Time-dependent variational principle for quantum lattices

Abstract

We develop a new algorithm based on the time-dependent variational principle applied to matrix product states to efficiently simulate the real- and imaginary time dynamics for infinite one-dimensional quantum lattice systems. This procedure: (1) is argued to be optimal; (2) does not rely on the Trotter decomposition and thus has no Trotter error; (3) explicitly preserves all symmetries and conservation laws; and (4) has low computational complexity. The algorithm is illustrated using both imaginary time and real-time examples.

main text (4+ pages, 2 figures, 1 table) + supplementary material (15 pages, 2 figures). Corrections and other small changes, added reference

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• Energy-filtered quantum states and the emergence of non-local correlations
• Splitting the local Hilbert space: MPS-based approach to large local dimensions
• The Kibble Zurek Mechanism of Topological Defect Formation in Quantum Field Theory with Matrix Product States
• Characterization of photoexcited states in the half-filled one-dimensional extended Hubbard model assisted by machine learning
• Stability and Dynamics of Atom-Molecule Superfluids Near a Narrow Feshbach Resonance
• Probing Confinement Through Dynamical Quantum Phase Transitions: From Quantum Spin Models to Lattice Gauge Theories
• Emergent statistical bubble localization in a Z2 lattice gauge theory
• Formation of Spatial Patterns by Spin-selective Excitations of Interacting Fermions
• Simulating real-time molecular electron dynamics efficiently using the time-dependent density matrix renormalization group
• Density Matrix Renormalization Group Study of Domain Wall Qubits
• Approximating Hamiltonian dynamics with the Nyström method
• Robust control of long distance entanglement in disordered spin chains
• Disorder in order: Localization without randomness in a cold atom system
• Forestalled Phase Separation as the Precursor to Stripe Order
• Tangent space generators of matrix product states and exact Floquet quantum scars
• Large-scale stochastic simulation of open quantum systems
• Quantum trails and memory effects in the phase space of chaotic quantum systems
• Order, Disorder and Monopole Confinement in the Spin-$1/2$ XXZ Model on a Pyrochlore Tube
• Page Curve and Entanglement Dynamics in an Interacting Fermionic Chain
• Extracting Off-Diagonal Order from Diagonal Basis Measurements
• Time-Evolving Weiss Fields in the Stochastic Approach to Quantum Spins
• Localization of Pairs in One-Dimensional Quasicrystals with Power-Law Hopping
• Finite-temperature Rydberg arrays: quantum phases and entanglement characterization
• On quenches to the critical point of the three states Potts model -- Matrix Product State simulations and CFT
• Embedding semiclassical periodic orbits into chaotic many-body Hamiltonians
• Detection of anyon braiding through pump-probe spectroscopy
• Scrambling under quench
• Variational Neural and Tensor Network Approximations of Thermal States
• Nanoscale engineering and dynamical stabilization of mesoscopic spin textures
• Tracking locality in time evolution of disordered systems
• Dynamical quantum phase transition and thermal equilibrium in the lattice Thirring model
• Gaussian trajectory description of fragmentation in an isolated spinor condensate
• Dynamical Phase Error in Interacting Topological Quantum Memories
• Conductance of correlated many-fermion systems from charge fluctuations
• Simulation of quantum physics with Tensor Processing Units: brute-force computation of ground states and time evolution
• Qubit-oscillator relationships in the open quantum Rabi model: the role of dissipation
• Two Dimensional Isometric Tensor Networks on an Infinite Strip
• Thermal and optical conductivity in the Holstein model at half filling and at finite temperature in the Luttinger-liquid and charge-density-wave regime
• Efficient tensor-network simulation for the few-atom multimode Dicke model via coupling-matrix transformation
• Optimal encoding of two dissipative interacting qubits
• Variational manifolds for ground states and scarred dynamics of blockade-constrained spin models on two and three dimensional lattices
• Fractonic Quantum Quench in Dipole-constrained Bosons
• Quench dynamics of two component dipolar fermions subject to a quasiperiodic potential
• Density Classification with Non-Unitary Quantum Cellular Automata
• Schwinger-Keldysh non-perturbative field theory of open quantum systems beyond the Markovian regime: Application to spin-boson and spin-chain-boson models
• Optimisation of ultrafast singlet fission in 1D rings towards unit efficiency
• A New Framework for Quantum Phases in Open Systems: Steady State of Imaginary-Time Lindbladian Evolution
• From Light-Cone to Supersonic Propagation of Correlations by Competing Short- and Long-Range Couplings
• Driven Critical Dynamics in Tricitical Point
• Time Evolution and Deterministic Optimisation of Correlator Product States
• Quantum dynamics of cosmological particle production: interacting quantum field theories with matrix product states
• Efficient optimization and conceptual barriers in variational finite Projected Entangled-Pair States
• Thermal pure matrix product state in two dimensions: tracking thermal equilibrium from paramagnet down to the Kitaev honeycomb spin liquid state
• Spreading of a local excitation in a Quantum Hierarchical Model
• Quantum Chaos in a Rydberg Atom System
• Importance Sampling Scheme for the Stochastic Simulation of Quantum Spin Dynamics
• Spin excitations arising from anisotropic Dirac spinons in YCu${}_3$(OD)${}_6$Br${}_2$[Br${}_{0.33}$(OD)${}_{0.67}$]
• Simulating Quantum Turbulence with Matrix Product States
• Extracting the spin excitation spectrum of a fermionic system using a quantum processor
• Macroproperties vs. Microstates in the Classical Simulation of Critical Phenomena in Quench Dynamics of 1D Ising Models
• Dynamical deconfinement transition driven by density of excitations
• Thermal Tensor Network Simulations of Lattice Fermions with Fixed Filling
• Accelerating two-dimensional tensor network optimization by preconditioning
• Ab-Initio Approach to Many-Body Quantum Spin Dynamics
• Clifford-Dressed Variational Principles for Precise Loschmidt Echoes
• Simulating quantum dynamics: Evolution of algorithms in the HPC context
• Self-consistent tensor network method for correlated super-moiré matter beyond one billion sites
• Assessing quantum dot SWAP gate fidelity using tensor network methods
• Generalized Hartree Fock Theory for Dispersion Relations of Interacting Fermionic Lattice Systems
• Incommensurate Matrix Product State for Quantum Spin Systems
• Spectroscopy and complex-time correlations using minimally entangled typical thermal states
• Prospects for NMR Spectral Prediction on Fault-Tolerant Quantum Computers
• Pseudogap with Fermi arcs and Fermi pockets in half-filled twisted transition metal dichalcogenides
• Parent Hamiltonian Reconstruction via Inverse Quantum Annealing
• Cost of Locally Approximating High-Dimensional Ground States of Contextual Quantum Models
• Chiral Gravitons on the Lattice
• Phonon state tomography of electron correlation dynamics in optically excited solids
• Monte Carlo Simulation of Operator Dynamics and Entanglement in Dual-Unitary Circuits
• Phase diagram of the antiferromagnetic $J_1$-$J_2$ spin-$1$ pyrochlore Heisenberg model
• String breaking dynamics in Ising chain with local vibrations
• Searching for superconductivity in doped triangular lattice Kitaev magnets
• Achieving the quantum field theory limit in far-from-equilibrium quantum link models
• Harnessing Quantum Dynamics for Robust and Scalable Quantum Extreme Learning Machines
• Tensor network method for real-space topology in quasicrystal Chern mosaics
• Matrix product state simulations of quantum quenches and transport in Coulomb blockaded superconducting devices
• Neuralized Fermionic Tensor Networks for Quantum Many-Body Systems
• Quasi-Fermi liquid behavior in a one-dimensional system of interacting spinless fermions
• Path Integral for Spin-1 Chain in the Fluctuating Matrix Product State Basis
• Floquet Schrieffer-Wolff transform based on Sylvester equations
• Temperature dependence of energy transport in the ${\mathbb{Z}}_3$ chiral clock model
• Magnon Damping as a Probe of Kondo Coupling in Magnetically Ordered Systems
• Universal quasi-Fermi liquid physics of one-dimensional interacting fermions
• Kondo spectral functions at low-temperatures: A dynamical-exchange-correlation-field perspective
• Blockwise Optimization for Projective Variational Quantum Dynamics (BLOP-VQD): Algorithm and Implementation for Lattice Systems
• ScarFinder: a detector of optimal scar trajectories in quantum many-body dynamics
• Emergence of topological states in relaxation dynamics of interacting bosons
• Dissipationless dynamics of spin supersolid states in a spin-1/2 triangular antiferromagnet with impurities
• The ITransverse.jl library for transverse tensor network contractions
• Finite Temperature Minimal Entangled Typical Thermal States Impurity Solver
• A Synthesis of Hidden Subgroup Quantum Algorithms and Quantum Chemical Dynamics
• Numerically exact quantum dynamics with tensor networks: Predicting the decoherence of interacting spin systems
• Overcoming disorder in superconducting globally driven quantum computing
• Variational approach to open quantum systems with long-range competing interactions
• Heat operator approach to quantum stochastic thermodynamics in the strong-coupling regime
• Efficient approximation for global functions of matrix product operators
• Spatiotemporal Quenches in Long-Range Hamiltonians
• Summing Real Time Feynman Paths of Lattice Polaron with Matrix Product States
• Simulating dynamics of the two-dimensional transverse-field Ising model: a comparative study of large-scale classical numerics
• Reciprocal Floquet thermalization in one-dimensional Rydberg atom array
• Investigating Stark many-body localization with continuous unitary transformation flows
• Phase structure and real-time dynamics of the massive Thirring model in 1+1 dimensions using the tensor-network method
• Quantum Utility in Simulating the Real-time Dynamics of the Fermi-Hubbard Model using Superconducting Quantum Computers
• Entanglement transitions in a boundary-driven open quantum many-body system
• The Software Landscape for the Density Matrix Renormalization Group
• Pseudospectral method for solving PDEs using Matrix Product States
• Quantum Fisher information from tensor network integration of Lyapunov equation
• Harnessing spin-qubit decoherence to probe strongly-interacting quantum systems
• Real-time evolution and quantized charge pumping in magnetic Weyl semimetals
• Artificial Gauge Field Engineered Excited-State Topology: Control of Dynamical Evolution of Localized Spinons
• Quantum algorithms for optimal effective theory of many-body systems
• Dual current anomalies and quantum transport within extended reservoir simulations
• Nonequilibrium steady-state dynamics of Markov processes on graphs
• Numerically efficient unitary evolution for Hamiltonians beyond nearest-neighbors
• Characterization of localized effective spins in gapped quantum spin chains
• Explicit properties of the simplest inhomogeneous Matrix-Product-State including the Riemann metric of the MPS manifold
• Fate of Bosonic Topological Edge Modes in the Presence of Many-Body Interactions
• Geometrically Taming Dynamical Entanglement Growth in Purified Quantum States
• Transport in a System with a Tower of Quantum Many-Body Scars
• Dynamical quantum phase transitions on random networks
• Protecting Hilbert space fragmentation through quantum Zeno dynamics
• Finding periodic orbits in projected quantum many-body dynamics
• Interaction quenches in Bose gases studied with a time-dependent hypernetted-chain Euler-Lagrange method
• TTNOpt: Tree tensor network package for high-rank tensor compression
• Locally accurate tensor networks for thermal states and time evolution
• Unconventional Spin Dynamics and Supersolid Excitations in the Triangular-Lattice XXZ Model
• Numerical Probe of Dynamical Properties of a Two-Dimensional Triangular Ising Lattice with Long-Range Interaction
• Trajectory-Resolved Weiss Fields for Quantum Spin Dynamics
• Beyond fragmented dopant dynamics in quantum spin lattices: Robust localization and non-Gaussian diffusion
• A method of an on-demand beamsplitter for trapped-ion quantum computers
• Photodynamic melting of phase-reversed charge stripes and enhanced condensation
• Universal scaling of higher-order cumulants in quantum isotropic spin chains
• Process Tensor Approaches to Non-Markovian Quantum Dynamics
• Temporal Entanglement Transitions in the Periodically Driven Ising Chain
• Dissipative Generation of Currents by Nonreciprocal Local and Global Environments
• Formation of CuO${}_2$ sublattices by suppression of interlattice correlations in tetragonal CuO
• Anomalous Dynamical Scaling at Topological Quantum Criticality
• Multi-orbital dynamical mean-field theory with a complex-time solver
• Dissipative dynamics in isolated quantum spin chains after a local quench
• Chiral Graviton Modes in Fermionic Fractional Chern Insulators
• Scaling and Luescher Term in a non-Abelian (2+1)d SU$(2)$ Quantum Link Model
• Using near-flat-band electrons for read-out of molecular spin qubit entangled states
• paces: Parallelized Application of Co-Evolving Subspaces, a method for computing quantum dynamics on GPUs
• Tangent equations of motion for nonlinear response functions
• Grassmann tensor networks
• Energy-filtered excited states and real-time dynamics served in a contour integral
• Matrix Product Wave Function of the Ground State and Elementary Excitation in the Spin-1/2 Chain
• Spin-polarization and resonant states in electronic conduction through a correlated magnetic layer
• Quantum Supercritical Crossover with Dynamical Singularity
• Phase Transitions in the Classical Simulability of Open Quantum Systems
• Hidden local adiabatic ramp in the modulated time evolution and the quantum approximate optimization algorithm