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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2404.16959 |
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| _version_ | 1866917790212947968 |
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| author | Dupuis, Nicolas |
| author_facet | Dupuis, Nicolas |
| contents | We study the superfluid--Bose-glass transition in a one-dimensional lattice boson model with power-law decaying hopping amplitude $t_{i-j}\sim 1/|i-j|^α$, using bosonization and the nonperturbative functional renormalization group (FRG). When $α$ is smaller than a critical value $α_c<3$, the U(1) symmetry is spontaneously broken, which leads to a density mode with nonlinear dispersion and dynamical exponent $z=(α-1)/2$; the superfluid phase is then stable for sufficiently weak disorder, contrary to the case of short-range hopping where the superfluid phase is destabilized by an infinitesimal disorder when the Luttinger parameter is smaller than $3/2$. In the presence of disorder, long-range hopping has however no effect in the infrared limit and the FRG flow eventually becomes similar to that of a boson system with short-range hopping. This implies that the superfluid phase, when stable, exhibits a density mode with linear dispersion ($z=1$) and the superfluid--Bose-glass transition remains in the Berezinskii-Kosterlitz-Thouless universality class, while the Bose-glass fixed point is insensitive to long-range hopping. We compare our findings with a recent numerical study. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16959 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Superfluid--Bose-glass transition in a system of disordered bosons with long-range hopping in one dimension Dupuis, Nicolas Quantum Gases We study the superfluid--Bose-glass transition in a one-dimensional lattice boson model with power-law decaying hopping amplitude $t_{i-j}\sim 1/|i-j|^α$, using bosonization and the nonperturbative functional renormalization group (FRG). When $α$ is smaller than a critical value $α_c<3$, the U(1) symmetry is spontaneously broken, which leads to a density mode with nonlinear dispersion and dynamical exponent $z=(α-1)/2$; the superfluid phase is then stable for sufficiently weak disorder, contrary to the case of short-range hopping where the superfluid phase is destabilized by an infinitesimal disorder when the Luttinger parameter is smaller than $3/2$. In the presence of disorder, long-range hopping has however no effect in the infrared limit and the FRG flow eventually becomes similar to that of a boson system with short-range hopping. This implies that the superfluid phase, when stable, exhibits a density mode with linear dispersion ($z=1$) and the superfluid--Bose-glass transition remains in the Berezinskii-Kosterlitz-Thouless universality class, while the Bose-glass fixed point is insensitive to long-range hopping. We compare our findings with a recent numerical study. |
| title | Superfluid--Bose-glass transition in a system of disordered bosons with long-range hopping in one dimension |
| topic | Quantum Gases |
| url | https://arxiv.org/abs/2404.16959 |