Numerical Simulation of Critical Quantum Dynamics without Finite Size Effects

Abstract

Classical $(1+1)D$ cellular automata, as for instance Domany-Kinzel cellular automata, are paradigmatic systems for the study of non-equilibrium phenomena. Such systems evolve in discrete time-steps, and are thus free of time-discretisation errors. Moreover, information about critical phenomena can be obtained by simulating the evolution of an initial seed that, at any finite time, has support only on a finite light-cone. This allows for essentially numerically exact simulations, free of finite-size errors or boundary effects. Here, we show how similar advantages can be gained in the quantum regime: The many-body critical dynamics occurring in $(1+1)D$ quantum cellular automata with an absorbing state can be studied directly on an infinite lattice when starting from seed initial conditions. This can be achieved efficiently by simulating the dynamics of an associated one-dimensional, non-unitary quantum cellular automaton using tensor networks. We apply our method to a model introduced recently and find accurate values for universal exponents, suggesting that this approach can be a powerful tool for precisely classifying non-equilibrium universal physics in quantum systems.

arXiv comment5 pages, 3 figures

References in corpus (27)

• The density-matrix renormalization group in the age of matrix product states
• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Time-evolution methods for matrix-product states
• Tensor networks for complex quantum systems
• Matrix product operator representations
• Universal scaling behavior of non-equilibrium phase transitions
• Matrix Product States for dynamical simulation of infinite chains
• Lecture Notes of Tensor Network Contractions
• Finite automata for caching in matrix product algorithms
• A review of Quantum Cellular Automata
• Matrix Product Unitaries: Structure, Symmetries, and Topological Invariants
• Absorbing state phase transition with competing quantum and classical fluctuations
• Unitary and non-unitary quantum cellular automata with Rydberg arrays
• Entanglement Dynamics in 1D Quantum Cellular Automata
• Quantum Cellular Automata, Tensor Networks, and Area Laws
• Quantum contact process
• Exact large deviation statistics and trajectory phase transition of a deterministic boundary driven cellular automaton
• Non-equilibrium effective field theory for absorbing state phase transitions in driven open quantum spin systems
• Light Cone Matrix Product
• Variational Matrix Product Ansatz for Nonuniform Dynamics in the Thermodynamic Limit
• Efficient description of many-body systems with Matrix Product Density Operators
• Phenomenology of a First Order Dark State Phase Transition
• Non-equilibrium phase transitions in $(1+1)$-dimensional quantum cellular automata with controllable quantum correlations
• Ergodicity of quantum cellular automata
• Absorbing phase transition with a continuously varying exponent in a quantum contact process: a neural network approach
• Numerical Simulation of Critical Dissipative Non-Equilibrium Quantum Systems with an Absorbing State
• Non-equilibrium absorbing state phase transitions in discrete-time quantum dynamics

Cited by in corpus (9)

• Characterizing a non-equilibrium phase transition on a quantum computer
• Light cone tensor network and time evolution
• Directed percolation in non-unitary quantum cellular automata
• Quantum and classical temporal correlations in $(1+1)D$ Quantum Cellular Automata
• Using (1 + 1)D Quantum Cellular Automata for Exploring Collective Effects in Large Scale Quantum Neural Networks
• Asynchronism and nonequilibrium phase transitions in $(1+1)$D quantum cellular automata
• Dissipative quantum many-body dynamics in (1+1)D quantum cellular automata and quantum neural networks
• Non-linear classification capability of quantum neural networks due to emergent quantum metastability
• Density Classification with Non-Unitary Quantum Cellular Automata