Strong Hilbert space fragmentation via emergent quantum drums in two dimensions
We introduce a disorder-free model of $S=1/2$ spins on the square lattice in a constrained Hilbert space where two up-spins are not allowed simultaneously on any two neighboring sites of the lattice. The interactions are given by ring-exchange terms on elementary plaquettes that conserve both the to...
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| Format: | Article |
| Language: | English |
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SciPost
2023-06-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.14.6.146 |
| _version_ | 1797809467928084480 |
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| author | Anwesha Chattopadhyay, Bhaskar Mukherjee, Krishnendu Sengupta, Arnab Sen |
| author_facet | Anwesha Chattopadhyay, Bhaskar Mukherjee, Krishnendu Sengupta, Arnab Sen |
| author_sort | Anwesha Chattopadhyay, Bhaskar Mukherjee, Krishnendu Sengupta, Arnab Sen |
| collection | DOAJ |
| description | We introduce a disorder-free model of $S=1/2$ spins on the square lattice in a constrained Hilbert space where two up-spins are not allowed simultaneously on any two neighboring sites of the lattice. The interactions are given by ring-exchange terms on elementary plaquettes that conserve both the total magnetization as well as dipole moment. We show that this model provides a tractable example of strong Hilbert space fragmentation in two dimensions with typical initial states evading thermalization with respect to the full Hilbert space. Given any product state, the system can be decomposed into disjoint spatial regions made of edge and/or vertex sharing plaquettes that we dub as "quantum drums". These quantum drums come in many shapes and sizes and specifying the plaquettes that belong to a drum fixes its spectrum. The spectra of some small drums is calculated analytically. We study two bigger quasi-one-dimensional drums numerically, dubbed "wire" and a "junction of two wires" respectively. We find that these possess a chaotic spectrum but also support distinct families of quantum many-body scars that cause periodic revivals from different initial states. The wire is shown to be equivalent to the one-dimensional PXP chain with open boundaries, a paradigmatic model for quantum many-body scarring; while the junction of two wires represents a distinct constrained model. |
| first_indexed | 2024-03-13T06:54:17Z |
| format | Article |
| id | doaj.art-e958357982c048ad94b26f9fcff0b866 |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-03-13T06:54:17Z |
| publishDate | 2023-06-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-e958357982c048ad94b26f9fcff0b8662023-06-07T13:08:00ZengSciPostSciPost Physics2542-46532023-06-0114614610.21468/SciPostPhys.14.6.146Strong Hilbert space fragmentation via emergent quantum drums in two dimensionsAnwesha Chattopadhyay, Bhaskar Mukherjee, Krishnendu Sengupta, Arnab SenWe introduce a disorder-free model of $S=1/2$ spins on the square lattice in a constrained Hilbert space where two up-spins are not allowed simultaneously on any two neighboring sites of the lattice. The interactions are given by ring-exchange terms on elementary plaquettes that conserve both the total magnetization as well as dipole moment. We show that this model provides a tractable example of strong Hilbert space fragmentation in two dimensions with typical initial states evading thermalization with respect to the full Hilbert space. Given any product state, the system can be decomposed into disjoint spatial regions made of edge and/or vertex sharing plaquettes that we dub as "quantum drums". These quantum drums come in many shapes and sizes and specifying the plaquettes that belong to a drum fixes its spectrum. The spectra of some small drums is calculated analytically. We study two bigger quasi-one-dimensional drums numerically, dubbed "wire" and a "junction of two wires" respectively. We find that these possess a chaotic spectrum but also support distinct families of quantum many-body scars that cause periodic revivals from different initial states. The wire is shown to be equivalent to the one-dimensional PXP chain with open boundaries, a paradigmatic model for quantum many-body scarring; while the junction of two wires represents a distinct constrained model.https://scipost.org/SciPostPhys.14.6.146 |
| spellingShingle | Anwesha Chattopadhyay, Bhaskar Mukherjee, Krishnendu Sengupta, Arnab Sen Strong Hilbert space fragmentation via emergent quantum drums in two dimensions SciPost Physics |
| title | Strong Hilbert space fragmentation via emergent quantum drums in two dimensions |
| title_full | Strong Hilbert space fragmentation via emergent quantum drums in two dimensions |
| title_fullStr | Strong Hilbert space fragmentation via emergent quantum drums in two dimensions |
| title_full_unstemmed | Strong Hilbert space fragmentation via emergent quantum drums in two dimensions |
| title_short | Strong Hilbert space fragmentation via emergent quantum drums in two dimensions |
| title_sort | strong hilbert space fragmentation via emergent quantum drums in two dimensions |
| url | https://scipost.org/SciPostPhys.14.6.146 |
| work_keys_str_mv | AT anweshachattopadhyaybhaskarmukherjeekrishnendusenguptaarnabsen stronghilbertspacefragmentationviaemergentquantumdrumsintwodimensions |