensor product of Bell states, that is, partially separable. We show this by introducing several novel tools for handling the Bloch representation.