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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2512.21847 |
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| _version_ | 1866908732041986048 |
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| author | Hu, Yu-Min Han, Zhaoyu Lian, Biao |
| author_facet | Hu, Yu-Min Han, Zhaoyu Lian, Biao |
| contents | We study the phase diagram of a one-dimensional spin quantum breakdown model, which has an exponential $U(1)$ symmetry with charge unit decaying as $2^{-j}$ with site position $j$. By exact diagonalization (ED), we show that the model with spin $S\ge2$ exhibits an exponential $U(1)$ spontaneous symmetry breaking (SSB) phase dubbed a quantum breakdown condensate. It exhibits a bulk gap violating the Goldstone theorem, and an edge mode only on the left edge if in open boundary condition. In a length $L$ lattice, the condensate has $\mathcal{O}(2^L)$ number of SSB ground states originating from the $\mathcal{O}(2^L)$ number of exponential $U(1)$ charge sectors, leading to a finite entropy density $\ln 2$. This enforces a first order SSB phase transition into this phase, as observed in ED and verified in the large $S$ limit on an exactly solvable Rokhsar-Kivelson line. The condensate has an SSB order parameter being the local in-plane spin, which points in angles related by the chaotic Bernoulli (dyadic) map and thus is effectively random. Moreover, we show the condensate exhibits non-decaying local autocorrelations, and does not have an off-diagonal long-range order. The quantum breakdown condensate thus behaves as a disorder-free quantum glass and is beyond the existing classifications of phases of matter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21847 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Breakdown Condensate as a Disorder-Free Quantum Glass Hu, Yu-Min Han, Zhaoyu Lian, Biao Strongly Correlated Electrons Quantum Gases Statistical Mechanics We study the phase diagram of a one-dimensional spin quantum breakdown model, which has an exponential $U(1)$ symmetry with charge unit decaying as $2^{-j}$ with site position $j$. By exact diagonalization (ED), we show that the model with spin $S\ge2$ exhibits an exponential $U(1)$ spontaneous symmetry breaking (SSB) phase dubbed a quantum breakdown condensate. It exhibits a bulk gap violating the Goldstone theorem, and an edge mode only on the left edge if in open boundary condition. In a length $L$ lattice, the condensate has $\mathcal{O}(2^L)$ number of SSB ground states originating from the $\mathcal{O}(2^L)$ number of exponential $U(1)$ charge sectors, leading to a finite entropy density $\ln 2$. This enforces a first order SSB phase transition into this phase, as observed in ED and verified in the large $S$ limit on an exactly solvable Rokhsar-Kivelson line. The condensate has an SSB order parameter being the local in-plane spin, which points in angles related by the chaotic Bernoulli (dyadic) map and thus is effectively random. Moreover, we show the condensate exhibits non-decaying local autocorrelations, and does not have an off-diagonal long-range order. The quantum breakdown condensate thus behaves as a disorder-free quantum glass and is beyond the existing classifications of phases of matter. |
| title | Quantum Breakdown Condensate as a Disorder-Free Quantum Glass |
| topic | Strongly Correlated Electrons Quantum Gases Statistical Mechanics |
| url | https://arxiv.org/abs/2512.21847 |