Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm

Abstract

We present an algorithm to study mixed-state dynamics in one-dimensional quantum lattice systems. The algorithm can be used, e.g., to construct thermal states or to simulate real time evolutions given by a generic master equation. Its two main ingredients are (i) a superoperator renormalization scheme to efficiently describe the state of the system and (ii) the time evolving block decimation (TEBD) technique to efficiently update the state during a time evolution. The computational cost of a simulation increases significantly with the amount of correlations between subsystems but it otherwise depends only linearly in the system size. We present simulations involving quantum spins and fermions in one spatial dimension.

See also F. Verstraete et al. cond-mat/0406426

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• Generalised ansatz for continuous Matrix Product States
• Quantum stabilization of photonic spatial correlations
• Symmetry between repulsive and attractive interactions in driven-dissipative Bose-Hubbard systems
• Construction of Many-Body-Localized Models where all the eigenstates are Matrix-Product-States
• A Riemannian Approach to the Lindbladian Dynamics of a Locally Purified Tensor Network
• Dynamical symmetry in quantum dissipative models
• Thermal modifications of mesons and energy-energy correlators from real-time simulations of a $U(1)$ lattice gauge theory
• Designing spin channel geometries for entanglement distribution
• Tomography-assisted noisy quantum circuit simulator using matrix product density operators
• Dynamic transition of the density-matrix topology under parity-time symmetry
• Thermal DMRG for highly frustrated quantum spin chains: a user perspective
• Loss-induced quantum information jet in an infinite temperature Hubbard chain
• The Software Landscape for the Density Matrix Renormalization Group
• DMRG and Monte Carlo studies of ${\text{CrI}}_3$ magnetic phases and the phase transition
• Efficient Simulation of Quantum Many-body Thermodynamics by Tailoring Zero-temperature Tensor Network
• Optimal sampling of tensor networks targeting wave function's fast decaying tails
• Towards a better understanding of the matrix product function approximation algorithm in application to quantum physics
• Finite Temperature Minimal Entangled Typical Thermal States Impurity Solver
• Temperature dependence of energy transport in the ${\mathbb{Z}}_3$ chiral clock model
• Heat operator approach to quantum stochastic thermodynamics in the strong-coupling regime
• Efficient approximation for global functions of matrix product operators
• The infinite occupation number basis of bosons - solving a numerical challenge
• Superdiffusive transport in chaotic quantum systems with nodal interactions
• Closed dynamical recursion equations for correlation functions and the application on the construction of Liouvillian spectrum in Lindbladian systems
• Projected Entangled Pair States for Lattice Gauge Theories with Dynamical Fermions
• Spatial reflection and renormalization group flow of quantum many-body systems with matrix product state representation
• Phase diagram of a QED-cavity array coupled via a N-type level scheme
• Dissipation-assisted quantum correlations in coupled qubits
• Lindblad quantum dynamics from correlation functions of classical spin chains
• Sample complexity of matrix product states at finite temperature
• Dual current anomalies and quantum transport within extended reservoir simulations
• A Thermofield-based Multilayer Multiconfigurational Time-Dependent Hartree Approach to Non-Adiabatic Quantum Dynamics at Finite Temperature
• Dynamical Quantum Phase Transitions and Many-Body Backflow in Open Quantum Systems
• Process Tensor Approaches to Non-Markovian Quantum Dynamics
• Determination of the critical exponents in dissipative phase transitions: Coherent anomaly approach
• Quantum typicality approach to energy flow between two spin-chain domains at different temperatures
• Classical simulation of noisy quantum circuits via locally entanglement-optimal unravelings
• Operator entanglement in $\mathrm{SU}(2)$-symmetric dissipative quantum many-body dynamics
• Tensor network states for the description of quantum many-body systems
• Continuous matrix product operators for quantum fields
• Hole-induced anomaly in the thermodynamic behavior of a one-dimensional Bose gas
• Out-of-equilibrium physics in driven dissipative coupled resonator arrays
• Approaching the scaling limit of transport through lattices with dephasing
• Dissipative Yao-Lee Spin-Orbital Model: Exact Solvability and $\mathcal{P}\mathcal{T}$ Symmetry Breaking
• Variational Quantum Algorithm for Solving the Liouvillian Gap
• Locally accurate tensor networks for thermal states and time evolution
• Genuine fidelity gaps associated with a sequential decomposition of genuinely entangling isometry and unitary operations
• Solving Sharp Bounded-error Quantum Polynomial Time Problem by Evolution methods