Light cone tensor network and time evolution

The transverse folding algorithm [M. C. Banuls et al., Phys. Rev. Lett. 102, 240603 (2009)] is a tensor network method to compute time-dependent local observables in out-of-equilibrium quantum spin chains that can overcome the limitations of matrix product states when entanglement grows slower in the time than in the space direction. We present a contraction strategy that makes use of the exact light cone structure of the tensor network representing the observables. The strategy can be combined with the hybrid truncation proposed for global quenches by Hastings and Mahajan Phys. Rev. A 91, 032306 (2015), which significantly improves the efficiency of the method. We demonstrate the performance of this transverse light cone contraction also for transport coefficients, and discuss how it can be extended to other dynamical quantities.

Automated summary

This paper presents a tensor network method, called the transverse folding algorithm, for computing time-dependent local observables in out-of-equilibrium quantum spin chains. The method overcomes the limitations of matrix product states when the entanglement grows slower in time than in space. A contraction strategy based on the exact light cone structure of the tensor network is proposed, which can be combined with the hybrid truncation approach to improve the efficiency of the method. The performance of this strategy is demonstrated for transport coefficients and potential extensions to other dynamical quantities are discussed.