Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-15T18:30:48.409873Z
Paper Citation Record · LEDGER
As of 19 August 2026, this Paper Citation Record lists 66 of 66 outbound references and 0 inbound Pith citation observations for arXiv:2506.19771.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-15T18:30:48.409873Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
66 of 66 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation bbf1abf1-aedd-4e9e-87c7-eac4eaf4b4ca · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase The nature of our solution crucially depends on the sign of the bare fermion mass parameterm 0
Reference 1
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation d2d2f53d-5f6a-400e-bf12-f3399a279515 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Tang and X
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 0ffce920-9769-4c93-bfce-465a5d9066fe · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Unresolved cited work
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation cac460e0-9694-4fa8-b9d6-6c1ebd1529c4 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Unresolved cited work
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 9f0fd9b3-e646-4f31-a617-996a72fefb29 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Fidkowski and A
Reference 5
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 915811c9-6804-4704-9da9-14098859006a · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Beenakker, Annual Review of Condensed Matter Physics4, 113 (2013)
Reference 6
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 39e06772-1b88-48e9-ba28-8670a070183f · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Ruhman, E
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation ae0ee12d-fcef-4505-aa21-0fc15c0d013f · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Ruhman and E
Reference 8
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8c64df57-182a-4572-bf1b-0db95c420823 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Symmetry protected topological Luttinger liquids and the phase transition between them
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 255cdbc6-7496-4fd9-a8f1-f66ed7048def · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Kainaris, R
Reference 10
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation dde9faf0-0b8d-4129-a204-d471daa00dac · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Unresolved cited work
Reference 11
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 546434b1-d61f-4ac6-befb-693bfc4f861f · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Unresolved cited work
Reference 12
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f31296b4-664a-4bce-8f92-0b7421e3d947 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Ruhman, E
Reference 13
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5a48323a-d384-4502-89eb-4fca3c6b1364 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Unresolved cited work
Reference 14
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 48f46884-ea30-454e-b5cd-01d05a9615b4 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Keselman and E
Reference 15
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 635d82c9-fa5e-4845-9388-74fcbd7bf9f4 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Iemini, L
Reference 16
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b1ea692b-ffda-4588-92ef-c7bc06bf2095 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Unresolved cited work
Reference 17
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation aeb2387e-9872-4ff3-98db-495e596bc04f · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Kainaris, S
Reference 18
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 11d5ab61-a967-4db7-8d99-982f3bf7f64a · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Scaffidi, D
Reference 19
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 1b73563e-9214-4e9a-b3a9-5ef4fd6f161a · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Keselman, E
Reference 20
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 38c8f3d1-c145-40b4-9dd3-93fa0950e438 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Haldane, Physics Letters A93, 464 (1983)
Reference 21
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c7153f04-9d1b-42fc-b282-8cd4e579f720 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Affleck, T
Reference 22
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a47c11dd-3eaa-4df1-aed3-f8d40bc2659c · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Unresolved cited work
Reference 23
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a93c47e3-561e-4106-81f8-576f3c1d7d88 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Unresolved cited work
Reference 24
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ae017e9b-d347-4626-96a9-14fb59a447e6 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Unresolved cited work
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 58f9eb22-6c80-480a-82f0-b58f596e3db2 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Bergknoff and H
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation d27cc5b4-ce65-4b8c-b69e-ab9538b598c4 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Coleman, Phys
Reference 27
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 002397b9-3324-4131-8f9c-539dec848151 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Realizing a Symmetry Protected Topological Phase in a Superconducting Circuit
Reference 28
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d2a964a6-e90b-48c3-8343-da172585f136 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Unresolved cited work
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 6cc4b4f6-dd13-40b4-9284-ea9e4e18c2f3 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Jackiw and C
Reference 30
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 31acf58b-0670-461a-a8ea-427b6041c690 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Jackiw, A
Reference 31
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0626edc3-0613-412f-83d2-4b6700fbbb1b · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Duality symmetry, zero energy modes and boundary spectrum of the sine-Gordon/massive Thirring model
Reference 32
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3e094e37-3251-422b-8968-fd9741724df4 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Unresolved cited work
Reference 33
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c5b12772-1c46-4d75-ac31-b8ef79fb96c7 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Unresolved cited work
Reference 34
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 9b579210-804b-4f85-92d1-aefa4911c388 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Gomes and J
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation a48003a2-4513-402f-8e3f-d789b2c1a443 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Unresolved cited work
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation a6ec6e0e-9d22-4d45-aa2e-26be0e1ea94e · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Hahlen, Nuclear Physics B102, 67 (1976)
Reference 37
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation d741959f-f629-4ae1-977d-6a33a2e8b981 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Seiler and D
Reference 38
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 11dcec98-2198-45a8-bc99-77aafaf3faeb · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Skorik and H
Reference 39
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 67ff986f-e27f-4c5c-b4e4-b3a746e44c12 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Japaridze, A
Reference 40
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation cd3d41d3-4203-4865-90f9-be741f3ca6eb · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Unresolved cited work
Reference 41
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 99464088-dde5-406d-b4e5-1f6bb633e30a · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Unresolved cited work
Reference 42
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 210b6187-a552-4a64-87c3-3ad999057f54 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Unresolved cited work
Reference 43
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 56049e35-8de5-4a51-9262-9081c1e03e07 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Unresolved cited work
Reference 44
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a6d75ec4-a77b-420b-970e-7915ba382ed2 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Emergent boundary supersymmetry in a one dimensional superconductor
Reference 45
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c7db5c76-1205-4618-8ca8-5f2ed96a77f2 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Grijalva, J
Reference 46
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b15b8606-0ee1-49f8-a614-e9337941cc63 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Unresolved cited work
Reference 47
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 57072b1d-dbd4-480f-b4b5-04b7a1114e0f · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Unresolved cited work
Reference 48
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 16c03046-55cc-462b-b5e6-e8613e8362a1 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Unresolved cited work
Reference 49
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation c7961a75-270b-4b86-8101-09962c8d17ee · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Due to the interactions in the Hamiltonian, the ordering of the particles is important
Reference 50
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 8d9538dd-d1e1-4e85-b6da-85083c8447a0 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase mid gap phase
Reference 51
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation c7135ccd-7161-4217-80c2-5caa7b4141ea · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Unresolved cited work
Reference 52
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation dbe86851-7fda-45d2-a466-bd2051bf8f0d · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Form 0 >0, they correspond to the following domains of the boundaries fields 0< ϕ L,R < u, (−u < ϕL < 0,0< ϕ R < u),(−u < ϕL <0,−u < ϕR <0),(0< ϕ L < u,−u < ϕR <0) respectively
Reference 53
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 232a62f9-348c-486c-a4ab-5812a6fac5e4 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Unresolved cited work
Reference 54
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 06a17fa4-df02-456d-86c3-71fb29bb393e · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase The energy difference between these states is mL +mR
Reference 55
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation b01191dc-c6f7-48db-ac1c-b7a8c605d7ef · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase The state|1⟩contains two bound states at each edge and has energym L +mR above the ground state
Reference 56
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 732ac0a9-b5d3-49be-8ac1-276feee8d2e8 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Unresolved cited work
Reference 57
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation bdb4111c-047b-4349-beb0-2a70a403e447 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Similarly, the state|0⟩ R has energy−m R with respect to the state|1⟩or equivalently, it has energym L with respect to the state|−1⟩
Reference 58
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation b63e051b-b6f6-4a7c-b0a0-95251adc3211 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Unresolved cited work
Reference 59
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 015919bc-f5f3-46d7-9d2a-23274d0117a4 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Unresolved cited work
Reference 60
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation e23a2157-0ff8-4afd-887e-3ae3c07d7f26 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase In this phase the boundary fieldsϕ L,R take values in the following range:−u < ϕL <0, 0< ϕ R < u
Reference 61
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 4702ec50-31f7-4985-9d52-f43aea81d614 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Unresolved cited work
Reference 62
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 68315814-8be6-495a-b0c1-ed2ebf8dfa76 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase The energy difference between these states is E|1⟩−E|−1⟩ =m R +mL, wherem R =msinγϕ R,m L =msinγϕ L
Reference 63
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 0fe7cceb-1cec-4f2b-94b6-f8afd4c38475 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Unresolved cited work
Reference 64
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation c2b1b4df-605a-439a-a7fd-d273c948b521 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Forϕ R <|ϕ L|, the states|0⟩ R,|0⟩L are obtained by adding the boundary strings±i(u+ϕ R),±i(u−ϕ ′ L) to the state|−1⟩respectively
Reference 65
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation c02f7472-49e2-4ed4-b9d5-f3bacfcc72d7 · outbound
Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase Sinceϕ L <0,ϕ R >|ϕ L|, we havem L <0,m R >|m L|
Reference 66
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
No inbound Pith citation observations are available.