Abstract
We analyze and discuss convergence properties of a numerically exact algorithm tailored to study the dynamics of interacting two-dimensional lattice systems. The method is based on the application of the time-dependent variational principle in a manifold of binary and quaternary Tree Tensor Network States. The approach is found to be competitive with existing matrix product state approaches. We discuss issues related to the convergence of the method, which could be relevant to a broader set of numerical techniques used for the study of two-dimensional systems.
Highlights
The exact simulation of the non-equilibrium dynamics of interacting quantum lattice systems is generally an unsolved challenge, due to the exponential growth of the Hilbert space with the size of the system
All calculations employ a regularization of the initial product state, which consists of addition of white noise sampled uniformly from the interval [−10−20, 10−20] and subsequent renormalization of the Tree Tensor Network States (TTNS)
In this work we have assessed the performance of TTNS for simulating the dynamics of twodimensional many-body lattice systems
Summary
The exact simulation of the non-equilibrium dynamics of interacting quantum lattice systems is generally an unsolved challenge, due to the exponential growth of the Hilbert space with the size of the system. Tensor network state (TNS) methods allow for a significant extension of accessible length scales by trading in the exponential cost in system size for an exponential cost in time. This becomes possible due to a reduction of the exact Hilbert space in terms of a structured product of low-order tensors, referred to as a tensor network. In one-dimensional systems, these timescales are often comparable to those attainable in experimental realizations [4], going to higher spatial dimensions becomes extremely challenging due to a number of reasons
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
