Pith Number

pith:WN47XVVX

pith:2023:WN47XVVX5OU2AN56VZ7MVBSOZL

not attested not anchored not stored refs resolved

Topologically Ordered Steady States in Open Quantum Systems

He-Ran Wang, Xu-Dong Dai, Zhong Wang, Zijian Wang

Steady-state topological degeneracy in open quantum systems is stable in three dimensions but fragile in two.

arxiv:2306.12482 v2 · 2023-06-21 · quant-ph · cond-mat.mes-hall · cond-mat.quant-gas · cond-mat.str-el

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\usepackage{pith}
\pithnumber{WN47XVVX5OU2AN56VZ7MVBSOZL}

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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

✓ Portable graph bundle live · download bundle · merged state

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

while the steady-state topological degeneracy is fragile under noise in two dimensions, it is stable in three dimensions, where a genuine many-body phase with topological degeneracy is realized

C2weakest assumption

The two representative Liouvillians constructed via engineered dissipation admit exact solutions whose steady states carry the claimed topological degeneracy (abstract, paragraph 2).

C3one line summary

Engineered dissipation produces topologically degenerate steady states that form a stable many-body phase in three dimensions but not two.

References

44 extracted · 44 resolved · 2 Pith anchors

[1] Contrary to L0, L† 0 deform/create the loop defects in a way that the loop length never decreases. Starting from the topological sec- tor µ, loop defects can be created and grow larger, but this proce

[2] Wen, International Journal of Modern Physics B 4, 239 (1990) 1990

[3] X.-G. Wen and Q. Niu, Physical Review B 41, 9377 (1990) 1990

[4] A. Kitaev and J. Preskill, Physical review letters 96, 110404 (2006) 2006

[5] M. Levin and X.-G. Wen, Physical review letters 96, 110405 (2006) 2006

Formal links

2 machine-checked theorem links

Cited by

3 papers in Pith

Topologically Ordered Steady States in Open Quantum Systems

Steady-state topological order

Spontaneous symmetry breaking in open quantum systems: strong, weak, and strong-to-weak

Receipt and verification

First computed	2026-05-27T01:04:46.336738Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b379fbd6b7eba9a037beae7eca864ecadca8a818ec533bfc1b993209e8e29a51

Aliases

arxiv: 2306.12482 · arxiv_version: 2306.12482v2 · doi: 10.48550/arxiv.2306.12482 · pith_short_12: WN47XVVX5OU2 · pith_short_16: WN47XVVX5OU2AN56 · pith_short_8: WN47XVVX

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/WN47XVVX5OU2AN56VZ7MVBSOZL \
  | 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: b379fbd6b7eba9a037beae7eca864ecadca8a818ec533bfc1b993209e8e29a51

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "314208e641b19047f28433d7ff4b23c2beedbe03afe6e49139641262a08a18db",
    "cross_cats_sorted": [
      "cond-mat.mes-hall",
      "cond-mat.quant-gas",
      "cond-mat.str-el"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2023-06-21T18:00:09Z",
    "title_canon_sha256": "7288e31fdd07092627e59d56ef762e2d3a4742dc9f1bea91852e5c27b5df0c67"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2306.12482",
    "kind": "arxiv",
    "version": 2
  }
}