Example codes: TEBD for MPS

Please look at the readme page if you have not done so already. Here we present an implementation of the time evolving block decimation (TEBD) algorithm, which implements real or imaginary time evolution of a matrix product state (MPS). This method is based on a suzuki-trotter decomposition of a local Hamiltonian. Our code first demonstrates the use of imaginary time evolution to find the ground state of an infinite (translation-invariant) quantum system in D=1 dimensions.

    

  • Computational cost: O(d χ^3)

 

  • Based on a 2-site unit cell (A-B pattern)

  • Makes use of the canonical form for MPS 

Code examples:
Network structure:
Edge fixed points:
Local updates:
Index ordering conventions:
Time evolution of MPS (Python module):
Initialization (Python script):
'mainTEBD' benchmark:

Method: TEBD for an MPS of bond dimension χ = 32

Test problem: 1D quantum XX model (on an infinite lattice)

Running time: approx 70 seconds

Quantities computed: ground energy density

Typical results:

Error in ground energy density (TEBD): approx 6e-5

Site maintained by:

Glen Evenbly (www.glenevenbly.com)

Email: contact@tensors.net