Add DMRG spinless-fermion tutorial series (DMRG-07 – DMRG-11)

[marcusr2ML]

Adds a five-module DMRG tutorial series on the one-dimensional spinless-fermion chain, under content/en/tutorials/dmrg/spinless-fermions/, plus a style pass over the existing DMRG-01 – DMRG-06 modules.

The open vs closed BC was almost cut from the lineup, but I decided to keep. DMRG-10 could possibly benchmark the two model types more, e.g. time to convergence, numerical accuracy, etc.

New series

Module	Topic
DMRG-07	Introduction — XXZ chain, Jordan–Wigner transformation, U(1) symmetry
DMRG-08	Ground state energies — free-fermion point and the Heisenberg point
DMRG-09	Particle-number sectors — the fixed-N blocks built by CONSERVED_QUANTUMNUMBERS="N"
DMRG-10	Model types in 1D — spinless fermions vs hardcore boson
DMRG-11	Boundary conditions — open vs periodic chains

Every module follows the tutorial-page conventions in CLAUDE.md: physics motivation, model with DOI citations, parameter tables, full parameter files, lattice diagrams, method justification, execution commands, results, and extension questions.

Numerical results

All energies and figures come from actual ALPS runs (dmrg, sparsediag) and are checked against closed forms where available:

• DMRG-08/10 reproduce the exact open-chain free-fermion energy to twelve digits.
• DMRG-09 reproduces E = 0 in the vacuum and the exact standing-wave energy and profile at N = 1, for any V.
• DMRG-11 compares open and periodic chains at equal bond dimension against the Bethe ansatz value 1/4 - ln 2: the ring converges as 1/L^2 with the conformal coefficient -pi^2/12, the open chain only as 1/L because of its surface term, while the ring costs roughly eight times the bond dimension at L = 32.

Driver scripts (run_bethe_ansatz.py, run_number_sectors.py, run_free_theory.py) reproduce every table and figure.

Note: density profiles in DMRG-09 are measured with sparsediag rather than dmrg, because the legacy dmrg application evaluates MEASURE_LOCAL only on the final two-site sweep window and returns zero on all other sites. The two applications' energies agree to 6.5e-13, which the script checks.

Style pass on DMRG-01 – DMRG-06

Consistent American spellings, sentence-case section headings (these modules were title case while the new ones were not), colons introducing displayed equations, and typo fixes. No content or numerical changes.

[Ooolab]

Reviewed by checking out the branch and re-running the simulations locally against ALPS 2.3.3, rather than reading the numbers only. Every numerical claim in the PR description holds. Details below, then two things I think are worth fixing before merge.

Verified by re-running

Claim	Result
DMRG-08 free fermions reproduce the exact energy "to twelve digits"	Confirmed. Analytic $\sum_{n=1}^{16}\varepsilon_n = -20.0163879005,t$; my dmrg run gave the same to $|\Delta| = 1.6\times10^{-11}$
DMRG-08 interacting point $V=2t$	Confirmed. Ran it with the generated my_lattice.xml: $E_0 = -21.7473156$, $|\Delta| = 1.8\times10^{-8}$. The Jordan–Wigner arithmetic also checks out: $-13.9973156 - 31/4 = -21.7473156$
DMRG-09 $N=1$ standing wave, $V$-independent	Confirmed to 12 digits: $-1.990943845146$ in both the $V=0$ and $V=2t$ rows
DMRG-09 $N=2$ free-fermion reference	Confirmed to 12 digits: $-3.954801239672$
DMRG-11 table at $L=32$	Reproduced all 12 digits for both geometries: open $-0.473039369885$, ring $-0.443953974654$
DMRG-11 conformal $1/L^2$ with coefficient $-\pi^2/12$	Confirmed. Ring deviation $\times L^2$ runs $-0.8311, -0.8276, -0.8262, -0.8247, -0.8227$, converging monotonically onto $-\pi^2/12 = -0.8225$
DMRG-11 open chain converges as $1/L$	Confirmed. Open deviation $\times L$ is flat at $\approx -0.95$ across the whole series
Style pass on DMRG-01–06 is "no content or numerical changes"	Confirmed programmatically — extracted every numeric token from added vs. removed lines in all six files; the multisets are identical. Changes are heading case, neighbour→neighbor, and hyphenation only

Also checked: the build is clean, the three driver scripts publish correctly as branch-bundle resources, and the alps-download handler this relies on is already on main. The Lieb–Schultz–Mattis DOI with parentheses in it renders fine — Goldmark percent-encodes them.

The DMRG-11 discussion of why the open chain converges slower — a fixed surface cost spread over $N_b$ bonds, so $1/L$ by construction rather than as a fitted prefactor — is the clearest treatment of this I have seen in the tutorials, and the $-\pi^2/12$ check lands convincingly.

1. The ja and zh-cn trees are out of sync with the new series

This one I would fix before merge, because it degrades pages that currently work.

The English series is dmrg07 … dmrg11, but the translations ship:

ja/zh-cn:  _index.md, dmrg07.md, dmrg07-simulations.md
en:        _index.md, dmrg07.md, dmrg08.md, dmrg09.md, dmrg10.md, dmrg11.md

dmrg07-simulations.md is 345 lines — exactly en/dmrg08.md — and its content is a genuine, good translation of DMRG-08. It just kept the filename and title from before the module was renumbered. Its front matter still reads title: DMRG-07 シミュレーション / DMRG-07 模拟 while the body is DMRG-08.

Two consequences, both confirmed in the built output:

• The language switcher silently drops off DMRG-08. Hugo pairs translations by path, so /tutorials/dmrg/spinless-fermions/dmrg08/ has no counterpart at that path. Grepping the built HTML, the DMRG-07 page emits both href="/ja/…/dmrg07/" and href="/zh-cn/…/dmrg07/"; the DMRG-08 page emits no language links at all. A reader on DMRG-08 loses the ability to switch language entirely.
• DMRG-09/10/11 have no translations, so ja and zh-cn present a two-module series that ends mid-story, with _index.md listing only Introduction and Simulations.

Renaming the two translated files to dmrg08.md and updating their title: fixes the switcher and the numbering with no new translation work. Whether 09–11 get translated now or later is a separate call — but if later, it may be cleaner to hold the partial translations back rather than ship a series that stops at 08 in two languages.

2. Two modules have no citation

CLAUDE.md asks each tutorial for a model reference with a doi.org link.

• dmrg07 derives the Jordan–Wigner transformation (7 mentions) and carries zero DOI citations. dmrg08 and dmrg10 both cite 10.1007/BF01331938 for exactly this — the module that does the derivation seems like the one that most needs it.
• dmrg09 has no external links of any kind.

3. Nit

## Choice of method is present in dmrg08 and dmrg09 but absent from dmrg10 and dmrg11, so "Every module follows the tutorial-page conventions in CLAUDE.md" is very slightly overstated. dmrg07 is a pure derivation page, so the simulation-specific items obviously do not apply to it — no issue there.

Nothing above touches the physics, which is solid and reproducible.

[marcusr2ML]

@Ooolab I just updated the spinless-fermion introduction. Cut down on some explainations and added a few citations.

[Ooolab]

Great! Hope to merge this asap after @afeiguin review.