Time-dependent variational principle of mixed matrix product states in the thermodynamic limit

Abstract

We describe a time evolution algorithm for quantum spin chains whose Hamiltonians are composed of an infinite uniform left and right bulk part, and an arbitrary finite region in between. The left and right bulk parts are allowed to be different from each other. The algorithm is based on the time-dependent variational principle (TDVP) of matrix product states. It is inversion-free and very simple to adapt from an existing TDVP code for finite systems. The importance of working in the projective Hilbert space is highlighted. We study the quantum Ising model as a benchmark and an illustrative example. The spread of information after a local quench is studied in both the ballistic and the diffusive case. We also offer a derivation of TDVP directly from symplectic geometry.

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Cited by in corpus (6)

• Non-Hermitian Physics
• Spectral properties of 1D extended Hubbard model from bosonization and time-dependent variational principle: applications to 1D cuprate
• Adaptive variational low-rank dynamics for open quantum systems
• Matrix product state simulations of quantum quenches and transport in Coulomb blockaded superconducting devices
• Dissipative dynamics in isolated quantum spin chains after a local quench
• Finding periodic orbits in projected quantum many-body dynamics