11/22/2023 0 Comments Entanglement entropyThe vast gain in efficiency of this method allows us to access unprecedented system sizes up to 192 × 96 spins for the square lattice Heisenberg antiferromagnet. You could also say that von Neumann entropy is the Shannon entropy of the vector of eigenvalues of the density matrix of. We use these ideas to extract universal information from quantum Monte Carlo simulations of SU( N) spin models in one and two dimensions. In the Heisenberg XY spin chain model, the Rényi entropy as a function of can be calculated explicitly because it is an automorphic function with respect to a particular subgroup of the modular group. This framework also naturally leads to the idea of using quench functions with spatially smooth profiles, providing us a way to average over lattice scale features of the entanglement entropy while preserving long distance universal information. The Rényi entropy is also important in quantum information, where it can be used as a measure of entanglement. Nonequilibrium fluctuation theorems of the work provide us with statistically exact estimates of the Rényi entanglement entropy. We introduce an external field λ that controls the partition function topology, allowing us to define a notion of nonequilibrium work as λ is varied smoothly. This implies that separable states have zero entanglement entropy-theyarenotentangled. The Rényi entanglement entropy in quantum many-body systems can be viewed as the difference in free energy between partition functions with different trace topologies.
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