Merge pull request #46 from ALPSim/fix/mcs-index-page

Restructure Monte Carlo tutorials index with intro and per-code subsections

Author: Ooolab

content/en/tutorials/mcs/_index.md

@@ -6,22 +6,58 @@ toc: true
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+The ALPS Monte Carlo tutorials cover both classical and quantum simulations of spin models and bosonic lattice systems.
+Classical Monte Carlo uses local Metropolis or cluster (Wolff) updates for systems described by a classical Boltzmann weight.
+Quantum Monte Carlo (QMC) algorithms — loop, directed-loop SSE, worm, and directed worm — work on path-integral or operator-series representations and give access to thermodynamic properties of quantum lattice models at finite temperature.
+An extended-ensemble quantum Wang-Landau method computes the full density of states and thermodynamic quantities across all temperatures in a single run.
+The tutorials progress from fundamental diagnostics such as autocorrelation times and equilibration, through specific observables such as susceptibilities and magnetization curves, to the detection of classical and quantum phase transitions.
+
+## Choosing a Code
+
+Before starting a simulation it is important to select the algorithm best suited to your model and observable.
+The guide below compares the four QMC representations available in ALPS — `looper`, `dirloop_sse`, `worm`, and `qwl` — and summarises their respective strengths and limitations.
+
 - [Which code to choose for your simulation?](com)
+
+## Classical Monte Carlo (`spinmc`)
+
+The `spinmc` application implements classical Monte Carlo with local Metropolis updates and cluster updates for classical spin models.
+The first two tutorials introduce the most important diagnostics for any MC run — autocorrelation time and equilibration — laying the groundwork for all subsequent work.
+The method is revisited later to study finite-size scaling and the second-order phase transition of the 2D Ising model.
+
 - [MC-01(a) Classical Monte Carlo simulations and autocorrelations](mc01a)
 - [MC-01(b) Classical Monte Carlo simulations and equilibration/convergence](mc01b)
-- [MC-02 Calculating magnetic susceptibilities by the classical MC and looper QMC codes](mc02)
-- [MC-03 Calculating magnetization curves by the directed loop QMC code](mc03) 
-- [MC-04 Custom measurements in the QMC codes](mc04) 
-- [MC-05 Simulating the Bose-Hubbard model using the worm QMC code](mc05) 
-- [MC-06 Extended ensemble simulations (Quantum Wang-Landau)](mc06) 
 - [MC-07 Phase transition in the Ising model](mc07)
-- [MC-08 Quantum phase transition in a quantum spin model](mc08) 
+
+## Loop and Directed-Loop QMC (`looper`, `dirloop_sse`)
+
+The `looper` code implements the loop algorithm in an operator-loop representation and is most efficient for isotropic spin models without a magnetic field.
+The `dirloop_sse` code uses directed loops in the stochastic series expansion (SSE) representation; it handles models with anisotropy or an external magnetic field that break the spin-inversion symmetry required by `looper`.
+These tutorials cover susceptibilities of Heisenberg chains and ladders, magnetization curves in a field, and the identification of a quantum phase transition in a dimerised lattice.
+
+- [MC-02 Calculating magnetic susceptibilities by the classical MC and looper QMC codes](mc02)
+- [MC-03 Calculating magnetization curves by the directed loop QMC code](mc03)
+- [MC-08 Quantum phase transition in a quantum spin model](mc08)
 - [MC-09 Quantum Monte Carlo](qmc)
-- [MC-10 Monte Carlo Simulations with Directed Worm](dwa)
 
+## Worm QMC (`worm`)
 
+The `worm` code uses the worm algorithm in the path-integral representation and is the method of choice for Bose-Hubbard models and for spin models in strong magnetic fields.
+The tutorials show how to enable and evaluate correlation functions and Green functions, and demonstrate the superfluid–Mott-insulator quantum phase transition in the Bose-Hubbard model.
 
+- [MC-04 Custom measurements in the QMC codes](mc04)
+- [MC-05 Simulating the Bose-Hubbard model using the worm QMC code](mc05)
 
+## Quantum Wang-Landau (`qwl`)
 
+The quantum Wang-Landau code stochastically constructs the density of states of a quantum Hamiltonian and derives the full thermodynamics — free energy, entropy, and specific heat — at all temperatures from a single simulation.
+This tutorial applies the method to ferromagnetic and antiferromagnetic Heisenberg spin chains and ladders.
 
+- [MC-06 Extended ensemble simulations (Quantum Wang-Landau)](mc06)
 
+## Directed Worm Algorithm (`dwa`)
+
+The directed worm algorithm is a highly efficient path-integral QMC method for lattice bosons that combines worm updates with improved estimators.
+The tutorials revisit the Bose-Hubbard physics of MC-05 with the `dwa` code and then study the density profile of a three-dimensional optical lattice in a harmonic trap — a system directly relevant to ultracold-atom experiments.
+
+- [MC-10 Monte Carlo Simulations with Directed Worm](dwa)