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pith:RZUE3TNH

pith:2026:RZUE3TNHFYK7XHMPFQPZD5AM7L
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Translation symmetry-enforced long-range entanglement in mixed states

Carolyn Zhang, Lei Gioia, Ryan Thorngren

The fixed-point state of strong-to-weak translation symmetry breaking is long-range entangled and cannot be a mixture of short-range entangled states.

arxiv:2605.15200 v1 · 2026-05-14 · quant-ph · cond-mat.mes-hall · cond-mat.str-el · math-ph · math.MP

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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

the fixed point strong-to-weak spontaneous symmetry breaking state of translation symmetry is long-range entangled: it cannot be written as a mixture of SRE states.

C2weakest assumption

That the counting argument correctly establishes an insufficient number of symmetric short-range entangled eigenstates to span the zero-momentum sector, relying on precise definitions of SRE states and the structure of the Hilbert space under translation symmetry.

C3one line summary

A counting argument proves that the fixed-point strong-to-weak spontaneous symmetry breaking state under translation symmetry is long-range entangled because symmetric short-range entangled states are insufficient to span the zero-momentum sector.

References

28 extracted · 28 resolved · 0 Pith anchors

[1] M. B. Hastings, Phys. Rev. Lett.107, 210501 (2011) 2011
[2] Y .-H. Chen and T. Grover, Phys. Rev. Lett.132, 170602 (2024) 2024
[3] Y .-H. Chen and T. Grover, PRX Quantum5, 030310 (2024) 2024
[4] C. de Groot, A. Turzillo, and N. Schuch, Quantum6, 856 (2022) 2022
[5] A. Moharramipour, L. A. Lessa, C. Wang, T. H. Hsieh, and S. Sahu, PRX Quantum5, 040336 (2024) 2024
Receipt and verification
First computed 2026-05-17T21:40:24.952697Z
Last reissued 2026-05-17T21:57:18.351118Z
Builder pith-number-builder-2026-05-17-v1
Signature unsigned_v0
Schema pith-number/v1.0

Canonical hash

8e684dcda72e15fb9d8f2c1f91f40cfaec9f1bfcb8485d6e9a5dd095034ba60b

Aliases

arxiv: 2605.15200 · arxiv_version: 2605.15200v1 · pith_short_12: RZUE3TNHFYK7 · pith_short_16: RZUE3TNHFYK7XHMP · pith_short_8: RZUE3TNH
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/RZUE3TNHFYK7XHMPFQPZD5AM7L \
  | 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: 8e684dcda72e15fb9d8f2c1f91f40cfaec9f1bfcb8485d6e9a5dd095034ba60b
Canonical record JSON 
{
  "metadata": {
    "abstract_canon_sha256": "f248122d2c6ece12d0a06dd086edc8909a76e65332b6511b656e91b0c205a00d",
    "cross_cats_sorted": [
      "cond-mat.mes-hall",
      "cond-mat.str-el",
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-05-14T17:59:57Z",
    "title_canon_sha256": "e5d9103ee00f5b58d28b2dfce2a37c7db31894f0257b9d75883f3e970d4d1d97"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15200",
    "kind": "arxiv",
    "version": 1
  }
}