Evaluation of time-dependent correlators after a local quench in iPEPS: hole motion in the t-J model

Abstract

Infinite projected entangled pair states (iPEPS) provide a convenient variational description of infinite, translationally-invariant two-dimensional quantum states. However, the simulation of local excitations is not directly possible due to the translationally-invariant ansatz. Furthermore, as iPEPS are either identical or orthogonal, expectation values between different states as required during the evaluation of non-equal-time correlators are ill-defined. Here, we show that by introducing auxiliary states on each site, it becomes possible to simulate both local excitations and evaluate non-equal-time correlators in an iPEPS setting under real-time evolution. We showcase the method by simulating the t-J model after a single hole has been placed in the half-filled antiferromagnetic background and evaluating both return probabilities and spin correlation functions, as accessible in quantum gas microscopes.

12 pages, 5 figures, minor revision requested by SciPost Physics

References in corpus (9)

• The density-matrix renormalization group in the age of matrix product states
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Time-evolving a matrix product state with long-ranged interactions
• Algorithms for finite Projected Entangled Pair States
• Fermionic Matrix Product States and One-Dimensional Topological Phases
• Fast convergence of imaginary time evolution tensor network algorithms by recycling the environment
• Nonequilibrium quantum dynamics of a charge carrier doped into a Mott insulator
• Ultrafast separation of photo-doped carriers in Mott antiferromagnets

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