Generating Function for Tensor Network Diagrammatic Summation

Abstract

The understanding of complex quantum many-body systems has been vastly boosted by tensor network (TN) methods. Among other things, excitation spectrum and long-range interacting systems can be studied using TNs, where one however confronts the intricate summation over an extensive number of tensor diagrams. Here, we introduce a set of generating functions, which encode the diagrammatic summations as leading order series expansion coefficients. Combined with automatic differentiation, the generating function allows us to solve the problem of TN diagrammatic summation. We illustrate this scheme by computing variational excited states and dynamical structure factor of a quantum spin chain, and further investigating entanglement properties of excited states. Extensions to infinite size systems and higher dimension are outlined.

Universal Rényi entanglement entropy of quasiparticle excitations

“…The universal Rényi and entanglement entropies we have obtained can also be used as a benchmark to other methods, for example the tensor network techniques [60][61][62][63]. The techniques to calculate the Rényi and entanglement entropies are also useful to calculate the subsystem Schatten and trace distances [55].…”

Efficient MPS methods for extracting spectral information on rings and cylinders

“…In the case of 1-D periodic systems, there have been a number of proposals for alleviating the computational cost of periodic MPS [23][24][25][26][27] and DMRG [28,29] simulations. In addition, a variational ansatz for capturing elementary excitations on top of a periodic MPS was proposed [30] and refined [27,31], which captures many low-lying energy levels that reflect the CFT finite-size spectrum of critical spin chains [27]. Here, it is crucial that translation invariance is explicitly conserved in the ground state -by choosing a uniform MPS ansatz -such that the momentum is a good quantum number for labeling the excited states.…”