Physics / research
Compute quantum many-body observables
Compare exact, stochastic, and tensor-network methods by identifying their controlled limits, finite-size errors, convergence tests, and computational bottlenecks.
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Module 01 research
Compute quantum many-body observables
Compare exact, stochastic, and tensor-network methods by identifying their controlled limits, finite-size errors, convergence tests, and computational bottlenecks.
- 01
Sparse exact diagonalization and symmetry sectors
Organize finite many-body Hilbert spaces using conserved quantities and test eigenpairs with residuals.
28 min - 02
Lanczos–Krylov spectra and dynamics
Construct normalized Krylov recurrences and distinguish eigenpair convergence from controlled time propagation.
28 min - 03
Variational Monte Carlo estimators
Sample a trial wavefunction and separate variational bias, local-energy fluctuations, and autocorrelated statistical error.
28 min - 04
Worldline quantum Monte Carlo
Map thermal traces into imaginary-time configurations and identify positivity, balance, and discretization assumptions.
28 min - 05
Auxiliary-field Monte Carlo and the sign problem
Decouple fermion interactions and identify the statistical cost and assumptions behind determinant reweighting.
28 min - 06
Matrix product state canonical forms
Relate tensor gauges to orthonormal block bases and identify the Schmidt spectrum without mistaking representation for approximation.
28 min - 07
DMRG sweeps and truncation errors
Interpret local variational optimization and Schmidt truncation while keeping fidelity, observable error, and sweep convergence distinct.
28 min - 08
Time-evolving block decimation
Factor local time evolution into gates and control Trotter and entanglement-truncation errors separately.
28 min - 09
Projected entangled-pair states
Extend virtual-bond representations to two dimensions while separating state expressiveness from environment-contraction cost.
28 min - 10
Finite-entanglement and finite-size extrapolation
Distinguish physical length, tensor-induced correlation length, and algorithmic cutoffs before fitting a many-body limit.
28 min