Pith Number

pith:E24JLCMX

pith:2026:E24JLCMXXSBRYHQQ5MUB5UDWQ7

not attested not anchored not stored refs resolved

Lattice fermion simulation of spontaneous time-reversal symmetry breaking in a helical Luttinger liquid

C. W. J. Beenakker, J. S\'anchez Fern\'an, V. A. Zakharov

Helical liquid enters gapped phase with broken time-reversal symmetry

arxiv:2601.09563 v2 · 2026-01-14 · cond-mat.str-el · quant-ph

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\usepackage{pith}
\pithnumber{E24JLCMXXSBRYHQQ5MUB5UDWQ7}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

A gapped phase with spontaneously broken time-reversal symmetry emerges when the Fermi level is tuned to the Dirac point and the Luttinger parameter crosses a critical value.

C2weakest assumption

The tangent dispersion relation faithfully captures the low-energy physics of the helical Luttinger liquid without introducing spurious artifacts, and the finite-lattice tensor network results extrapolate to the infinite-system analytic limit.

C3one line summary

Numerical lattice simulation confirms spontaneous time-reversal symmetry breaking and gap opening in a helical Luttinger liquid at the Dirac point above a critical Luttinger parameter.

References

35 extracted · 35 resolved · 0 Pith anchors

[1] Intra-band scattering Point splitting [31, 32] is the operation that replaces the product of fermion fields at the same position by an infinitesimal displacement±ϵ, ψσ(x)ψσ(x)7→ 1 2 ψσ(x)ψσ(x+ϵ)+ 1 2

[2] The termK n is again a second derivative, X n Kn = 2 X k (1−cos 2ka)c † k↑ck↓,(A10) which becomes irrelevant in the long-wave length regime

[3] For that purpose we make the replacementsc nσ ↔ cn+1,σ, with an error that vanishes askain the long-wave length limit

[4] M. Z. Hasan and C. L. Kane,Topological insulators, Rev. Mod. Phys.82, 3045 (2010) 2010

[5] J. Maciejko, T. L. Hughes, and S.-C. Zhang,The quan- tum spin Hall effect, Annu. Rev. Condens. Matter Phys. 2, 31 (2011) 2011

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-22T01:03:16.951886Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

26b8958997bc831c1e10eb281ed07687e2c2ee0edb11c91dc5134776f72cfa67

Aliases

arxiv: 2601.09563 · arxiv_version: 2601.09563v2 · doi: 10.48550/arxiv.2601.09563 · pith_short_12: E24JLCMXXSBR · pith_short_16: E24JLCMXXSBRYHQQ · pith_short_8: E24JLCMX

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/E24JLCMXXSBRYHQQ5MUB5UDWQ7 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 26b8958997bc831c1e10eb281ed07687e2c2ee0edb11c91dc5134776f72cfa67

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5b4b2496520a29df5e0d80b0e589a7ceac0309c17b89330f77b806717c57b542",
    "cross_cats_sorted": [
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.str-el",
    "submitted_at": "2026-01-14T15:32:20Z",
    "title_canon_sha256": "f9ebc4842baf5bb3c5fdbee3cd03896df5e018c6e3e70901658be80ae793c350"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.09563",
    "kind": "arxiv",
    "version": 2
  }
}